Hyperspectral Data Processing: Algorithm Design and Analysis

5.4 VD Determined by Data Representation-Driven Criteria

In Section 5.3, VD is determined by data characterization where all the developed criteria provide no specific algorithms to find signal sources. Accordingly, VD remains the same if different applications are considered. Although some criteria can use a parameter such as error threshold ε or false alarm probability P_F to fine-tune VD, this practice still has its limitations in real applications. For example, the number of endmembers in endmember extraction is certainly different from the number of anomalies in anomaly detection. It seems that a constraint in using data characterization to determine VD is the lack of algorithms to find signal sources that generally vary with applications. In order to resolve this dilemma, one feasible approach is to use data representation to determine VD where the basic elements to construct the entire data are those signal sources that determine VD. In this case, VD is tied together with an algorithm to find these basic signal sources. The most commonly used data representation is a linear regression model in multivariate data analysis where data samples are modeled as linear combinations of a finite set of basic elements. For example, a real number can be expressed by a binary representation where the basic elements are integer powers of 2. A one-dimensional signal can also be represented by a set of sinusoidal functions known as Fourier transform/series or by a wavelet representation in ...