Feature Clustering in Direct Eigen-Vector Data Reduction Using Support Vector Machines

Principal Component Analysis (PCA) has been used in a variety of applications like feature extraction for classification, data compression and dimensionality reduction. Often, a small set of principal components are sufficient to capture the largest variations in the data. As a result, the eigen-values of the data covariance matrix with the lowest magnitude are ignored (along with their corresponding eigen-vectors) and the remaining eigen-vectors are used for a 'coarse' representation of the data. It is well known that this process of choosing a few principal components naturally induces a loss in information from a signal reconstruction standpoint. We propose a new technique to represent the data in terms of a new set of basis vectors where the high-frequency detail is preserved, at the expense of a 'feature-scale blurring'. In other words, the 'blurring' that occurs due to possible co-linearities in the bases vectors is relative to the eigen-features' scales; this is inherently different from a systematic blurring function. Instead of thresholding the eigen-values, we retain all eigen-values, and apply thresholds on the components of each eigen-vector separately. The resulting basis vectors can no longer be interpreted as eigen-vectors and will, in general, lose their orthogonality properties, but offer benefits in terms of preserving detail that is crucial for classification tasks. We test the merits of this new basis representation for magnitude synthetic aperture radar (SAR) Automatic Target Recognition (ATR). A feature vector is obtained by projecting a SAR image onto the aforementioned basis. Decision engines such as support vector machines (SVMs) are trained on example feature vectors per class and ultimately used to recognize the target class in real-time. Experimental validation are performed on the MSTAR database and involve comparisons against a PCA based ATR algorithm.