--- /dev/null
+# Created by Octave 3.6.1, Mon Apr 23 21:08:02 2012 UTC <root@brouzouf>
+# name: cache
+# type: cell
+# rows: 3
+# columns: 81
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 12
+bland_altman
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 865
+ BLAND_ALTMANN shows the Bland-Altman plot of two columns of measurements
+ and computes several summary results.
+
+ bland_altman(m1, m2 [,group])
+ bland_altman(data [, group])
+ R = bland_altman(...)
+
+ m1,m2 are two colums with the same number of elements
+ containing the measurements. m1,m2 can be also combined
+ in a single two column data matrix.
+ group [optional] indicates which measurements belong to the same group
+ This is useful to account for repeated measurements.
+
+
+ References:
+ [1] JM Bland and DG Altman, Measuring agreement in method comparison studies.
+ Statistical Methods in Medical Research, 1999; 8; 135.
+ doi:10.1177/09622802990080204
+ [2] P.S. Myles, Using the Bland– Altman method to measure agreement with repeated measures
+ British Journal of Anaesthesia 99(3):309–11 (2007)
+ doi:10.1093/bja/aem214
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ BLAND_ALTMANN shows the Bland-Altman plot of two columns of measurements
+ and
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+cat2bin
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 755
+ CAT2BIN converts categorial into binary data
+ each category of each column in D is converted into a logical column
+
+ B = cat2bin(C);
+ [B,BinLabel] = cat2bin(C,Label);
+ [B,BinLabel] = cat2bin(C,Label,MODE)
+
+ C categorial data
+ B binary data
+ Label description of each column in C
+ BinLabel description of each column in B
+ MODE default [], ignores NaN
+ 'notIgnoreNAN' includes binary column for NaN
+ 'IgnoreZeros' zeros do not get a separate category
+ 'IgnoreZeros+NaN' zeros and NaN are ignored
+
+ example:
+ cat2bin([1;2;5;1;5]) results in
+ 1 0 0
+ 0 1 0
+ 0 0 1
+ 1 0 0
+ 0 0 1
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ CAT2BIN converts categorial into binary data
+ each category of each column i
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+cdfplot
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 565
+ CDFPLOT plots empirical commulative distribution function
+
+ cdfplot(X)
+ cdfplot(X, FMT)
+ cdfplot(X, PROPERTY, VALUE,...)
+ h = cdfplot(...)
+ [h,stats] = cdfplot(X)
+
+ X contains the data vector
+ (matrix data is currently changed to a vector, this might change in future)
+ FMT,PROPERTY,VALUE
+ are used for formating; see HELP PLOT for more details
+ h graphics handle to the cdf curve
+ stats
+ a struct containing various summary statistics including
+ mean, std, median, min, max.
+
+ see also: ecdf, median, statistics, hist2res, plot
+
+ References:
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 59
+ CDFPLOT plots empirical commulative distribution function
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+center
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 505
+ CENTER removes the mean
+
+ [z,mu] = center(x,DIM,W)
+ removes mean x along dimension DIM
+
+ x input data
+ DIM dimension
+ 1: column
+ 2: row
+ default or []: first DIMENSION, with more than 1 element
+ W weights to computed weighted mean (default: [], all weights = 1)
+ numel(W) must be equal to size(x,DIM)
+
+ features:
+ - can deal with NaN's (missing values)
+ - weighting of data
+ - dimension argument
+ - compatible to Matlab and Octave
+
+ see also: SUMSKIPNAN, MEAN, STD, DETREND, ZSCORE
+
+ REFERENCE(S):
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 26
+ CENTER removes the mean
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+classify
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 792
+ CLASSIFY classifies sample data into categories
+ defined by the training data and its group information
+
+ CLASS = classify(sample, training, group)
+ CLASS = classify(sample, training, group, TYPE)
+ [CLASS,ERR,POSTERIOR,LOGP,COEF] = CLASSIFY(...)
+
+ CLASS contains the assigned group.
+ ERR is the classification error on the training set weighted by the
+ prior propability of each group.
+
+ The same classifier as in TRAIN_SC are supported.
+
+ ATTENTION: no cross-validation is applied, therefore the
+ classification error is too optimistic (overfitting).
+ Use XVAL instead to obtain cross-validated performance.
+
+ see also: TRAIN_SC, TEST_SC, XVAL
+
+ References:
+ [1] R. Duda, P. Hart, and D. Stork, Pattern Classification, second ed.
+ John Wiley & Sons, 2001.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ CLASSIFY classifies sample data into categories
+ defined by the training data
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 24
+coefficient_of_variation
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 221
+ COEFFICIENT_OF_VARIATION returns STD(X)/MEAN(X)
+
+ cv=coefficient_of_variation(x [,DIM])
+ cv=std(x)/mean(x)
+
+ see also: SUMSKIPNAN, MEAN, STD
+
+ REFERENCE(S):
+ http://mathworld.wolfram.com/VariationCoefficient.html
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ COEFFICIENT_OF_VARIATION returns STD(X)/MEAN(X)
+
+ cv=coefficient_of_variation(
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+cor
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 576
+ COR calculates the correlation matrix
+ X and Y can contain missing values encoded with NaN.
+ NaN's are skipped, NaN do not result in a NaN output.
+ (Its assumed that the occurence of NaN's is uncorrelated)
+ The output gives NaN only if there are insufficient input data
+
+ COR(X);
+ calculates the (auto-)correlation matrix of X
+ COR(X,Y);
+ calculates the crosscorrelation between X and Y
+
+ c = COR(...);
+ c is the correlation matrix
+
+ W weights to compute weighted mean (default: [])
+ if W=[], all weights are 1.
+ number of elements in W must match size(x,DIM)
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ COR calculates the correlation matrix
+ X and Y can contain missing values encod
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+corrcoef
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4692
+ CORRCOEF calculates the correlation matrix from pairwise correlations.
+ The input data can contain missing values encoded with NaN.
+ Missing data (NaN's) are handled by pairwise deletion [15].
+ In order to avoid possible pitfalls, use case-wise deletion or
+ or check the correlation of NaN's with your data (see below).
+ A significance test for testing the Hypothesis
+ 'correlation coefficient R is significantly different to zero'
+ is included.
+
+ [...] = CORRCOEF(X);
+ calculates the (auto-)correlation matrix of X
+ [...] = CORRCOEF(X,Y);
+ calculates the crosscorrelation between X and Y
+
+ [...] = CORRCOEF(..., Mode);
+ Mode='Pearson' or 'parametric' [default]
+ gives the correlation coefficient
+ also known as the 'product-moment coefficient of correlation'
+ or 'Pearson''s correlation' [1]
+ Mode='Spearman' gives 'Spearman''s Rank Correlation Coefficient'
+ This replaces SPEARMAN.M
+ Mode='Rank' gives a nonparametric Rank Correlation Coefficient
+ This is the "Spearman rank correlation with proper handling of ties"
+ This replaces RANKCORR.M
+
+ [...] = CORRCOEF(..., param1, value1, param2, value2, ... );
+ param value
+ 'Mode' type of correlation
+ 'Pearson','parametric'
+ 'Spearman'
+ 'rank'
+ 'rows' how do deal with missing values encoded as NaN's.
+ 'complete': remove all rows with at least one NaN
+ 'pairwise': [default]
+ 'alpha' 0.01 : significance level to compute confidence interval
+
+ [R,p,ci1,ci2,nansig] = CORRCOEF(...);
+ R is the correlation matrix
+ R(i,j) is the correlation coefficient r between X(:,i) and Y(:,j)
+ p gives the significance of R
+ It tests the null hypothesis that the product moment correlation coefficient is zero
+ using Student's t-test on the statistic t = r*sqrt(N-2)/sqrt(1-r^2)
+ where N is the number of samples (Statistics, M. Spiegel, Schaum series).
+ p > alpha: do not reject the Null hypothesis: 'R is zero'.
+ p < alpha: The alternative hypothesis 'R is larger than zero' is true with probability (1-alpha).
+ ci1 lower (1-alpha) confidence interval
+ ci2 upper (1-alpha) confidence interval
+ If no alpha is provided, the default alpha is 0.01. This can be changed with function flag_implicit_significance.
+ nan_sig p-value whether H0: 'NaN''s are not correlated' could be correct
+ if nan_sig < alpha, H1 ('NaNs are correlated') is very likely.
+
+ The result is only valid if the occurence of NaN's is uncorrelated. In
+ order to avoid this pitfall, the correlation of NaN's should be checked
+ or case-wise deletion should be applied.
+ Case-Wise deletion can be implemented
+ ix = ~any(isnan([X,Y]),2);
+ [...] = CORRCOEF(X(ix,:),Y(ix,:),...);
+
+ Correlation (non-random distribution) of NaN's can be checked with
+ [nan_R,nan_sig]=corrcoef(X,isnan(X))
+ or [nan_R,nan_sig]=corrcoef([X,Y],isnan([X,Y]))
+ or [R,p,ci1,ci2] = CORRCOEF(...);
+
+ Further recommandation related to the correlation coefficient:
+ + LOOK AT THE SCATTERPLOTS to make sure that the relationship is linear
+ + Correlation is not causation because
+ it is not clear which parameter is 'cause' and which is 'effect' and
+ the observed correlation between two variables might be due to the action of other, unobserved variables.
+
+ see also: SUMSKIPNAN, COVM, COV, COR, SPEARMAN, RANKCORR, RANKS,
+ PARTCORRCOEF, flag_implicit_significance
+
+ REFERENCES:
+ on the correlation coefficient
+ [ 1] http://mathworld.wolfram.com/CorrelationCoefficient.html
+ [ 2] http://www.geography.btinternet.co.uk/spearman.htm
+ [ 3] Hogg, R. V. and Craig, A. T. Introduction to Mathematical Statistics, 5th ed. New York: Macmillan, pp. 338 and 400, 1995.
+ [ 4] Lehmann, E. L. and D'Abrera, H. J. M. Nonparametrics: Statistical Methods Based on Ranks, rev. ed. Englewood Cliffs, NJ: Prentice-Hall, pp. 292, 300, and 323, 1998.
+ [ 5] Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 634-637, 1992
+ [ 6] http://mathworld.wolfram.com/SpearmanRankCorrelationCoefficient.html
+ on the significance test of the correlation coefficient
+ [11] http://www.met.rdg.ac.uk/cag/STATS/corr.html
+ [12] http://www.janda.org/c10/Lectures/topic06/L24-significanceR.htm
+ [13] http://faculty.vassar.edu/lowry/ch4apx.html
+ [14] http://davidmlane.com/hyperstat/B134689.html
+ [15] http://www.statsoft.com/textbook/stbasic.html%Correlations
+ others
+ [20] http://www.tufts.edu/~gdallal/corr.htm
+ [21] Fisher transformation http://en.wikipedia.org/wiki/Fisher_transformation
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 71
+ CORRCOEF calculates the correlation matrix from pairwise correlations.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+cov
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1606
+ COV covariance matrix
+ X and Y can contain missing values encoded with NaN.
