An enhanced approach to the robust discriminant analysis and class sparsity based embedding

In recent times, feature extraction attracted much attention in machine learning and pattern recognition fields. This paper extends and improves a scheme for linear feature extraction that can be used in supervised multi-class classification problems. Inspired by recent frameworks for robust sparse LDA and Inter-class sparsity, we propose a unifying criterion able to retain the advantages of these two powerful linear discriminant methods. We introduce an iterative alternating minimization scheme in order to estimate the linear transformation and the orthogonal matrix. The linear transformation is efficiently updated via the steepest descent gradient technique. The proposed framework is generic in the sense that it allows the combination and tuning of other linear discriminant embedding methods. We used our proposed method to fine tune the linear solutions delivered by two recent linear methods: RSLDA and RDA_FSIS. Experiments have been conducted on public image datasets of different types including objects, faces, and digits. The proposed framework compared favorably with several competing methods.

A continuous linear optimal transport approach for pattern analysis in image datasets

We present a new approach to facilitate the application of the optimal transport metric to pattern recognition on image databases. The method is based on a linearized version of the optimal transport metric, which provides a linear embedding for the images. Hence, it enables shape and appearance modeling using linear geometric analysis techniques in the embedded space. In contrast to previous work, we use Monge's formulation of the optimal transport problem, which allows for reasonably fast computation of the linearized optimal transport embedding for large images. We demonstrate the application of the method to recover and visualize meaningful variations in a supervised-learning setting on several image datasets, including chromatin distribution in the nuclei of cells, galaxy morphologies, facial expressions, and bird species identification. We show that the new approach allows for high-resolution construction of modes of variations and discrimination and can enhance classification accuracy in a variety of image discrimination problems.