Virtual dimensionality (VD) has been widely used to estimate number of endmembers in the past. Unfortunately, the original idea of VD was developed to specify the number of spectrally distinct signatures in hyperspectral data where there is no provided specific definition of what “spectrally distinct signatures” are. As a result, many techniques developed to estimate VD have produced various values for VD. This paper addresses this issue by develops a target specified VD (TSVD) theory where the value of VD is completely determined by targets of interest. In particular, the VD techniques can be categorized according to targets characterized by eigenvalues/eigenvectors and real target signal sources which are used for a binary composite hypothesis testing problem. For the latter case the Automatic Target Generation Process (ATGP) is particularly used to generate real target signal sources to replace eigenvalues/eigenvectors as signal sources to be used for the binary hypothesis testing problem. In order to find probability distributions under each hypothesis the extreme theory used by Maximum Orthogonal Complement Algorithm (MOCA) is used for their derivations. As a result, VD can be estimated by two types of signals sources, eigenvalues/eigenvectors along with two types of detectors, maximum likelihood detector and Neyman-Pearson detector.
Virtual dimensionality (VD) has received considerable interest in its use of specifying the number of spectrally distinct signatures, denoted by <i>p</i>. So far all techniques are eigen-based approaches which use eigenvalues or eigenvectors to estimate the value of <i>p</i>. However, when eigenvalues are used to estimate VD such as Harsanyi-Farrand-Chang’s method or hyperspectral signal subspace identification by minimum error (HySime), there will be no way to find what the spectrally distinct signatures are. On the other hand, if eigenvectors/singular vectors are used to estimate VD such as maximal orthogonal complement algorithm (MOCA), eigenvectors/singular vectors do not represent real signal sources. Most importantly, current available methods used to estimate VD run into two major issues. One is the value of VD being fixed at a constant. The other is a lack of providing a means of finding signal sources of interest. As a matter of fact, the spectrally distinct signatures defined by VD should adapt its value to various target signal sources of interest. For example, the number of endmembers should be different from the number of anomalies. In this paper we develop a second-order statistics approach to determining the value of the VD and the virtual endmember basis.
Anomaly detection finds data samples whose signatures are spectrally distinct from their surrounding data samples. Unfortunately, it cannot discriminate the anomalies it detected one from another. In order to accomplish this task it requires a way of measuring spectral similarity such as spectral angle mapper (SAM) or spectral information divergence (SID) to determine if a detected anomaly is different from another. However, this arises in a challenging issue of how to find an appropriate thresholding value for this purpose. Interestingly, this issue has not received much attention in the past. This paper investigates the issue of anomaly discrimination which can differentiate detected anomalies without using any spectral measure. The ideas are to makes use unsupervised target detection algorithms, Automatic Target Generation Process (ATGP) coupled with an anomaly detector to distinguish detected anomalies. Experimental results show that the proposed methods are indeed very effective in anomaly discrimination.
Virtual dimensionality (VD) has received considerable interest where VD is used to estimate the number of spectral distinct signatures, denoted by p. Unfortunately, no specific definition is provided by VD for what a spectrally distinct signature is. As a result, various types of spectral distinct signatures determine different values of VD. There is no one value-fit-all for VD. In order to address this issue this paper presents a new concept, referred to as anomaly-specified VD (AS-VD) which determines the number of anomalies of interest present in the data. Specifically, two types of anomaly detection algorithms are of particular interest, sample covariance matrix K-based anomaly detector developed by Reed and Yu, referred to as K-RXD and sample correlation matrix R-based RXD, referred to as R-RXD. Since K-RXD is only determined by 2<sup>nd</sup> order statistics compared to R-RXD which is specified by statistics of the first two orders including sample mean as the first order statistics, the values determined by K-RXD and R-RXD will be different. Experiments are conducted in comparison with widely used eigen-based approaches.
Virtual dimensionality (VD) has received considerable interest in its use of specifying the number of spectrally distinct signatures. So far all techniques are decomposition approaches which use eigenvalues, eigenvectors or singular vectors to estimate the virtual dimensionality. However, when eigenvalues are used to estimate VD such as Harsanyi-Farrand- Chang’s method or hyperspectral signal subspace identification by minimum error (HySime), there will be no way to find what the spectrally distinct signatures are. On the other hand, if eigenvectors/singular vectors are used to estimate VD such as maximal orthogonal complement algorithm (MOCA), eigenvectors/singular vectors do not represent real signal sources. In this paper we introduce a new concept, referred to as target-specified VD (TSVD), which operates on the signal sources themselves to both determine the number of distinct sources and identify their signature. The underlying idea of TSVD was derived from that used to develop high-order statistics (HOS) VD where its applicability to second order statistics (2OS) was not explored. In this paper we investigate a 2OS-based target finding algorithm, called automatic target generation process (ATGP) to determine VD. Experiments are conducted in comparison with well-known and widely used eigen-based approaches.