Categories &

Functions List

Function Reference: robustcov

statistics: sig = robustcov (X)
statistics: [sig, mu] = robustcov (X)
statistics: [sig, mu, mah] = robustcov (X)
statistics: [sig, mu, mah, outliers] = robustcov (X)
statistics: [sig, mu, mah, outliers, s] = robustcov (X)
statistics: […] = robustcov (…, name, value)

Robust multivariate covariance and mean estimate.

sig = robustcov (X) returns a robust estimate sig of the covariance matrix of the N×P data matrix X, computed so that it is not distorted by outlying observations. Rows of X are observations and columns are variables. Rows containing NaN values are removed.

[sig, mu, mah, outliers, s] = robustcov (…) also returns the robust mean mu (1×P), the robust Mahalanobis distances mah (N×1) of each observation from the estimated distribution, a logical vector outliers (N×1) flagging observations whose distance exceeds sqrt (chi2inv (0.975, P)), and a structure s holding the estimate metadata.

Additional parameters can be specified by Name-Value pair arguments.

NameValue
'Method'the estimator, either 'fmcd' (default, the Fast Minimum Covariance Determinant algorithm) or 'ogk' (the Orthogonalized Gnanadesikan-Kettenring estimator). 'olivehawkins' is not implemented.
'OutlierFraction'the maximum fraction of outliers, a scalar in [0, 0.5] (default 0.5), used to set the size of the elemental subsets in 'fmcd'.
'NumTrials'the number of random elemental subsets drawn by 'fmcd', a positive integer (default 500).
'BiasCorrection'a logical scalar (default true) that applies the small-sample bias correction to the 'fmcd' estimate.
'NumOGKIterations'the number of orthogonalization iterations for 'ogk', a positive integer (default 2).
'UnivariateEstimator'the robust univariate location/scale estimator used by 'ogk', either 'tauscale' (default) or 'qn'.

Source Code: robustcov

Note on reproducibility. 'fmcd' draws random subsets, so its exact estimate depends on the random number generator and is not identical to MATLAB’s on data where the optimal subset is ambiguous; on well-separated data both converge to the same estimate. For 'fmcd' with 'BiasCorrection' enabled, the small-sample factor uses the published Pison-Van Aelst-Willems asymptotic formula, which differs from MATLAB’s tabulated simulation values by up to about 1.6% for very small samples.

See also: mahal, cov, mad, dbscan

Source Code: robustcov

Robust covariance is unaffected by a cluster of outliers.

 X = [randn(80,2); 8 + randn(10,2)];
 [sig, mu, mah, outliers] = robustcov (X);
plotted figure 

 gscatter (X(:,1), X(:,2), outliers);
error: Invalid call to legend.  Correct usage is:

 -- legend ()
 -- legend COMMAND
 -- legend (STR1, STR2, ...)
 -- legend (CHARMAT)
 -- legend ({CELLSTR})
 -- legend (..., PROPERTY, VALUE, ...)
 -- legend (HOBJS, ...)
 -- legend ("COMMAND")
 -- legend (HAX, ...)
 -- legend (HLEG, ...)
 -- HLEG = legend (...)
 title ("robustcov: inliers vs. flagged outliers");