+ NaN's are skipped, NaN do not result in a NaN output.
+ The output gives NaN only if there are insufficient input data
+ The mean is removed from the data.
+
+ Remark: for data contains missing values, the resulting
+ matrix might not be positiv definite, and its elements have magnitudes
+ larger than one. This ill-behavior is more likely for small sample
+ sizes, but there is no garantee that the result "behaves well" for larger
+ sample sizes. If you want the a "well behaved" result (i.e. positive
+ definiteness and magnitude of elements not larger than 1), use CORRCOEF.
+ However, COV is faster than CORRCOEF and might be good enough in some cases.
+
+ C = COV(X [,Mode]);
+ calculates the (auto-)correlation matrix of X
+ C = COV(X,Y [,Mode]);
+ calculates the crosscorrelation between X and Y.
+ C(i,j) is the correlation between the i-th and jth
+ column of X and Y, respectively.
+ NOTE: Octave and Matlab have (in some special cases) incompatible implemenations.
+ This implementation follows Octave. If the result could be ambigous or
+ incompatible, a warning will be presented in Matlab. To avoid this warning use:
+ a) use COV([X(:),Y(:)]) if you want the traditional Matlab result.
+ b) use C = COV([X,Y]), C = C(1:size(X,2),size(X,2)+1:size(C,2)); if you want to be compatible with this software.
+
+ Mode = 0 [default] scales C by (N-1)
+ Mode = 1 scales C by N.
+
+ see also: COVM, COR, CORRCOEF, SUMSKIPNAN
+
+ REFERENCES:
+ http://mathworld.wolfram.com/Covariance.html
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 76
+ COV covariance matrix
+ X and Y can contain missing values encoded with NaN.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+covm
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1182
+ COVM generates covariance matrix
+ X and Y can contain missing values encoded with NaN.
+ NaN's are skipped, NaN do not result in a NaN output.
+ The output gives NaN only if there are insufficient input data
+
+ COVM(X,Mode);
+ calculates the (auto-)correlation matrix of X
+ COVM(X,Y,Mode);
+ calculates the crosscorrelation between X and Y
+ COVM(...,W);
+ weighted crosscorrelation
+
+ Mode = 'M' minimum or standard mode [default]
+ C = X'*X; or X'*Y correlation matrix
+
+ Mode = 'E' extended mode
+ C = [1 X]'*[1 X]; % l is a matching column of 1's
+ C is additive, i.e. it can be applied to subsequent blocks and summed up afterwards
+ the mean (or sum) is stored on the 1st row and column of C
+
+ Mode = 'D' or 'D0' detrended mode
+ the mean of X (and Y) is removed. If combined with extended mode (Mode='DE'),
+ the mean (or sum) is stored in the 1st row and column of C.
+ The default scaling is factor (N-1).
+ Mode = 'D1' is the same as 'D' but uses N for scaling.
+
+ C = covm(...);
+ C is the scaled by N in Mode M and by (N-1) in mode D.
+ [C,N] = covm(...);
+ C is not scaled, provides the scaling factor N
+ C./N gives the scaled version.
+
+ see also: DECOVM, XCOVF
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ COVM generates covariance matrix
+ X and Y can contain missing values encoded wi
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 13
+cumsumskipnan
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 249
+ CUMSUMSKIPNAN Cumulative sum while skiping NaN's.
+ If DIM is omitted, it defaults to the first non-singleton dimension.
+
+ Y = cumsumskipnan(x [,DIM])
+
+ x input data
+ DIM dimension (default: [])
+ y resulting sum
+
+ see also: CUMSUM, SUMSKIPNAN
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 51
+ CUMSUMSKIPNAN Cumulative sum while skiping NaN's.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+decovm
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 384
+ decompose extended covariance matrix into mean (mu),
+ standard deviation, the (pure) Covariance (COV),
+ correlation (xc) matrix and the correlation coefficients R2.
+ NaN's are condsidered as missing values.
+ [mu,sd,COV,xc,N,R2]=decovm(ECM[,NN])
+
+ ECM is the extended covariance matrix
+ NN is the number of elements, each estimate (in ECM) is based on
+
+ see also: MDBC, COVM, R2
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ decompose extended covariance matrix into mean (mu),
+ standard deviation, the
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+detrend
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 837
+ DETREND removes the trend from data, NaN's are considered as missing values
+
+ DETREND is fully compatible to previous Matlab and Octave DETREND with the following features added:
+ - handles NaN's by assuming that these are missing values
+ - handles unequally spaced data
+ - second output parameter gives the trend of the data
+ - compatible to Matlab and Octave
+
+ [...]=detrend([t,] X [,p])
+ removes trend for unequally spaced data
+ t represents the time points
+ X(i) is the value at time t(i)
+ p must be a scalar
+
+ [...]=detrend(X,0)
+ [...]=detrend(X,'constant')
+ removes the mean
+
+ [...]=detrend(X,p)
+ removes polynomial of order p (default p=1)
+
+ [...]=detrend(X,1) - default
+ [...]=detrend(X,'linear')
+ removes linear trend
+
+ [X,T]=detrend(...)
+
+ X is the detrended data
+ T is the removed trend
+
+ see also: SUMSKIPNAN, ZSCORE
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ DETREND removes the trend from data, NaN's are considered as missing values
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+ecdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 443
+ ECDF empirical cumulative function
+ NaN's are considered Missing values and are ignored.
+
+ [F,X] = ecdf(Y)
+ calculates empirical cumulative distribution functions (i.e Kaplan-Meier estimate)
+ ecdf(Y)
+ ecdf(gca,Y)
+ without output arguments plots the empirical cdf, in axis gca.
+
+ Y input data
+ must be a vector or matrix, in case Y is a matrix, the ecdf for every column is computed.
+
+ see also: HISTO2, HISTO3, PERCENTILE, QUANTILE
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ ECDF empirical cumulative function
+ NaN's are considered Missing values and
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 19
+flag_accuracy_level
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1033
+ FLAG_ACCURACY_LEVEL sets and gets accuracy level
+ used in SUMSKIPNAN_MEX and COVM_MEX
+ The error margin of the naive summation is N*eps (N is the number of samples),
+ the error margin is only 2*eps if Kahan's summation is used [1].
+
+ 0: maximum speed [default]
+ accuracy of double (64bit) with naive summation (error = N*2^-52)
+ 1: accuracy of extended (80bit) with naive summation (error = N*2^-64)
+ 2: accuracy of double (64bit) with Kahan summation (error = 2^-52)
+ 3: accuracy of extended (80bit) with Kahan summation (error = 2^-64)
+
+ Please note, level 3 might be equally accurate but slower than 1 or 2 on
+ some platforms. In order to determine what is good for you, you might want
+ to run ACCTEST.
+
+ FLAG = flag_accuracy_level()
+ gets current level
+ flag_accuracy_level(FLAG)
+ sets accuracy level
+
+ see also: ACCTEST
+
+ Reference:
+ [1] David Goldberg,
+ What Every Computer Scientist Should Know About Floating-Point Arithmetic
+ ACM Computing Surveys, Vol 23, No 1, March 1991.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ FLAG_ACCURACY_LEVEL sets and gets accuracy level
+ used in SUMSKIPNAN_MEX and
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 26
+flag_implicit_significance
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 928
+ The use of FLAG_IMPLICIT_SIGNIFICANCE is in experimental state.
+ flag_implicit_significance might even become obsolete.
+
+ FLAG_IMPLICIT_SIGNIFICANCE sets and gets default alpha (level) of any significance test
+ The default alpha-level is stored in the global variable FLAG_implicit_significance
+ The idea is that the significance must not be assigned explicitely.
+ This might yield more readable code.
+
+ Choose alpha low enough, because in alpha*100% of the cases, you will
+ reject the Null hypothesis just by change. For this reason, the default
+ alpha is 0.01.
+
+ flag_implicit_significance(0.01)
+ sets the alpha-level for the significance test
+
+ alpha = flag_implicit_significance()
+ gets default alpha
+
+ flag_implicit_significance(alpha)
+ sets default alpha-level
+
+ alpha = flag_implicit_significance(alpha)
+ gets and sets alpha
+
+ features:
+ - compatible to Matlab and Octave
+
+ see also: CORRCOEF, PARTCORRCOEF
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 64
+ The use of FLAG_IMPLICIT_SIGNIFICANCE is in experimental state.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 22
+flag_implicit_skip_nan
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 934
+ FLAG_IMPLICIT_SKIP_NAN sets and gets default mode for handling NaNs
+ 1 skips NaN's (the default mode if no mode is set)
+ 0 NaNs are propagated; input NaN's give NaN's at the output
+
+ FLAG = flag_implicit_skip_nan()
+ gets current mode
+
+ flag_implicit_skip_nan(FLAG)
+ sets mode
+
+ prevFLAG = flag_implicit_skip_nan(nextFLAG)
+ gets previous set FLAG and sets FLAG for the future
+ flag_implicit_skip_nan(prevFLAG)
+ resets FLAG to previous mode
+
+ It is used in:
+ SUMSKIPNAN, MEDIAN, QUANTILES, TRIMEAN
+ and affects many other functions like:
+ CENTER, KURTOSIS, MAD, MEAN, MOMENT, RMS, SEM, SKEWNESS,
+ STATISTIC, STD, VAR, ZSCORE etc.
+
+ The mode is stored in the global variable FLAG_implicit_skip_nan
+ It is recommended to use flag_implicit_skip_nan(1) as default and
+ flag_implicit_skip_nan(0) should be used for exceptional cases only.
+ This feature might disappear without further notice, so you should really not
+ rely on it.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ FLAG_IMPLICIT_SKIP_NAN sets and gets default mode for handling NaNs
+ 1 skips Na
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 17
+flag_nans_occured
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 430
+ FLAG_NANS_OCCURED checks whether the last call(s) to sumskipnan or covm
+ contained any not-a-numbers in the input argument. Because many other
+ functions like mean, std, etc. are also using sumskipnan,
+ also these functions can be checked for NaN's in the input data.
+
+ A call to FLAG_NANS_OCCURED() resets also the flag whether NaN's occured.
+ Only sumskipnan or covm can set the flag again.
+
+ see also: SUMSKIPNAN, COVM
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ FLAG_NANS_OCCURED checks whether the last call(s) to sumskipnan or covm
+ conta
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+fss
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1739
+ FSS - feature subset selection and feature ranking
+ the method is motivated by the max-relevance-min-redundancy (mRMR)
+ approach [1]. However, the default method uses partial correlation,
+ which has been developed from scratch. PCCM [3] describes
+ a similar idea, but is more complicated.
+ An alternative method based on FSDD is implemented, too.
+
+ [idx,score] = fss(D,cl)
+ [idx,score] = fss(D,cl,MODE)
+ [idx,score] = fss(D,cl,MODE)
+
+ D data - each column represents a feature
+ cl classlabel
+ Mode 'Pearson' [default] correlation
+ 'rank' correlation
+ 'FSDD' feature selection algorithm based on a distance discriminant [2]
+ %%% 'MRMR','MID','MIQ' max-relevance, min redundancy [1] - not supported yet.
