Effective Discriminative Feature Selection with Non-trivial Solutions

Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation based dimensionality reduction method Linear Discriminant Analysis (LDA) and sparsity regularization. We impose row sparsity on the transformation matrix of LDA through ${\ell}_{2,1}$-norm regularization to achieve feature selection, and the resultant formulation optimizes for selecting the most discriminative features and removing the redundant ones simultaneously. The formulation is extended to the ${\ell}_{2,p}$-norm regularized case: which is more likely to offer better sparsity when $0<p<1$. Thus the formulation is a better approximation to the feature selection problem. An efficient algorithm is developed to solve the ${\ell}_{2,p}$-norm based optimization problem and it is proved that the algorithm converges when $0<p\le 2$. Systematical experiments are conducted to understand the work of the proposed method. Promising experimental results on various types of real-world data sets demonstrate the effectiveness of our algorithm

Generalized Sparse Discriminant Analysis for Event-Related Potential Classification

A brain computer interface (BCI) is a system which provides direct communication between the mind of a person and the outside world by using only brain activity (EEG). The event-related potential (ERP)-based BCI problem consists of a binary pattern recognition. Linear discriminant analysis (LDA) is widely used to solve this type of classification problems, but it fails when the number of features is large relative to the number of observations. In this work we propose a penalized version of the sparse discriminant analysis (SDA), called generalized sparse discriminant analysis (GSDA), for binary classification. This method inherits both the discriminative feature selection and classification properties of SDA and it also improves SDA performance through the addition of Kullback-Leibler class discrepancy information. The GSDA method is designed to automatically select the optimal regularization parameters. Numerical experiments with two real ERP-EEG datasets show that, on one hand, GSDA outperforms standard SDA in the sense of classification performance, sparsity and required computing time, and, on the other hand, it also yields better overall performances, compared to well-known ERP classification algorithms, for single-trial ERP classification when insufficient training samples are available. Hence, GSDA constitute a potential useful method for reducing the calibration times in ERP-based BCI systems.Fil: Peterson, Victoria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; ArgentinaFil: Rufiner, Hugo Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; Argentina. Universidad Nacional de Entre Ríos. Facultad de Ingeniería; ArgentinaFil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentin

Spatially Aware Dictionary Learning and Coding for Fossil Pollen Identification

We propose a robust approach for performing automatic species-level recognition of fossil pollen grains in microscopy images that exploits both global shape and local texture characteristics in a patch-based matching methodology. We introduce a novel criteria for selecting meaningful and discriminative exemplar patches. We optimize this function during training using a greedy submodular function optimization framework that gives a near-optimal solution with bounded approximation error. We use these selected exemplars as a dictionary basis and propose a spatially-aware sparse coding method to match testing images for identification while maintaining global shape correspondence. To accelerate the coding process for fast matching, we introduce a relaxed form that uses spatially-aware soft-thresholding during coding. Finally, we carry out an experimental study that demonstrates the effectiveness and efficiency of our exemplar selection and classification mechanisms, achieving $86.13\%$ accuracy on a difficult fine-grained species classification task distinguishing three types of fossil spruce pollen.Comment: CVMI 201