Analysis, detection and classification of signals using scalar and vector sparse matrix transforms

Leonardo R Bachega, Purdue University

Abstract

Several pattern recognition problems require accurate modeling of signals with high dimensionality, p, often from a limited number of samples, n. We present high-dimensional signal analysis techniques based on the Sparse Matrix Transform (SMT). The recently proposed SMT successfully models high-dimensional signals in various application domains when n is small, including the case with n < p. The resulting decorrelating transform is sparse, full rank, and inexpensive to apply, typically requiring only O(p) computation. Our main contribution is the vector SMT, a novel method for sparse matrix transform computation in distributed environments such as in wireless sensor networks (WSNs). We envision a scenario where each sensor generates a vector output. Together, all sensor outputs form a p-dimensional aggregated vector, x. The vector SMT algorithm then performs distributed decorrelation of x by applying pair-wise transforms to pairs of sensor outputs (i.e., subvectors of x) until x is fully decorrelated. Simulations with multi-view camera networks show that the vector SMT effectively decorrelates the multiple camera views with low total communication between sensors. Because our method enables joint processing of multiple views, we observe significant improvements to anomaly detection accuracy in artificial and real data sets compared to when the views are processed independently. Another important contribution is the graphical-SMT algorithm, a new, fast design method for sparse matrix transforms, suited for signals with underlying graphical structure such as images and networks. Finally, we develop an SMT-based, sparse framework for hypotheses testing and apply it to classification and anomaly detection using human faces and hyperspectral image data sets.

Degree

Ph.D.

Advisors

Bouman, Purdue University.

Subject Area

Electrical engineering

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