supervised Dictionary Learning

This paper proposes a novel discriminative formulation for sparse representation of images using learned dictionaries.

Introduction

Sparse models were originated from two different communities under two different names, one by neurologists mainly by the salient work done by Olshausen in [Olshausen1996] as sparse coding, and second by researchers in the field of signal processing as independent component analysis (ICA) (for example see [ICABook] for a comprehensive overview of ICA). Although SC and ICA originated from two different problems (the former as the model of simple cells in visual cortex and the latter as the solution to decompose the independent sources of some mixed signals), they merged, eventually, into similar technique (with somewhat different description).
On the other hand, representation of a signal using a learned dictionary instead of predefined operators (such as wavelets in signal and image processing or local binary patterns (LBP) in texture classification) has led to state-of-the-art results in various applications such as denoising [2 of the paper] and texture classification [VZ2009].
It is well known that sparsity captures higher order statistics of the data. For example, in comparing PCA and ICA, while PCA can only capture up to the second order statistics of the data and hence is appropriate for Gaussian models, ICA can capture higher order statistics of the data. Whitening data is a preprocessing step in ICA and. ICA is hence appropriate for supergaussian models (such as data with Laplacian distributions) [ICABook].
The previous work in the literature on sparse representation is done on either predefined (fixed) operators or learned dictionaries for reconstructive, discriminative, or generative models in various applications such as signal and face recognition [3, 4, 5, 6, and 7].
In this paper, the authors extend these approaches by proposing a framework for learning simultaneously a single shared dictionary as well as sparse models (for all classes) in a mixed generative and discriminative formulation. Although, this joint generative/discriminative framework have been also reported in probabilistic approaches and in neural networks, but not in sparse dictionary learning.