Separability-based multiscale basis selection and feature extraction for signal and image classification

Algorithms for multiscale basis selection and feature extraction for pattern classification problems are presented. The basis selection algorithm is based on class separability measures rather than energy or entropy. At each level the "accumulated" tree-structured class separabilities obtained from the tree which includes a parent node and the one which includes its children are compared. The decomposition of the node (or subband) is performed (creating the children), if it provides larger combined separability. The suggested feature extraction algorithm focuses on dimensionality reduction of a multiscale feature space subject to maximum preservation of information useful for classification. At each level of decomposition, an optimal linear transform that preserves class separabilities and results in a reduced dimensional feature space is obtained. Classification and feature extraction is then performed at each scale and resulting "soft decisions" obtained for each area are integrated across scales. The suggested algorithms have been tested for classification and segmentation of one-dimensional (1-D) radar signals and two-dimensional (2-D) texture and document images. The same idea can be used for other tree structured local basis, e.g., local trigonometric basis functions, and even for nonorthogonal, redundant and composite basis dictionaries.