Kernel least absolute shrinkage and selection operator regression classifier for pattern classification

The feature vectors in feature space are more likely to be linearly separable than the observations in input space. To enhance the separability of the feature vectors, the authors perform least absolute shrinkage and selection operator (LASSO) regression in the reproducing kernel Hilbert space and develop a kernel LASSO regression classifier (LASSO-KRC). Based on the theory of calculus, least squares optimisation with L1-norm regularised constraints can be reformulated into another equivalent form. Without an explicit mapping function, the solution to the optimisation problem can be obtained by solving a convex optimisation problem with any symmetric kernel function. LASSO-KRC is applied to pattern classification and appears to outperform nearest neighbour classifier, minimum distance classifier, sparse representation classifier and linear regression classifier.