+
+ score score of the feature
+ idx ranking of the feature
+ [tmp,idx]=sort(-score)
+
+ see also: TRAIN_SC, XVAL, ROW_COL_DELETION
+
+ REFERENCES:
+ [1] Peng, H.C., Long, F., and Ding, C.,
+ Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy,
+ IEEE Transactions on Pattern Analysis and Machine Intelligence,
+ Vol. 27, No. 8, pp.1226-1238, 2005.
+ [2] Jianning Liang, Su Yang, Adam Winstanley,
+ Invariant optimal feature selection: A distance discriminant and feature ranking based solution,
+ Pattern Recognition, Volume 41, Issue 5, May 2008, Pages 1429-1439.
+ ISSN 0031-3203, DOI: 10.1016/j.patcog.2007.10.018.
+ [3] K. Raghuraj Rao and S. Lakshminarayanan
+ Partial correlation based variable selection approach for multivariate data classification methods
+ Chemometrics and Intelligent Laboratory Systems
+ Volume 86, Issue 1, 15 March 2007, Pages 68-81
+ http://dx.doi.org/10.1016/j.chemolab.2006.08.007
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ FSS - feature subset selection and feature ranking
+ the method is motivated
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+geomean
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1207
+ GEOMEAN calculates the geomentric mean of data elements.
+
+ y = geomean(x [,DIM [,W]]) is the same as
+ y = mean(x,'G' [,DIM])
+
+ DIM dimension
+ 1 STD of columns
+ 2 STD of rows
+ default or []: first DIMENSION, with more than 1 element
+ W weights to compute weighted mean (default: [])
+ if W=[], all weights are 1.
+ number of elements in W must match size(x,DIM)
+
+ features:
+ - can deal with NaN's (missing values)
+ - weighting of data
+ - dimension argument also in Octave
+ - compatible to Matlab and Octave
+
+ see also: SUMSKIPNAN, MEAN, HARMMEAN
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 3 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 57
+ GEOMEAN calculates the geomentric mean of data elements.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+gscatter
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 471
+ GSCATTER scatter plot of groups
+
+ gscatter(x,y,group)
+ gscatter(x,y,group,clr,sym,siz)
+ gscatter(x,y,group,clr,sym,siz,doleg)
+ gscatter(x,y,group,clr,sym,siz,doleg,xname,yname)
+ h = gscatter(...)
+
+ x,y, group: vectors with equal length
+ clf: color vector, default 'bgrcmyk'
+ sym: symbol, default '.'
+ siz: size of Marker
+ doleg: 'on' (default) shows legend, 'off' turns of legend
+ xname, yname: name of axis
+
+
+ see also: ecdf, cdfplot
+
+ References:
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 34
+ GSCATTER scatter plot of groups
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+harmmean
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 629
+ HARMMEAN calculates the harmonic mean of data elements.
+ The harmonic mean is the inverse of the mean of the inverse elements.
+
+ y = harmmean(x [,DIM [,W]]) is the same as
+ y = mean(x,'H' [,DIM [,W]])
+
+ DIM dimension
+ 1 STD of columns
+ 2 STD of rows
+ default or []: first DIMENSION, with more than 1 element
+ W weights to compute weighted mean (default: [])
+ if W=[], all weights are 1.
+ number of elements in W must match size(x,DIM)
+
+ features:
+ - can deal with NaN's (missing values)
+ - weighting of data
+ - dimension argument also in Octave
+ - compatible to Matlab and Octave
+
+ see also: SUMSKIPNAN, MEAN, GEOMEAN
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 56
+ HARMMEAN calculates the harmonic mean of data elements.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+hist2res
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 700
+ Evaluates Histogram data
+ [R]=hist2res(H)
+
+ [y]=hist2res(H,fun)
+ estimates fun-statistic
+
+ fun 'mean' mean
+ 'std' standard deviation
+ 'var' variance
+ 'sem' standard error of the mean
+ 'rms' root mean square
+ 'meansq' mean of squares
+ 'sum' sum
+ 'sumsq' sum of squares
+ 'CM#' central moment of order #
+ 'skewness' skewness
+ 'kurtosis' excess coefficient (Fisher kurtosis)
+
+ see also: NaN/statistic
+
+ REFERENCES:
+ [1] C.L. Nikias and A.P. Petropulu "Higher-Order Spectra Analysis" Prentice Hall, 1993.
+ [2] C.E. Shannon and W. Weaver "The mathematical theory of communication" University of Illinois Press, Urbana 1949 (reprint 1963).
+ [3] http://www.itl.nist.gov/
+ [4] http://mathworld.wolfram.com/
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 43
+ Evaluates Histogram data
+ [R]=hist2res(H)
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+iqr
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 372
+ IQR calculates the interquartile range
+ Missing values (encoded as NaN) are ignored.
+
+ Q = iqr(Y)
+ Q = iqr(Y,DIM)
+ returns the IQR along dimension DIM of sample array Y.
+
+ Q = iqr(HIS)
+ returns the IQR from the histogram HIS.
+ HIS must be a HISTOGRAM struct as defined in HISTO2 or HISTO3.
+
+ see also: MAD, RANGE, HISTO2, HISTO3, PERCENTILE, QUANTILE
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ IQR calculates the interquartile range
+ Missing values (encoded as NaN) are
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+kappa
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1760
+ KAPPA estimates Cohen's kappa coefficient
+ and related statistics
+
+ [...] = kappa(d1,d2);
+ NaN's are handled as missing values and are ignored
+ [...] = kappa(d1,d2,'notIgnoreNAN');
+ NaN's are handled as just another Label.
+ [kap,sd,H,z,ACC,sACC,MI] = kappa(...);
+ X = kappa(...);
+
+ d1 data of scorer 1
+ d2 data of scorer 2
+
+ kap Cohen's kappa coefficient point
+ se standard error of the kappa estimate
+ H Concordance matrix, i.e. confusion matrix
+ z z-score
+ ACC overall agreement (accuracy)
+ sACC specific accuracy
+ MI Mutual information or transfer information (in [bits])
+ X is a struct containing all the fields above
+ For two classes, a number of additional summary statistics including
+ TPR, FPR, FDR, PPV, NPF, F1, dprime, Matthews Correlation coefficient (MCC) or
+ Phi coefficient (PHI=MCC), Specificity and Sensitivity
+ are provided. Note, the positive category must the larger label (in d and c), otherwise
+ the confusion matrix becomes transposed and the summary statistics are messed up.
+
+
+ Reference(s):
+ [1] Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 37-46.
+ [2] J Bortz, GA Lienert (1998) Kurzgefasste Statistik f|r die klassische Forschung, Springer Berlin - Heidelberg.
+ Kapitel 6: Uebereinstimmungsmasze fuer subjektive Merkmalsurteile. p. 265-270.
+ [3] http://www.cmis.csiro.au/Fiona.Evans/personal/msc/html/chapter3.html
+ [4] Kraemer, H. C. (1982). Kappa coefficient. In S. Kotz and N. L. Johnson (Eds.),
+ Encyclopedia of Statistical Sciences. New York: John Wiley & Sons.
+ [5] http://ourworld.compuserve.com/homepages/jsuebersax/kappa.htm
+ [6] http://en.wikipedia.org/wiki/Receiver_operating_characteristic
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 70
+ KAPPA estimates Cohen's kappa coefficient
+ and related statistics
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+kurtosis
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 461
+ KURTOSIS estimates the kurtosis
+
+ y = kurtosis(x,DIM)
+ calculates kurtosis of x in dimension DIM
+
+ DIM dimension
+ 1: STATS of columns
+ 2: STATS of rows
+ default or []: first DIMENSION, with more than 1 element
+
+ features:
+ - can deal with NaN's (missing values)
+ - dimension argument
+ - compatible to Matlab and Octave
+
+ see also: SUMSKIPNAN, VAR, STD, VAR, SKEWNESS, MOMENT, STATISTIC,
+ IMPLICIT_SKIP_NAN
+
+ REFERENCE(S):
+ http://mathworld.wolfram.com/
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 33
+ KURTOSIS estimates the kurtosis
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 15
+load_fisheriris
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 446
+ LOAD_FISHERIRIS
+ loads famous iris data set from Fisher, 1936 [1].
+
+ References:
+ [1] Fisher,R.A. "The use of multiple measurements in taxonomic problems"
+ Annual Eugenics, 7, Part II, 179-188 (1936); also in "Contributions to Mathematical Statistics" (John Wiley, NY, 1950).
+ [2] Duda,R.O., & Hart,P.E. (1973) Pattern Classification and Scene Analysis.
+ (Q327.D83) John Wiley & Sons. ISBN 0-471-22361-1. See page 218.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 75
+ LOAD_FISHERIRIS
+ loads famous iris data set from Fisher, 1936 [1].
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+mad
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 855
+ MAD estimates the Mean Absolute deviation
+ (note that according to [1,2] this is the mean deviation;
+ not the mean absolute deviation)
+
+ y = mad(x,DIM)
+ calculates the mean deviation of x in dimension DIM
+
+ DIM dimension
+ 1: STATS of columns
+ 2: STATS of rows
+ default or []: first DIMENSION, with more than 1 element
+
+ features:
+ - can deal with NaN's (missing values)
+ - dimension argument
+ - compatible to Matlab and Octave
+
+ see also: SUMSKIPNAN, VAR, STD,
+
+ REFERENCE(S):
+ [1] http://mathworld.wolfram.com/MeanDeviation.html
+ [2] L. Sachs, "Applied Statistics: A Handbook of Techniques", Springer-Verlag, 1984, page 253.
+
+ [3] http://mathworld.wolfram.com/MeanAbsoluteDeviation.html
+ [4] Kenney, J. F. and Keeping, E. S. "Mean Absolute Deviation." §6.4 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 76-77 1962.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ MAD estimates the Mean Absolute deviation
+ (note that according to [1,2] this i
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+mahal
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 395
+ MAHAL return the Mahalanobis' D-square distance between the
+ multivariate samples x and y, which must have the same number
+ of components (columns), but may have a different number of observations (rows).
+
+ d = mahal(X,Y)
+
+ d(k) = (X(k,:)-MU)*inv(SIGMA)*(X(k,:)-MU)'
+
+ where MU and SIGMA are the mean and the covariance matrix of Y
+
+
+ see also: TRAIN_SC, TEST_SC, COVM
+
+ References:
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ MAHAL return the Mahalanobis' D-square distance between the
+ multivariate samp
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+make
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 46
+ This make.m is used for Matlab under Windows
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 11
+ This make.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+mean
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 735
+ MEAN calculates the mean of data elements.
