Hyperspectral Data Processing: Algorithm Design and Analysis

5.3 VD Determined by Data Characterization-Driven Criteria

Many criteria have been reported in the literature to estimate the number of signal sources from various perspectives. This section briefly reviews criteria that use characterization of data properties to determine VD. The first criterion, referred to as the eigenvalue distribution criterion, calculates the cumulative eigenvalues to account for the energy contributed by signals sources, which is determined by a given error threshold ε. This criterion involves finding eigenvalues of a sample data covariance/correlation matrix. A second criterion is also eigen-based component analysis that includes singular value decomposition (SVD) and PCA, both of which find a smallest singular value or eigenvalue bounded below from a given error threshold ε. A third criterion is referred to as factor analysis (FA)-based Malinowski's error theory where four measures, real error (RE), extracted error (XE), imbedded error (IE), and empirical indicator function (EIF), are used to implement the FA criterion. A fourth criterion is information theoretic criterion (ITC) that includes an information criterion (AIC) and minimum description length (MDL), both of which are developed based on the logarithm of likelihood functions. A fifth criterion is a Gershgorin radius that is developed by separating the Gershgorin disks formed by Gershgorin radii into two classes, signal class and noise class. The error threshold ε is used to determine how well ...