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

Supporting the reconciliation of models of object behaviour

This paper presents Reconciliation+, a method which identifies overlaps between models of software systems behaviour expressed as UML object interaction diagrams (i.e., sequence and/or collaboration diagrams), checks whether the overlapping elements of these models satisfy specific consistency rules and, in cases where they violate these rules, guides software designers in handling the detected inconsistencies. The method detects overlaps between object interaction diagrams by using a probabilistic message matching algorithm that has been developed for this purpose. The guidance to software designers on when to check for inconsistencies and how to deal with them is delivered by enacting a built-in process model that specifies the consistency rules that can be checked against overlapping models and different ways of handling violations of these rules. Reconciliation+ is supported by a toolkit. It has also been evaluated in a case study. This case study has produced positive results which are discussed in the paper

Discriminative variable selection for clustering with the sparse Fisher-EM algorithm

The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results. Existing approaches have demonstrated the efficiency of variable selection for clustering but turn out to be either very time consuming or not sparse enough in high-dimensional spaces. This work proposes to perform a selection of the discriminative variables by introducing sparsity in the loading matrix of the Fisher-EM algorithm. This clustering method has been recently proposed for the simultaneous visualization and clustering of high-dimensional data. It is based on a latent mixture model which fits the data into a low-dimensional discriminative subspace. Three different approaches are proposed in this work to introduce sparsity in the orientation matrix of the discriminative subspace through $\ell_{1}$-type penalizations. Experimental comparisons with existing approaches on simulated and real-world data sets demonstrate the interest of the proposed methodology. An application to the segmentation of hyperspectral images of the planet Mars is also presented

An Effective Feature Selection Method Based on Pair-Wise Feature Proximity for High Dimensional Low Sample Size Data

Feature selection has been studied widely in the literature. However, the efficacy of the selection criteria for low sample size applications is neglected in most cases. Most of the existing feature selection criteria are based on the sample similarity. However, the distance measures become insignificant for high dimensional low sample size (HDLSS) data. Moreover, the variance of a feature with a few samples is pointless unless it represents the data distribution efficiently. Instead of looking at the samples in groups, we evaluate their efficiency based on pairwise fashion. In our investigation, we noticed that considering a pair of samples at a time and selecting the features that bring them closer or put them far away is a better choice for feature selection. Experimental results on benchmark data sets demonstrate the effectiveness of the proposed method with low sample size, which outperforms many other state-of-the-art feature selection methods.Comment: European Signal Processing Conference 201

Learning Discriminative Stein Kernel for SPD Matrices and Its Applications

Stein kernel has recently shown promising performance on classifying images represented by symmetric positive definite (SPD) matrices. It evaluates the similarity between two SPD matrices through their eigenvalues. In this paper, we argue that directly using the original eigenvalues may be problematic because: i) Eigenvalue estimation becomes biased when the number of samples is inadequate, which may lead to unreliable kernel evaluation; ii) More importantly, eigenvalues only reflect the property of an individual SPD matrix. They are not necessarily optimal for computing Stein kernel when the goal is to discriminate different sets of SPD matrices. To address the two issues in one shot, we propose a discriminative Stein kernel, in which an extra parameter vector is defined to adjust the eigenvalues of the input SPD matrices. The optimal parameter values are sought by optimizing a proxy of classification performance. To show the generality of the proposed method, three different kernel learning criteria that are commonly used in the literature are employed respectively as a proxy. A comprehensive experimental study is conducted on a variety of image classification tasks to compare our proposed discriminative Stein kernel with the original Stein kernel and other commonly used methods for evaluating the similarity between SPD matrices. The experimental results demonstrate that, the discriminative Stein kernel can attain greater discrimination and better align with classification tasks by altering the eigenvalues. This makes it produce higher classification performance than the original Stein kernel and other commonly used methods.Comment: 13 page