+
+ y = mean(x [,DIM] [,opt] [, W])
+
+ DIM dimension
+ 1 MEAN of columns
+ 2 MEAN of rows
+ N MEAN of N-th dimension
+ default or []: first DIMENSION, with more than 1 element
+
+ opt options
+ 'A' arithmetic mean
+ 'G' geometric mean
+ 'H' harmonic mean
+
+ W weights to compute weighted mean (default: [])
+ if W=[], all weights are 1.
+ number of elements in W must match size(x,DIM)
+
+ usage:
+ mean(x)
+ mean(x,DIM)
+ mean(x,opt)
+ mean(x,opt,DIM)
+ mean(x,DIM,opt)
+ mean(x,DIM,W)
+ mean(x,DIM,opt,W); '
+
+ features:
+ - can deal with NaN's (missing values)
+ - weighting of data
+ - dimension argument also in Octave
+ - compatible to Matlab and Octave
+
+ see also: SUMSKIPNAN, MEAN, GEOMEAN, HARMMEAN
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 43
+ MEAN calculates the mean of data elements.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+meandev
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 856
+ MEANDEV estimates the Mean deviation
+ (note that according to [1,2] this is the mean deviation;
+ not the mean absolute deviation)
+
+ y = meandev(x,DIM)
+ calculates the mean deviation of x in dimension DIM
+
+ DIM dimension
+ 1: STATS of columns
+ 2: STATS of rows
+ default or []: first DIMENSION, with more than 1 element
+
+ features:
+ - can deal with NaN's (missing values)
+ - dimension argument
+ - compatible to Matlab and Octave
+
+ see also: SUMSKIPNAN, VAR, STD, MAD
+
+ REFERENCE(S):
+ [1] http://mathworld.wolfram.com/MeanDeviation.html
+ [2] L. Sachs, "Applied Statistics: A Handbook of Techniques", Springer-Verlag, 1984, page 253.
+ [3] http://mathworld.wolfram.com/MeanAbsoluteDeviation.html
+ [4] Kenney, J. F. and Keeping, E. S. "Mean Absolute Deviation." §6.4 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 76-77 1962.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ MEANDEV estimates the Mean deviation
+ (note that according to [1,2] this is the
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+meansq
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 527
+ MEANSQ calculates the mean of the squares
+
+ y = meansq(x,DIM,W)
+
+ DIM dimension
+ 1 STD of columns
+ 2 STD of rows
+ N STD of N-th dimension
+ default or []: first DIMENSION, with more than 1 element
+ W weights to compute weighted mean (default: [])
+ if W=[], all weights are 1.
+ number of elements in W must match size(x,DIM)
+
+ features:
+ - can deal with NaN's (missing values)
+ - weighting of data
+ - dimension argument also in Octave
+ - compatible to Matlab and Octave
+
+ see also: SUMSQ, SUMSKIPNAN, MEAN, VAR, STD, RMS
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 43
+ MEANSQ calculates the mean of the squares
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 9
+medAbsDev
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 373
+ medAbsDev calculates the median absolute deviation
+
+ Usage: D = medAbsDev(X, DIM)
+ or: [D, M] = medAbsDev(X, DIM)
+ Input: X : data
+ DIM: dimension along which mad should be calculated (1=columns, 2=rows)
+ (optional, default=first dimension with more than 1 element
+ Output: D : median absolute deviations
+ M : medians (optional)
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 53
+ medAbsDev calculates the median absolute deviation
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+median
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 366
+ MEDIAN data elements,
+ [y]=median(x [,DIM])
+
+ DIM dimension
+ 1: median of columns
+ 2: median of rows
+ N: median of N-th dimension
+ default or []: first DIMENSION, with more than 1 element
+
+ features:
+ - can deal with NaN's (missing values)
+ - accepts dimension argument like in Matlab in Octave, too.
+ - compatible to Matlab and Octave
+
+ see also: SUMSKIPNAN
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 46
+ MEDIAN data elements,
+ [y]=median(x [,DIM])
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+moment
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 627
+ MOMENT estimates the p-th moment
+
+ M = moment(x, p [,opt] [,DIM])
+ M = moment(H, p [,opt])
+ calculates p-th central moment from data x in dimension DIM
+ of from Histogram H
+
+ p moment of order p
+ opt 'ac': absolute 'a' and/or central ('c') moment
+ DEFAULT: '' raw moments are estimated
+ DIM dimension
+ 1: STATS of columns
+ 2: STATS of rows
+ default or []: first DIMENSION, with more than 1 element
+
+ features:
+ - can deal with NaN's (missing values)
+ - dimension argument
+ - compatible to Matlab and Octave
+
+ see also: STD, VAR, SKEWNESS, KURTOSIS, STATISTIC,
+
+ REFERENCE(S):
+ http://mathworld.wolfram.com/Moment.html
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ MOMENT estimates the p-th moment
+
+ M = moment(x, p [,opt] [,DIM])
+ M = moment
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+nanconv
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 616
+ NANCONV computes the convolution for data with missing values.
+ X and Y can contain missing values encoded with NaN.
+ NaN's are skipped, NaN do not result in a NaN output.
+ The output gives NaN only if there are insufficient input data
+
+ [...] = NANCONV(X,Y);
+ calculates 2-dim convolution between X and Y
+ [C] = NANCONV(X,Y);
+
+ WARNING: missing values can introduce aliasing - causing unintended results.
+ Moreover, the behavior of bandpass and highpass filters in case of missing values
+ is not fully understood, and might contain some pitfalls.
+
+ see also: CONV, NANCONV2, NANFFT, NANFILTER
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 63
+ NANCONV computes the convolution for data with missing values.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+nanfft
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 618
+ NANFFT calculates the Fourier-Transform of X for data with missing values.
+ NANFFT is the same as FFT but X can contain missing values encoded with NaN.
+ NaN's are skipped, NaN do not result in a NaN output.
+
+ Y = NANFFT(X)
+ Y = NANFFT(X,N)
+ Y = NANFFT(X,[],DIM)
+
+ [Y,N] = NANFFT(...)
+ returns the number of valid samples N
+
+
+ WARNING: missing values can introduce aliasing - causing unintended results.
+ Moreover, the behavior of bandpass and highpass filters in case of missing values
+ is not fully understood, and might contain some pitfalls.
+
+ see also: FFT, XCORR, NANCONV, NANFILTER
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 75
+ NANFFT calculates the Fourier-Transform of X for data with missing values.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 9
+nanfilter
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 519
+ NANFILTER is able to filter data with missing values encoded as NaN.
+
+ [Y,Z] = nanfilter(B,A,X [, Z]);
+
+ If X contains no missing data, NANFILTER should behave like FILTER.
+ NaN-values are handled gracefully.
+
+ WARNING: missing values can introduce aliasing - causing unintended results.
+ Moreover, the behavior of bandpass and highpass filters in case of missing values
+ is not fully understood, and might contain some pitfalls.
+
+ see also: FILTER, SUMSKIPNAN, NANFFT, NANCONV, NANFILTER1UC
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 69
+ NANFILTER is able to filter data with missing values encoded as NaN.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 12
+nanfilter1uc
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 257
+ NANFILTER1UC is an adaptive filter for data with missing values encoded as NaN.
+
+ [Y,Z] = nanfilter1uc(uc,X [, Z]);
+
+ if X contains no missing data, NANFILTER behaves like FILTER(uc,[1,uc-1],X[,Z]).
+
+ see also: FILTER, NANFILTER, SUMSKIPNAN
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ NANFILTER1UC is an adaptive filter for data with missing values encoded as NaN.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 11
+naninsttest
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 112
+ NANINSTTEST checks whether the functions from NaN-toolbox have been
+ correctly installed.
+
+ see also: NANTEST
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ NANINSTTEST checks whether the functions from NaN-toolbox have been
+ correctly
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+nanmean
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 330
+ NANMEAN same as SUM but ignores NaN's.
+ NANMEAN is OBSOLETE; use MEAN instead. NANMEAN is included
+ to provide backward compatibility
+
+ Y = nanmean(x [,DIM])
+
+ DIM dimension
+ 1 sum of columns
+ 2 sum of rows
+ default or []: first DIMENSION with more than 1 element
+ Y resulting mean
+
+
+ see also: MEAN, SUMSKIPNAN, NANSUM
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 39
+ NANMEAN same as SUM but ignores NaN's.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+nanstd
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 518
+ NANSTD same as STD but ignores NaN's.
+ NANSTD is OBSOLETE; use NaN/STD instead. NANSTD is included
+ to fix a bug in alternative implementations and to
+ provide some compatibility.
+
+ Y = nanstd(x, FLAG, [,DIM])
+
+ x data
+ FLAG 0: [default] normalizes with (N-1), N = sample size
+ FLAG 1: normalizes with N, N = sample size
+ DIM dimension
+ 1 sum of columns
+ 2 sum of rows
+ default or []: first DIMENSION with more than 1 element
+ Y resulting standard deviation
+
+ see also: SUM, SUMSKIPNAN, NANSUM, STD
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 38
+ NANSTD same as STD but ignores NaN's.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+nansum
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 333
+ NANSUM same as SUM but ignores NaN's.
+ NANSUM is OBSOLETE; use SUMSKIPNAN instead. NANSUM is included
+ to fix a bug in some other versions.
+
+ Y = nansum(x [,DIM])
+
+ DIM dimension
+ 1 sum of columns
+ 2 sum of rows
+ default or []: first DIMENSION with more than 1 element
+ Y resulting sum
+
+
+ see also: SUM, SUMSKIPNAN, NANSUM
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 38
+ NANSUM same as SUM but ignores NaN's.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+nantest
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 366
+ NANTEST checks several mathematical operations and a few
+ statistical functions for their correctness related to NaN's.
+ e.g. it checks norminv, normcdf, normpdf, sort, matrix division and multiplication.
+
+
+ see also: NANINSTTEST
+
+ REFERENCE(S):
+ [1] W. Kahan (1996) Lecture notes on the Status of "IEEE Standard 754 for
+ Binary Floating-point Arithmetic.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ NANTEST checks several mathematical operations and a few
+ statistical function
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+normcdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 290
+ NORMCDF returns normal cumulative distribtion function
+
+ cdf = normcdf(x,m,s);
+
+ Computes the CDF of a the normal distribution
+ with mean m and standard deviation s
+ default: m=0; s=1;
+ x,m,s must be matrices of same size, or any one can be a scalar.
+
+ see also: NORMPDF, NORMINV
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 56
+ NORMCDF returns normal cumulative distribtion function
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+norminv
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 341
+ NORMINV returns inverse cumulative function of the normal distribution
+
+ x = norminv(p,m,s);
+
+ Computes the quantile (inverse of the CDF) of a the normal
+ cumulative distribution with mean m and standard deviation s
+ default: m=0; s=1;
+ p,m,s must be matrices of same size, or any one can be a scalar.
+
+ see also: NORMPDF, NORMCDF
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 72
+ NORMINV returns inverse cumulative function of the normal distribution
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+normpdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 279
+ NORMPDF returns normal probability density
+
+ pdf = normpdf(x,m,s);
+
+ Computes the PDF of a the normal distribution
+ with mean m and standard deviation s
+ default: m=0; s=1;
+ x,m,s must be matrices of same size, or any one can be a scalar.
