  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.
