Variable and feature selection have become the focus of much research in areas of application for which datasets with tens or hundreds of thousands of variables are available.

We present a biologically-motivated system for the recognition of actions from video sequences. The approach builds on recent work on object recognition based on hierarchical feedforward architectures [25, 16, 20] and extends a neurobiological model of motion processing in the visual cortex [10]. The system consists of a hierarchy of spatio-temporal feature detectors of increasing complexity: an input sequence is first analyzed by an array of motiondirection sensitive units which, through a hierarchy of processing stages, lead to position-invariant spatio-temporal feature detectors. We experiment with different types of motion-direction sensitive units as well as different system architectures. As in [16], we find that sparse features in intermediate stages outperform dense ones and that using a simple feature selection approach leads to an efficient system that performs better with far fewer features. We test the approach on different publicly available action datasets, in all cases achieving the highest results reported to date. 1.

Recently developed methods for learning sparse classifiers are among the state-of-the-art in supervised learning. These methods learn classifiers that incorporate weighted sums of basis functions with sparsity-promoting priors encouraging the weight estimates to be either significantly large or exactly zero. From a learning-theoretic perspective, these methods control the capacity of the learned classifier by minimizing the number of basis functions used, resulting in better generalization. This paper presents three contributions related to learning sparse classifiers. First, we introduce a true multiclass formulation based on multinomial logistic regression. Second, by combining a bound optimization approach with a component-wise update procedure, we derive fast exact algorithms for learning sparse multiclass classifiers that scale favorably in both the number of training samples and the feature dimensionality, making them applicable even to large data sets in high-dimensional feature spaces. To the best of our knowledge, these are the first algorithms to perform exact multinomial logistic regression with a sparsity-promoting prior. Third, we show how nontrivial generalization bounds can be derived for our classifier in the binary case. Experimental results on standard benchmark data sets attest to the accuracy, sparsity, and efficiency of the proposed methods.

The problem of feature selection is a difficult combinatorial task in Machine Learning and of high practical relevance, e.g. in bioinformatics. Genetic Algorithms (GAs) offer a natural way to solve this problem. In this paper we present a special Genetic Algorithm, which especially takes into account the existing bounds on the generalization error for Support Vector Machines (SVMs). This new approach is compared to the traditional method of performing crossvalidation and to other existing algorithms for feature selection.

Abstract. L1 regularization is effective for feature selection, but the resulting optimization is challenging due to the non-differentiability of the 1-norm. In this paper we compare state-of-the-art optimization techniques to solve this problem across several loss functions. Furthermore, we propose two new techniques. The first is based on a smooth (differentiable) convex approximation for the L1 regularizer that does not depend on any assumptions about the loss function used. The other technique is a new strategy that addresses the non-differentiability of the L1-regularizer by casting the problem as a constrained optimization problem that is then solved using a specialized gradient projection method. Extensive comparisons show that our newly proposed approaches consistently rank among the best in terms of convergence speed and efficiency by measuring the number of function evaluations required. 1

This paper considers the problem of selecting the most informative experiments x to get measurements y for learning a regression model y = f(x). We propose a novel and simple concept for active learning, transductive experimental design, that explores available unmeasured experiments (i.e.,unlabeled data) and has a better scalability in comparison with classic experimental design methods. Our in-depth analysis shows that the new method tends to favor experiments that are on the one side hardto-predict and on the other side representative for the rest of the experiments. Efficient optimization of the new design problem is achieved through alternating optimization and sequential greedy search. Extensive experimental results on synthetic problems and three real-world tasks, including questionnaire design for preference learning, active learning for text categorization, and spatial sensor placement, highlight the advantages of the proposed approaches. 1.

Designing a Brain Computer Interface (BCI) system one can choose from a variety of features that may be useful for classifying brain activity during a mental task. For the special case of classifying EEG signals we propose the usage of the state of the art feature selection algorithms Recursive Feature Elimination [1] and Zero-Norm Optimization [2] which are based on the training of Support Vector Machines (SVM) [3]. These algorithms can provide more accurate solutions than standard filter methods for feature selection [4]. We adapt the methods for the purpose of selecting EEG channels. For a motor imagery paradigm we show that the number of used channels can be reduced significantly without increasing the classification error. The resulting best channels agree well with the expected underlying cortical activity patterns during the mental tasks. Furthermore we show how time dependent task specific information can be visualized.

Eigenvalue problems are rampant in machine learning and statistics and appear in the context of classification, dimensionality reduction, etc. In this paper, we consider a cardinality constrained variational formulation of generalized eigenvalue problem with sparse principal component analysis (PCA) as a special case. Using ℓ1-norm approximation to the cardinality constraint, previous methods have proposed both convex and non-convex solutions to the sparse PCA problem. In contrast, we propose a tighter approximation that is related to the negative log-likelihood of a Student’s t-distribution. The problem is then framed as a d.c. (difference of convex functions) program and is solved as a sequence of locally convex programs. We show that the proposed method not only explains more variance with sparse loadings on the principal directions but also has better scalability compared to other methods. We demonstrate these results on a collection of datasets of varying dimensionality, two of which are high-dimensional gene datasets where the goal is to find few relevant genes that explain as much variance as possible. 1.

Summary. Protein function prediction, i.e. classification of protein sequences according to their biological function is an important task in bioinformatics. In this chapter we illustrate that the presence of sequence motifs – elements that are conserved across different proteins – are highly discriminative features for predicting the function of a protein. This is in agreement with the biological thinking that considers motifs to be the building blocks of protein sequences. We focus on proteins annotated as enzymes, and show that despite the fact that motif composition is a very high dimensional representation of a sequence, that most classes of enzymes can be classified using a handful of motifs, yielding accurate and interpretable classifiers. The enzyme data falls into a large number of classes; we find that the one-againstthe-rest multi-class method works better than the one-against-one method on this data. 1

We address the problem of feature selection in a kernel space to select the most discriminative and informative features for classification and data analysis. This is a difficult problem because the dimension of a kernel space may be infinite. In the past, little work has been done on feature selection in a kernel space. To solve this problem, we derive a basis set in the kernel space as a first step for feature selection. Using the basis set, we then extend the margin-based feature selection algorithms that are proven effective even when many features are dependent. The selected features form a subspace of the kernel space, in which different state-of-the-art classification algorithms can be applied for classification. We conduct extensive experiments over real and simulated data to compare our proposed method with four baseline algorithms. Both theoretical analysis and experimental results validate the effectiveness of our proposed method.