+
+ see also: NORMCDF, NORMINV
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 45
+ NORMPDF returns normal probability density
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 12
+partcorrcoef
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2015
+ PARTCORRCOEF calculates the partial correlation between X and Y
+ after removing the influence of Z.
+ X, Y and Z can contain missing values encoded with NaN.
+ NaN's are skipped, NaN do not result in a NaN output.
+ (Its assumed that the occurence of NaN's is uncorrelated)
+ The output gives NaN, only if there are insufficient input data.
+
+ The partial correlation is defined as
+ pcc(xy|z)=(cc(x,y)-cc(x,z)*cc(y,z))/sqrt((1-cc(x,y)�)*((1-cc(x,z)�)))
+
+
+ PARTCORRCOEF(X [,Mode]);
+ calculates the (auto-)correlation matrix of X
+ PARTCORRCOEF(X,Y,Z);
+ PARTCORRCOEF(X,Y,Z,[]);
+ PARTCORRCOEF(X,Y,Z,'Pearson');
+ PARTCORRCOEF(X,Y,Z,'Rank');
+ PARTCORRCOEF(X,Y,Z,'Spearman');
+
+ Mode=[] [default]
+ removes from X and Y the part that can be explained by Z
+ and computes the correlation of the remaining part.
+ Ideally, this is equivalent to Mode='Pearson', however, in practice
+ this is more accurate.
+ Mode='Pearson' or 'parametric'
+ Mode='Spearman'
+ Mode='Rank'
+ computes the partial correlation based on cc(x,y),cc(x,z) and cc(y,z)
+ with the respective mode.
+
+ [R,p,ci1,ci2] = PARTCORRCOEF(...);
+ r is the partialcorrelation matrix
+ r(i,j) is the partial correlation coefficient r between X(:,i) and Y(:,j)
+ when influence of Z is removed.
+ p gives the significance of PCC
+ It tests the null hypothesis that the product moment correlation coefficient is zero
+ using Student's t-test on the statistic t = r sqrt(N-Nz-2)/sqrt(1-r^2)
+ where N is the number of samples (Statistics, M. Spiegel, Schaum series).
+ p > alpha: do not reject the Null hypothesis: "R is zero".
+ p < alpha: The alternative hypothesis "R2 is larger than zero" is true with probability (1-alpha).
+ ci1 lower 0.95 confidence interval
+ ci2 upper 0.95 confidence interval
+
+ see also: SUMSKIPNAN, COVM, COV, COR, SPEARMAN, RANKCORR, RANKS, CORRCOEF
+
+ REFERENCES:
+ on the partial correlation coefficient
+ [1] http://www.tufts.edu/~gdallal/partial.htm
+ [2] http://www.nag.co.uk/numeric/fl/manual/pdf/G02/g02byf.pdf
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ PARTCORRCOEF calculates the partial correlation between X and Y
+ after removing
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 10
+percentile
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 554
+ PERCENTILE calculates the percentiles of histograms and sample arrays.
+
+ Q = percentile(Y,q)
+ Q = percentile(Y,q,DIM)
+ returns the q-th percentile along dimension DIM of sample array Y.
+ size(Q) is equal size(Y) except for dimension DIM which is size(Q,DIM)=length(Q)
+
+ Q = percentile(HIS,q)
+ returns the q-th percentile from the histogram HIS.
+ HIS must be a HISTOGRAM struct as defined in HISTO2 or HISTO3.
+ If q is a vector, the each row of Q returns the q(i)-th percentile
+
+ see also: HISTO2, HISTO3, QUANTILE
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 71
+ PERCENTILE calculates the percentiles of histograms and sample arrays.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+prctile
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 576
+ PRCTILE calculates the percentiles of histograms and sample arrays.
+ (its the same than PERCENTILE.M)
+
+ Q = prctile(Y,q)
+ Q = prctile(Y,q,DIM)
+ returns the q-th percentile along dimension DIM of sample array Y.
+ size(Q) is equal size(Y) except for dimension DIM which is size(Q,DIM)=length(Q)
+
+ Q = prctile(HIS,q)
+ returns the q-th percentile from the histogram HIS.
+ HIS must be a HISTOGRAM struct as defined in HISTO2 or HISTO3.
+ If q is a vector, the each row of Q returns the q(i)-th percentile
+
+ see also: HISTO2, HISTO3, QUANTILE
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 68
+ PRCTILE calculates the percentiles of histograms and sample arrays.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+quantile
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 528
+ QUANTILE calculates the quantiles of histograms and sample arrays.
+
+ Q = quantile(Y,q)
+ Q = quantile(Y,q,DIM)
+ returns the q-th quantile along dimension DIM of sample array Y.
+ size(Q) is equal size(Y) except for dimension DIM which is size(Q,DIM)=length(Q)
+
+ Q = quantile(HIS,q)
+ returns the q-th quantile from the histogram HIS.
+ HIS must be a HISTOGRAM struct as defined in HISTO2 or HISTO3.
+ If q is a vector, the each row of Q returns the q(i)-th quantile
+
+ see also: HISTO2, HISTO3, PERCENTILE
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 67
+ QUANTILE calculates the quantiles of histograms and sample arrays.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+range
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 371
+ RANGE calculates the range of Y
+ Missing values (encoded as NaN) are ignored.
+
+ Q = range(Y)
+ Q = range(Y,DIM)
+ returns the range along dimension DIM of sample array Y.
+
+ Q = range(HIS)
+ returns the RANGE from the histogram HIS.
+ HIS must be a HISTOGRAM struct as defined in HISTO2 or HISTO3.
+
+ see also: IQR, MAD, HISTO2, HISTO3, PERCENTILE, QUANTILE
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ RANGE calculates the range of Y
+ Missing values (encoded as NaN) are ignored.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+rankcorr
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 668
+ RANKCORR calculated the rank correlation coefficient.
+ This function is replaced by CORRCOEF.
+ Significance test and confidence intervals can be obtained from CORRCOEF, too.
+
+ R = CORRCOEF(X, [Y, ] 'Rank');
+
+ The rank correlation r = corrcoef(ranks(x)).
+ is often confused with Spearman's rank correlation.
+ Spearman's correlation is defined as
+ r(x,y) = 1-6*sum((ranks(x)-ranks(y)).^2)/(N*(N*N-1))
+ The results are different. Here, the former version is implemented.
+
+ see also: CORRCOEF, SPEARMAN, RANKS
+
+ REFERENCES:
+ [1] http://mathworld.wolfram.com/SpearmanRankCorrelationCoefficient.html
+ [2] http://mathworld.wolfram.com/CorrelationCoefficient.html
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 54
+ RANKCORR calculated the rank correlation coefficient.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+ranks
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1062
+ RANKS gives the rank of each element in a vector.
+ This program uses an advanced algorithm with averge effort O(m.n.log(n))
+ NaN in the input yields NaN in the output.
+
+ r = ranks(X[,DIM])
+ if X is a vector, return the vector of ranks of X adjusted for ties.
+ if X is matrix, the rank is calculated along dimension DIM.
+ if DIM is zero or empty, the lowest dimension with more then 1 element is used.
+ r = ranks(X,DIM,'traditional')
+ implements the traditional algorithm with O(n^2) computational
+ and O(n^2) memory effort
+ r = ranks(X,DIM,'mtraditional')
+ implements the traditional algorithm with O(n^2) computational
+ and O(n) memory effort
+ r = ranks(X,DIM,'advanced ')
+ implements an advanced algorithm with O(n*log(n)) computational
+ and O(n.log(n)) memory effort
+ r = ranks(X,DIM,'advanced-ties')
+ implements an advanced algorithm with O(n*log(n)) computational
+ and O(n.log(n)) memory effort
+ but without correction for ties
+ This is the fastest algorithm
+
+ see also: CORRCOEF, SPEARMAN, RANKCORR
+
+ REFERENCES:
+ --
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 50
+ RANKS gives the rank of each element in a vector.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+rms
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 560
+ RMS calculates the root mean square
+ can deal with complex data.
+
+ y = rms(x,DIM,W)
+
+ DIM dimension
+ 1 STD of columns
+ 2 STD of rows
+ N STD of N-th dimension
+ default or []: first DIMENSION, with more than 1 element
+ W weights to compute weighted s.d. (default: [])
+ if W=[], all weights are 1.
+ number of elements in W must match size(x,DIM)
+
+ y estimated standard deviation
+
+ features:
+ - can deal with NaN's (missing values)
+ - weighting of data
+ - dimension argument also in Octave
+ - compatible to Matlab and Octave
+
+ see also: SUMSKIPNAN, MEAN
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 67
+ RMS calculates the root mean square
+ can deal with complex data.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 16
+row_col_deletion
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 739
+ ROW_COL_DELETION selects the rows and columns for removing any missing values.
+ A heuristic based on maximizing the number of remaining sample values
+ is used. In other words, if there are more rows than columns, it is
+ more likely that a row-wise deletion will be applied and vice versa.
+
+ [rix,cix] = row_col_deletion(d)
+ [rix,cix] = row_col_deletion(d,c,w)
+
+ Input:
+ d data (each row is a sample, each column a feature)
+ c classlabels (not really used) [OPTIONAL]
+ w weight for each sample vector [OPTIONAL]
+ Output:
+ rix selected samples
+ cix selected columns
+
+ d(rix,cix) does not contain any NaN's i.e. missing values
+
+ see also: TRAIN_SC, TEST_SC
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 79
+ ROW_COL_DELETION selects the rows and columns for removing any missing values.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+sem
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 695
+ SEM calculates the standard error of the mean
+
+ [SE,M] = SEM(x [, DIM [,W]])
+ calculates the standard error (SE) in dimension DIM
+ the default DIM is the first non-single dimension
+ M returns the mean.
+ Can deal with complex data, too.
+
+ DIM dimension
+ 1: SEM of columns
+ 2: SEM of rows
+ N: SEM of N-th dimension
+ default or []: first DIMENSION, with more than 1 element
+ W weights to compute weighted mean and s.d. (default: [])
+ if W=[], all weights are 1.
+ number of elements in W must match size(x,DIM)
+
+ features:
+ - can deal with NaN's (missing values)
+ - weighting of data
+ - dimension argument
+ - compatible to Matlab and Octave
+
+ see also: SUMSKIPNAN, MEAN, VAR, STD
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ SEM calculates the standard error of the mean
+
+ [SE,M] = SEM(x [, DIM [,W]])
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+skewness
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 405
+ SKEWNESS estimates the skewness
+
+ y = skewness(x,DIM)
+ calculates skewness of x in dimension DIM
+
+ DIM dimension
+ 1: STATS of columns
+ 2: STATS of rows
+ default or []: first DIMENSION, with more than 1 element
+
+ features:
+ - can deal with NaN's (missing values)
+ - dimension argument
+ - compatible to Matlab and Octave
+
+ see also: SUMSKIPNAN, STATISTIC
+
+ REFERENCE(S):
+ http://mathworld.wolfram.com/
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 34
+ SKEWNESS estimates the skewness
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+spearman
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 683
+ SPEARMAN Spearman's rank correlation coefficient.
