JL-lemma derived Optimal Projections for Discriminative Dictionary Learning

To overcome difficulties in classifying large dimensionality data with a large number of classes, we propose a novel approach called JLSPCADL. This paper uses the Johnson-Lindenstrauss (JL) Lemma to select the dimensionality of a transformed space in which a discriminative dictionary can be learned for signal classification. Rather than reducing dimensionality via random projections, as is often done with JL, we use a projection transformation matrix derived from Modified Supervised PC Analysis (M-SPCA) with the JL-prescribed dimension. JLSPCADL provides a heuristic to deduce suitable distortion levels and the corresponding Suitable Description Length (SDL) of dictionary atoms to derive an optimal feature space and thus the SDL of dictionary atoms for better classification. Unlike state-of-the-art dimensionality reduction-based dictionary learning methods, a projection transformation matrix derived in a single step from M-SPCA provides maximum feature-label consistency of the transformed space while preserving the cluster structure of the original data. Despite confusing pairs, the dictionary for the transformed space generates discriminative sparse coefficients, with fewer training samples. Experimentation demonstrates that JLSPCADL scales well with an increasing number of classes and dimensionality. Improved label consistency of features due to M-SPCA helps to classify better. Further, the complexity of training a discriminative dictionary is significantly reduced by using SDL. Experimentation on OCR and face recognition datasets shows relatively better classification performance than other supervised dictionary learning algorithms.