+ This function is replaced by CORRCOEF.
+ Significance test and confidence intervals can be obtained from CORRCOEF.
+
+ [R,p,ci1,ci2] = CORRCOEF(x, [y, ] 'Rank');
+
+ For some (unknown) reason, in previous versions Spearman's rank correlation
+ r = corrcoef(ranks(x)).
+ But according to [1], Spearman's correlation is defined as
+ r = 1-6*sum((ranks(x)-ranks(y)).^2)/(N*(N*N-1))
+ The results are different. Here, the later version is implemented.
+
+ see also: CORRCOEF, RANKCORR
+
+ REFERENCES:
+ [1] http://mathworld.wolfram.com/SpearmanRankCorrelationCoefficient.html
+ [2] http://mathworld.wolfram.com/CorrelationCoefficient.html
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 50
+ SPEARMAN Spearman's rank correlation coefficient.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 9
+statistic
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 938
+ STATISTIC estimates various statistics at once.
+
+ R = STATISTIC(x,DIM)
+ calculates all statistic (see list of fun) in dimension DIM
+ R is a struct with all statistics
+
+ y = STATISTIC(x,fun)
+ estimate of fun on dimension DIM
+ y gives the statistic of fun
+
+ DIM dimension
+ 1: STATS of columns
+ 2: STATS of rows
+ N: STATS of N-th dimension
+ default or []: first DIMENSION, with more than 1 element
+
+ fun 'mean' mean
+ 'std' standard deviation
+ 'var' variance
+ 'sem' standard error of the mean
+ 'rms' root mean square
+ 'meansq' mean of squares
+ 'sum' sum
+ 'sumsq' sum of squares
+ 'CM#' central moment of order #
+ 'skewness' skewness
+ 'kurtosis' excess coefficient (Fisher kurtosis)
+ 'mad' mean absolute deviation
+
+ features:
+ - can deal with NaN's (missing values)
+ - dimension argument
+ - compatible to Matlab and Octave
+
+ see also: SUMSKIPNAN
+
+ REFERENCE(S):
+ [1] http://www.itl.nist.gov/
+ [2] http://mathworld.wolfram.com/
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 48
+ STATISTIC estimates various statistics at once.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+std
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 983
+ STD calculates the standard deviation.
+
+ [y,v] = std(x [, opt[, DIM [, W]]])
+
+ opt option
+ 0: normalizes with N-1 [default]
+ provides the square root of best unbiased estimator of the variance
+ 1: normalizes with N,
+ this provides the square root of the second moment around the mean
+ otherwise:
+ best unbiased estimator of the standard deviation (see [1])
+
+ DIM dimension
+ N STD of N-th dimension
+ default or []: first DIMENSION, with more than 1 element
+ W weights to compute weighted s.d. (default: [])
+ if W=[], all weights are 1.
+ number of elements in W must match size(x,DIM)
+
+ y estimated standard deviation
+
+ features:
+ - provides an unbiased estimation of the S.D.
+ - can deal with NaN's (missing values)
+ - weighting of data
+ - dimension argument also in Octave
+ - compatible to Matlab and Octave
+
+ see also: RMS, SUMSKIPNAN, MEAN, VAR, MEANSQ,
+
+
+ References(s):
+ [1] http://mathworld.wolfram.com/StandardDeviationDistribution.html
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 39
+ STD calculates the standard deviation.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 10
+sumskipnan
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1234
+ SUMSKIPNAN adds all non-NaN values.
+
+ All NaN's are skipped; NaN's are considered as missing values.
+ SUMSKIPNAN of NaN's only gives O; and the number of valid elements is return.
+ SUMSKIPNAN is also the elementary function for calculating
+ various statistics (e.g. MEAN, STD, VAR, RMS, MEANSQ, SKEWNESS,
+ KURTOSIS, MOMENT, STATISTIC etc.) from data with missing values.
+ SUMSKIPNAN implements the DIMENSION-argument for data with missing values.
+ Also the second output argument return the number of valid elements (not NaNs)
+
+ Y = sumskipnan(x [,DIM])
+ [Y,N,SSQ] = sumskipnan(x [,DIM])
+ [...] = sumskipnan(x, DIM, W)
+
+ x input data
+ DIM dimension (default: [])
+ empty DIM sets DIM to first non singleton dimension
+ W weight vector for weighted sum, numel(W) must fit size(x,DIM)
+ Y resulting sum
+ N number of valid (not missing) elements
+ SSQ sum of squares
+
+ the function FLAG_NANS_OCCURED() returns whether any value in x
+ is a not-a-number (NaN)
+
+ features:
+ - can deal with NaN's (missing values)
+ - implements dimension argument.
+ - computes weighted sum
+ - compatible with Matlab and Octave
+
+ see also: FLAG_NANS_OCCURED, SUM, NANSUM, MEAN, STD, VAR, RMS, MEANSQ,
+ SSQ, MOMENT, SKEWNESS, KURTOSIS, SEM
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 36
+ SUMSKIPNAN adds all non-NaN values.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+sumsq
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 391
+ SUMSQ calculates the sum of squares.
+
+ [y] = sumsq(x [, DIM])
+
+ DIM dimension
+ N STD of N-th dimension
+ default or []: first DIMENSION, with more than 1 element
+
+ y estimated standard deviation
+
+ features:
+ - can deal with NaN's (missing values)
+ - dimension argument also in Octave
+ - compatible to Matlab and Octave
+
+ see also: RMS, SUMSKIPNAN, MEAN, VAR, MEANSQ,
+
+
+ References(s):
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 37
+ SUMSQ calculates the sum of squares.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+tcdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 254
+ TCDF returns student cumulative distribtion function
+
+ cdf = tcdf(x,DF);
+
+ Computes the CDF of the students distribution
+ with DF degrees of freedom
+ x,DF must be matrices of same size, or any one can be a scalar.
+
+ see also: NORMCDF, TPDF, TINV
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 54
+ TCDF returns student cumulative distribtion function
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+test_sc
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1441
+ TEST_SC: apply statistical and SVM classifier to test data
+
+ R = test_sc(CC,D,TYPE [,target_Classlabel])
+ R.output output: "signed" distance for each class.
+ This represents the distances between sample D and the separating hyperplane
+ The "signed distance" is possitive if it matches the target class, and
+ and negative if it lays on the opposite side of the separating hyperplane.
+ R.classlabel class for output data
+ The target class is optional. If it is provided, the following values are returned.
+ R.kappa Cohen's kappa coefficient
+ R.ACC Classification accuracy
+ R.H Confusion matrix
+
+ The classifier CC is typically obtained by TRAIN_SC. If a statistical
+ classifier is used, TYPE can be used to modify the classifier.
+ TYPE = 'MDA' mahalanobis distance based classifier
+ TYPE = 'MD2' mahalanobis distance based classifier
+ TYPE = 'MD3' mahalanobis distance based classifier
+ TYPE = 'GRB' Gaussian radial basis function
+ TYPE = 'QDA' quadratic discriminant analysis
+ TYPE = 'LD2' linear discriminant analysis
+ TYPE = 'LD3', 'LDA', 'FDA, 'FLDA' (Fisher's) linear discriminant analysis
+ TYPE = 'LD4' linear discriminant analysis
+ TYPE = 'GDBC' general distance based classifier
+
+ see also: TRAIN_SC
+
+ References:
+ [1] R. Duda, P. Hart, and D. Stork, Pattern Classification, second ed.
+ John Wiley & Sons, 2001.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 61
+ TEST_SC: apply statistical and SVM classifier to test data
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+tiedrank
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 272
+ TIEDRANK compute rank of samples, the mean value is used in case of ties
+ this function is just a wrapper for RANKS, and provided for compatibility
+ with the statistics toolbox of matlab(tm)
+
+ R = tiedrank(X)
+ computes the rank R of vector X
+
+ see also: RANKS
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ TIEDRANK compute rank of samples, the mean value is used in case of ties
+ this
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+tinv
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 330
+ TINV returns inverse cumulative function of the student distribution
+
+ x = tinv(p,v);
+
+ Computes the quantile (inverse of the CDF) of a the student
+ cumulative distribution with mean m and standard deviation s
+ p,v must be matrices of same size, or any one can be a scalar.
+
+ see also: TPDF, TCDF, NORMPDF, NORMCDF, NORMINV
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 70
+ TINV returns inverse cumulative function of the student distribution
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+tpdf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 261
+ TPDF returns student probability density
+
+ pdf = tpdf(x,DF);
+
+ Computes the PDF of a the student distribution
+ with DF degreas of freedom
+ x,DF must be matrices of same size, or any one can be a scalar.
+
+ see also: TINV, TCDF, NORMPDF, NORMCDF, NORMINV
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 43
+ TPDF returns student probability density
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 16
+train_lda_sparse
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1689
+ Linear Discriminant Analysis for the Small Sample Size Problem as described in
+ Algorithm 1 of J. Duintjer Tebbens, P. Schlesinger: 'Improving
+ Implementation of Linear Discriminant Analysis for the High Dimension/Small Sample Size
+ Problem', Computational Statistics and Data Analysis, vol. 52, no. 1, pp. 423-437, 2007.
+ Input:
+ X ...... (sparse) training data matrix
+ G ...... group coding matrix of the training data
+ test ...... (sparse) test data matrix
+ Gtest ...... group coding matrix of the test data
+ par ...... if par = 0 then classification exploits sparsity too
+ tol ...... tolerance to distinguish zero eigenvalues
+ Output:
+ err ...... Wrong classification rate (in %)
+ trafo ...... LDA transformation vectors
+
+ Reference(s):
+ J. Duintjer Tebbens, P. Schlesinger: 'Improving
+ Implementation of Linear Discriminant Analysis for the High Dimension/Small Sample Size
+ Problem', Computational Statistics and Data Analysis, vol. 52, no. 1,
+ pp. 423-437, 2007.
+
+ Copyright (C) by J. Duintjer Tebbens, Institute of Computer Science of the Academy of Sciences of the Czech Republic,
+ Pod Vodarenskou vezi 2, 182 07 Praha 8 Liben, 18.July.2006.
+ This work was supported by the Program Information Society under project
+ 1ET400300415.
+
+
+ Modified for the use with Matlab6.5 by A. Schloegl, 22.Aug.2006
+
+ $Id$
+ This function is part of the NaN-toolbox
+ http://pub.ist.ac.at/~schloegl/matlab/NaN/
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ Linear Discriminant Analysis for the Small Sample Size Problem as described in
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+train_sc
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7655
+ Train a (statistical) classifier
+
+ CC = train_sc(D,classlabel)
+ CC = train_sc(D,classlabel,MODE)
+ CC = train_sc(D,classlabel,MODE, W)
+ weighting D(k,:) with weight W(k) (not all classifiers supported weighting)
+
+ CC contains the model parameters of a classifier which can be applied
+ to test data using test_sc.
+ R = test_sc(CC,D,...)
+
+ D training samples (each row is a sample, each column is a feature)
+ classlabel labels of each sample, must have the same number of rows as D.
+ Two different encodings are supported:
+ {-1,1}-encoding (multiple classes with separate columns for each class) or
+ 1..M encoding.
+ So [1;2;3;1;4] is equivalent to
+ [+1,-1,-1,-1;
+ [-1,+1,-1,-1;
+ [-1,-1,+1,-1;
+ [+1,-1,-1,-1]
+ [-1,-1,-1,+1]
+ Note, samples with classlabel=0 are ignored.
+
+ The following classifier types are supported MODE.TYPE
+ 'MDA' mahalanobis distance based classifier [1]
+ 'MD2' mahalanobis distance based classifier [1]
+ 'MD3' mahalanobis distance based classifier [1]
+ 'GRB' Gaussian radial basis function [1]
+ 'QDA' quadratic discriminant analysis [1]
+ 'LD2' linear discriminant analysis (see LDBC2) [1]
+ MODE.hyperparameter.gamma: regularization parameter [default 0]
+ 'LD3', 'FDA', 'LDA', 'FLDA'
+ linear discriminant analysis (see LDBC3) [1]
+ MODE.hyperparameter.gamma: regularization parameter [default 0]
+ 'LD4' linear discriminant analysis (see LDBC4) [1]
+ MODE.hyperparameter.gamma: regularization parameter [default 0]
+ 'LD5' another LDA (motivated by CSP)
+ MODE.hyperparameter.gamma: regularization parameter [default 0]
+ 'RDA' regularized discriminant analysis [7]
+ MODE.hyperparameter.gamma: regularization parameter
+ MODE.hyperparameter.lambda =
+ gamma = 0, lambda = 0 : MDA
+ gamma = 0, lambda = 1 : LDA [default]
+ Hint: hyperparameter are used only in test_sc.m, testing different
+ the hyperparameters do not need repetitive calls to train_sc,
+ it is sufficient to modify CC.hyperparameter before calling test_sc.
+ 'GDBC' general distance based classifier [1]
+ '' statistical classifier, requires Mode argument in TEST_SC
+ '###/DELETION' if the data contains missing values (encoded as NaNs),
+ a row-wise or column-wise deletion (depending on which method
+ removes less data values) is applied;
+ '###/GSVD' GSVD and statistical classifier [2,3],
+ '###/sparse' sparse [5]
+ '###' must be 'LDA' or any other classifier
+ 'PLS' (linear) partial least squares regression
+ 'REG' regression analysis;
+ 'WienerHopf' Wiener-Hopf equation
+ 'NBC' Naive Bayesian Classifier [6]
+ 'aNBC' Augmented Naive Bayesian Classifier [6]
+ 'NBPW' Naive Bayesian Parzen Window [9]
+
+ 'PLA' Perceptron Learning Algorithm [11]
+ MODE.hyperparameter.alpha = alpha [default: 1]
+ w = w + alpha * e'*x
+ 'LMS', 'AdaLine' Least mean squares, adaptive line element, Widrow-Hoff, delta rule
+ MODE.hyperparameter.alpha = alpha [default: 1]
+ 'Winnow2' Winnow2 algorithm [12]
+
+ 'PSVM' Proximal SVM [8]
+ MODE.hyperparameter.nu (default: 1.0)
+ 'LPM' Linear Programming Machine
+ uses and requires train_LPM of the iLog CPLEX optimizer
+ MODE.hyperparameter.c_value =
+ 'CSP' CommonSpatialPattern is very experimental and just a hack
+ uses a smoothing window of 50 samples.
+ 'SVM','SVM1r' support vector machines, one-vs-rest
+ MODE.hyperparameter.c_value =
+ 'SVM11' support vector machines, one-vs-one + voting
+ MODE.hyperparameter.c_value =
+ 'RBF' Support Vector Machines with RBF Kernel
+ MODE.hyperparameter.c_value =
+ MODE.hyperparameter.gamma =
+ 'SVM:LIB' libSVM [default SVM algorithm)
+ 'SVM:bioinfo' uses and requires svmtrain from the bioinfo toolbox
+ 'SVM:OSU' uses and requires mexSVMTrain from the OSU-SVM toolbox
+ 'SVM:LOO' uses and requires svcm_train from the LOO-SVM toolbox
+ 'SVM:Gunn' uses and requires svc-functios from the Gunn-SVM toolbox
+ 'SVM:KM' uses and requires svmclass-function from the KM-SVM toolbox
+ 'SVM:LINz' LibLinear [10] (requires train.mex from LibLinear somewhere in the path)
+ z=0 (default) LibLinear with -- L2-regularized logistic regression
+ z=1 LibLinear with -- L2-loss support vector machines (dual)
+ z=2 LibLinear with -- L2-loss support vector machines (primal)
+ z=3 LibLinear with -- L1-loss support vector machines (dual)
+ 'SVM:LIN4' LibLinear with -- multi-class support vector machines by Crammer and Singer
+ 'DT' decision tree - not implemented yet.
+
+ {'REG','MDA','MD2','QDA','QDA2','LD2','LD3','LD4','LD5','LD6','NBC','aNBC','WienerHopf','LDA/GSVD','MDA/GSVD', 'LDA/sparse','MDA/sparse', 'PLA', 'LMS','LDA/DELETION','MDA/DELETION','NBC/DELETION','RDA/DELETION','REG/DELETION','RDA','GDBC','SVM','RBF','PSVM','SVM11','SVM:LIN4','SVM:LIN0','SVM:LIN1','SVM:LIN2','SVM:LIN3','WINNOW', 'DT'};
+
+ CC contains the model parameters of a classifier. Some time ago,
+ CC was a statistical classifier containing the mean
+ and the covariance of the data of each class (encoded in the
+ so-called "extended covariance matrices". Nowadays, also other
+ classifiers are supported.
+
+ see also: TEST_SC, COVM, ROW_COL_DELETION
+
+ References:
+ [1] R. Duda, P. Hart, and D. Stork, Pattern Classification, second ed.
+ John Wiley & Sons, 2001.
+ [2] Peg Howland and Haesun Park,
+ Generalizing Discriminant Analysis Using the Generalized Singular Value Decomposition
+ IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(8), 2004.
+ dx.doi.org/10.1109/TPAMI.2004.46
+ [3] http://www-static.cc.gatech.edu/~kihwan23/face_recog_gsvd.htm
+ [4] Jieping Ye, Ravi Janardan, Cheong Hee Park, Haesun Park
+ A new optimization criterion for generalized discriminant analysis on undersampled problems.
+ The Third IEEE International Conference on Data Mining, Melbourne, Florida, USA
+ November 19 - 22, 2003
+ [5] J.D. Tebbens and P. Schlesinger (2006),
+ Improving Implementation of Linear Discriminant Analysis for the Small Sample Size Problem
+ Computational Statistics & Data Analysis, vol 52(1): 423-437, 2007
+ http://www.cs.cas.cz/mweb/download/publi/JdtSchl2006.pdf
+ [6] H. Zhang, The optimality of Naive Bayes,
+ http://www.cs.unb.ca/profs/hzhang/publications/FLAIRS04ZhangH.pdf
+ [7] J.H. Friedman. Regularized discriminant analysis.
+ Journal of the American Statistical Association, 84:165–175, 1989.
+ [8] G. Fung and O.L. Mangasarian, Proximal Support Vector Machine Classifiers, KDD 2001.
+ Eds. F. Provost and R. Srikant, Proc. KDD-2001: Knowledge Discovery and Data Mining, August 26-29, 2001, San Francisco, CA.
+ p. 77-86.
+ [9] Kai Keng Ang, Zhang Yang Chin, Haihong Zhang, Cuntai Guan.
+ Filter Bank Common Spatial Pattern (FBCSP) in Brain-Computer Interface.
+ IEEE International Joint Conference on Neural Networks, 2008. IJCNN 2008. (IEEE World Congress on Computational Intelligence).
+ 1-8 June 2008 Page(s):2390 - 2397
+ [10] R.-E. Fan, K.-W. Chang, C.-J. Hsieh, X.-R. Wang, and C.-J. Lin.
+ LIBLINEAR: A Library for Large Linear Classification, Journal of Machine Learning Research 9(2008), 1871-1874.
+ Software available at http://www.csie.ntu.edu.tw/~cjlin/liblinear
+ [11] http://en.wikipedia.org/wiki/Perceptron#Learning_algorithm
+ [12] Littlestone, N. (1988)
+ "Learning Quickly When Irrelevant Attributes Abound: A New Linear-threshold Algorithm"
+ Machine Learning 285-318(2)
+ http://en.wikipedia.org/wiki/Winnow_(algorithm)
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ Train a (statistical) classifier
+
+ CC = train_sc(D,classlabel)
+ CC = train_s
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+trimean
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 266
+ TRIMEAN yields the weighted mean of the median and the quartiles
+ m = TRIMEAN(y).
+
+ The trimean is m = (Q1+2*MED+Q3)/4
+ with quartile Q1 and Q3 and median MED
+
+ N-dimensional data is supported
+
+ REFERENCES:
+ [1] http://mathworld.wolfram.com/Trimean.html
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ TRIMEAN yields the weighted mean of the median and the quartiles
+ m = TRIMEA
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 8
+trimmean
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 664
+ TRIMMEAN calculates the trimmed mean by removing the fraction of p/2 upper and
+ p/2 lower samples. Missing values (encoded as NaN) are ignored and not taken into account.
+ The same number from the upper and lower values are removed, and is compatible to various
+ spreadsheet programs including GNumeric [1], LibreOffice, OpenOffice and MS Excel.
+
+ Q = trimmean(Y,p)
+ Q = trimmean(Y,p,DIM)
+ returns the TRIMMEAN along dimension DIM of sample array Y.
+ If p is a vector, the TRIMMEAN for each p is computed.
+
+ see also: MAD, RANGE, HISTO2, HISTO3, PERCENTILE, QUANTILE
+
+ References:
+ [1] http://www.fifi.org/doc/gnumeric-doc/html/C/gnumeric-trimmean.html
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ TRIMMEAN calculates the trimmed mean by removing the fraction of p/2 upper and
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+ttest
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1474
+ TTEST (paired) t-test
+ For a sample X from a normal distribution with unknown mean and
+ variance, perform a t-test of the null hypothesis `mean (X) == M'.
+ Under the null, the test statistic T follows a Student
+ distribution with `DF = length (X) - 1' degrees of freedom.
+
+ TTEST treads NaNs as "Missing values" and ignores these.
+
+ H = ttest(x,m)
+ tests Null-hypothesis that mean of x is m.
+ H = ttest(x,y)
+ size of x and size of y must match, it is tested whether the
+ difference x-y is significantly different to m=0;
+ H = ttest(x,y,alpha)
+ H = ttest(x,y,alpha,tail)
+ H = ttest(x,y,alpha,tail,DIM)
+ [H,PVAL] = ttest(...)
+
+ H=1 indicates a rejection of the Null-hypothesis at a significance
+ level of alpha (default alpha = 0.05).
+
+ With the optional argument string TAIL, the alternative of interest
+ can be selected. If TAIL is '!=' or '<>' or 'both', the null is tested
+ against the two-sided Alternative `mean (X) ~= mean (Y)'. If TAIL
+ is '>' or 'right', the one-sided Alternative `mean (X) > mean (Y)' is used.
+ Similarly for '<' or 'left', the one-sided Alternative `mean (X) < mean
+ (Y)' is used. The default is the two-sided case.
+
+ H returns whether the Null-Hypotheses must be rejected.
+ The p-value of the test is returned in PVAL.
+
+ TTEST works on the first non-singleton dimension or on DIM.
+
+ If no output argument is given, the p-value of the test is
+ displayed.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ TTEST (paired) t-test
+ For a sample X from a normal distribution with unkno
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+ttest2
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1514
+ TTEST2 (unpaired) t-test
+ For two samples x and y from normal distributions with unknown
+ means and unknown equal variances, perform a two-sample t-test of
+ the null hypothesis of equal means. Under the null, the test
+ statistic T follows a Student distribution with DF degrees of
+ freedom.
+
+ TTEST2 treads NaNs as "Missing values" and ignores these.
+
+ H = ttest2(x,y)
+ H = ttest2([x;y],C,W)
+ H = ttest2(x,y,alpha)
+ H = ttest2(x,y,alpha,tail)
+ H = ttest2(x,y,alpha,tail,vartype)
+ H = ttest2(x,y,alpha,tail,vartype,DIM)
+ [H,PVAL] = ttest2(...)
+ [h,p,ci,stats] = ttest2(...)
+
+ H=1 indicates a rejection of the Null-hypothesis at a significance
+ level of alpha (default alpha = 0.05).
+
+ With the optional argument string TAIL, the Alternative of interest
+ can be selected. If TAIL is '!=' or '<>' or 'both', the null is tested
+ against the two-sided Alternative `mean (X) ~= mean (Y)'. If TAIL
+ is '>' or 'right', the one-sided Alternative `mean (X) > mean (Y)' is used.
+ Similarly for '<' or 'left', the one-sided Alternative `mean (X) < mean
+ (Y)' is used. The default is the two-sided case.
+
+ vartype support only 'equal' (default value); the value 'unequal' is not supported.
+
+ H returns whether the Null-Hypotheses must be rejected.
+ The p-value of the test is returned in PVAL.
+
+ TTEST2 works on the first non-singleton dimension or on DIM.
+
+ If no output argument is given, the p-value of the test is
+ displayed.
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ TTEST2 (unpaired) t-test
+ For two samples x and y from normal distributions
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 3
+var
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 772
+ VAR calculates the variance.
+
+ y = var(x [, opt[, DIM]])
+ calculates the variance in dimension DIM
+ the default DIM is the first non-single dimension
+
+ opt 0: normalizes with N-1 [default]
+ 1: normalizes with N
+ DIM dimension
+ 1: VAR of columns
+ 2: VAR of rows
+ N: VAR of N-th dimension
+ default or []: first DIMENSION, with more than 1 element
+ W weights to compute weighted variance (default: [])
+ if W=[], all weights are 1.
+ number of elements in W must match size(x,DIM)
+
+ usage:
+ var(x)
+ var(x, opt, DIM)
+ var(x, [], DIM)
+ var(x, W, DIM)
+ var(x, opt, DIM, W)
+
+ features:
+ - can deal with NaN's (missing values)
+ - weighting of data
+ - dimension argument
+ - compatible to Matlab and Octave
+
+ see also: MEANSQ, SUMSQ, SUMSKIPNAN, MEAN, RMS, STD,
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 29
+ VAR calculates the variance.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 5
+xcovf
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1059
+ XCOVF generates cross-covariance function.
+ XCOVF is the same as XCORR except
+ X and Y can contain missing values encoded with NaN.
+ NaN's are skipped, NaN do not result in a NaN output.
+ The output gives NaN only if there are insufficient input data
+
+ [C,N,LAGS] = xcovf(X,MAXLAG,SCALEOPT);
+ calculates the (auto-)correlation function of X
+ [C,N,LAGS] = xcovf(X,Y,MAXLAG,SCALEOPT);
+ calculates the crosscorrelation function between X and Y
+
+ SCALEOPT [character string] specifies the type of scaling applied
+ to the correlation vector (or matrix). is one of:
+ 'none' return the unscaled correlation, R,
+ 'biased' return the biased average, R/N,
+ 'unbiased' return the unbiassed average, R(k)/(N-|k|),
+ 'coeff' return the correlation coefficient, R/(rms(x).rms(y)),
+ where "k" is the lag, and "N" is the length of X.
+ If omitted, the default value is "none".
+ If Y is supplied but does not have the ame length as X,
+ scale must be "none".
+
+
+ see also: COVM, XCORR
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 43
+ XCOVF generates cross-covariance function.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7
+xptopen
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 723
+ XPTOPEN read of several file formats and writing of the SAS Transport Format (*.xpt)
+ Supported are ARFF, SAS-XPT and STATA files.
+ XPTOPEN is a mex-file and must be compiled before use.
+ More detailed help can be obtained by the command
+ xptopen
+ without an additional argument
+
+ X = xptopen(filename)
+ X = xptopen(filename,'r')
+ read file with filename and return variables in struct X
+
+ X = xptopen(filename,'w',X)
+ save fields of struct X in filename.
+
+ The fields of X must be column vectors of equal length.
+ Each vector is either a numeric vector or a cell array of strings.
+ The SAS-XPT format stores Date/Time as numeric value counting the number of days since 1960-01-01.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+ XPTOPEN read of several file formats and writing of the SAS Transport Format (*
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 4
+xval
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 2980
+ XVAL is used for crossvalidation
+
+ [R,CC] = xval(D,classlabel)
+ .. = xval(D,classlabel,CLASSIFIER)
+ .. = xval(D,classlabel,CLASSIFIER,type)
+ .. = xval(D,{classlabel,W},CLASSIFIER)
+ .. = xval(D,{classlabel,W,NG},CLASSIFIER)
+
+ example:
+ load_fisheriris; %builtin iris dataset
+ C = species;
+ K = 5; NG = [1:length(C)]'*K/length(C);
+ [R,CC] = xval(meas,{C,[],NG},'NBC');
+
+ Input:
+ D: data features (one feature per column, one sample per row)
+ classlabel labels of each sample, must have the same number of rows as D.
+ Two different encodings are supported:
+ {-1,1}-encoding (multiple classes with separate columns for each class) or
+ 1..M encoding.
+ So [1;2;3;1;4] is equivalent to
+ [+1,-1,-1,-1;
+ [-1,+1,-1,-1;
+ [-1,-1,+1,-1;
+ [+1,-1,-1,-1]
+ [-1,-1,-1,+1]
+ Note, samples with classlabel=0 are ignored.
+
+ CLASSIFIER can be any classifier supported by train_sc (default='LDA')
+ {'REG','MDA','MD2','QDA','QDA2','LD2','LD3','LD4','LD5','LD6','NBC','aNBC','WienerHopf', 'RDA','GDBC',
+ 'SVM','RBF','PSVM','SVM11','SVM:LIN4','SVM:LIN0','SVM:LIN1','SVM:LIN2','SVM:LIN3','WINNOW'}
+ these can be modified by ###/GSVD, ###/sparse and ###/DELETION.
+ /DELETION removes in case of NaN's either the rows or the columns (which removes less data values) with any NaN
+ /sparse and /GSVD preprocess the data an reduce it to some lower-dimensional space.
+ Hyperparameters (like alpha for PLA, gamma/lambda for RDA, c_value for SVM, etc) can be defined as
+ CLASSIFIER.hyperparameter.alpha, etc. and
+ CLASSIFIER.TYPE = 'PLA' (as listed above).
+ See train_sc for details.
+ W: weights for each sample (row) in D.
+ default: [] (i.e. all weights are 1)
+ number of elements in W must match the number of rows of D
+ NG: used to define the type of cross-valdiation
+ Leave-One-Out-Method (LOOM): NG = [1:length(classlabel)]' (default)
+ Leave-K-Out-Method: NG = ceil([1:length(classlabel)]'/K)
+ K-fold XV: NG = ceil([1:length(classlabel)]'*K/length(classlabel))
+ group-wise XV (if samples are not indepentent) can be also defined here
+ samples from the same group (dependent samples) get the same identifier
+ samples from different groups get different classifiers
+ TYPE: defines the type of cross-validation procedure if NG is not specified
+ 'LOOM' leave-one-out-method
+ k k-fold crossvalidation
+
+ OUTPUT:
+ R contains the resulting performance metric
+ CC contains the classifier
+
+ plota(R) shows the confusion matrix of the results
+
+ see also: TRAIN_SC, TEST_SC, CLASSIFY, PLOTA
+
+ References:
+ [1] R. Duda, P. Hart, and D. Stork, Pattern Classification, second ed.
+ John Wiley & Sons, 2001.
+ [2] A. Schlögl, J. Kronegg, J.E. Huggins, S. G. Mason;
+ Evaluation criteria in BCI research.
+ (Eds.) G. Dornhege, J.R. Millan, T. Hinterberger, D.J. McFarland, K.-R.Müller;
+ Towards Brain-Computer Interfacing, MIT Press, 2007, p.327-342
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 35
+ XVAL is used for crossvalidation
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 12
+zScoreMedian
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 326
+ zScoreMedian removes the median and standardizes by the 1.483*median absolute deviation
+
+ Usage: Z = zScoreMedian(X, DIM)
+ Input: X : data
+ DIM: dimension along which z-score should be calculated (1=columns, 2=rows)
+ (optional, default=first dimension with more than 1 element
+ Output: Z : z-scores
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 59
+ zScoreMedian removes the median and standardizes by the 1.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 6
+zscore
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 622
+ ZSCORE removes the mean and normalizes the data
+ to a variance of 1. Can be used for Pre-Whitening of the data, too.
+
+ [z,r,m] = zscore(x,DIM)
+ z z-score of x along dimension DIM
+ r is the inverse of the standard deviation
+ m is the mean of x
+
+ The data x can be reconstrated with
+ x = z*diag(1./r) + repmat(m,size(z)./size(m))
+ z = x*diag(r) - repmat(m.*v,size(z)./size(m))
+
+ DIM dimension
+ 1: STATS of columns
+ 2: STATS of rows
+ default or []: first DIMENSION, with more than 1 element
+
+ see also: SUMSKIPNAN, MEAN, STD, DETREND
+
+ REFERENCE(S):
+ [1] http://mathworld.wolfram.com/z-Score.html
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 70
+ ZSCORE removes the mean and normalizes the data
+ to a variance of 1.
+
+
+
+
+
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff