Linear Time Feature Selection for Regularized Least-Squares

We propose a novel algorithm for greedy forward feature selection for regularized least-squares (RLS) regression and classification, also known as the least-squares support vector machine or ridge regression. The algorithm, which we call greedy RLS, starts from the empty feature set, and on each iteration adds the feature whose addition provides the best leave-one-out cross-validation performance. Our method is considerably faster than the previously proposed ones, since its time complexity is linear in the number of training examples, the number of features in the original data set, and the desired size of the set of selected features. Therefore, as a side effect we obtain a new training algorithm for learning sparse linear RLS predictors which can be used for large scale learning. This speed is possible due to matrix calculus based short-cuts for leave-one-out and feature addition. We experimentally demonstrate the scalability of our algorithm and its ability to find good quality feature sets.Comment: 17 pages, 15 figure

A Simple Iterative Algorithm for Parsimonious Binary Kernel Fisher Discrimination

By applying recent results in optimization theory variously known as optimization transfer or majorize/minimize algorithms, an algorithm for binary, kernel, Fisher discriminant analysis is introduced that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The problem is converted into a smooth optimization that can be solved iteratively with no greater overhead than iteratively re-weighted least-squares. The result is simple, easily programmed and is shown to perform, in terms of both accuracy and parsimony, as well as or better than a number of leading machine learning algorithms on two well-studied and substantial benchmarks

Analyzing sparse dictionaries for online learning with kernels

Many signal processing and machine learning methods share essentially the same linear-in-the-parameter model, with as many parameters as available samples as in kernel-based machines. Sparse approximation is essential in many disciplines, with new challenges emerging in online learning with kernels. To this end, several sparsity measures have been proposed in the literature to quantify sparse dictionaries and constructing relevant ones, the most prolific ones being the distance, the approximation, the coherence and the Babel measures. In this paper, we analyze sparse dictionaries based on these measures. By conducting an eigenvalue analysis, we show that these sparsity measures share many properties, including the linear independence condition and inducing a well-posed optimization problem. Furthermore, we prove that there exists a quasi-isometry between the parameter (i.e., dual) space and the dictionary's induced feature space.Comment: 10 page

A survey of outlier detection methodologies

Outlier detection has been used for centuries to detect and, where appropriate, remove anomalous observations from data. Outliers arise due to mechanical faults, changes in system behaviour, fraudulent behaviour, human error, instrument error or simply through natural deviations in populations. Their detection can identify system faults and fraud before they escalate with potentially catastrophic consequences. It can identify errors and remove their contaminating effect on the data set and as such to purify the data for processing. The original outlier detection methods were arbitrary but now, principled and systematic techniques are used, drawn from the full gamut of Computer Science and Statistics. In this paper, we introduce a survey of contemporary techniques for outlier detection. We identify their respective motivations and distinguish their advantages and disadvantages in a comparative review

Labeling the Features Not the Samples: Efficient Video Classification with Minimal Supervision

Feature selection is essential for effective visual recognition. We propose an efficient joint classifier learning and feature selection method that discovers sparse, compact representations of input features from a vast sea of candidates, with an almost unsupervised formulation. Our method requires only the following knowledge, which we call the \emph{feature sign}---whether or not a particular feature has on average stronger values over positive samples than over negatives. We show how this can be estimated using as few as a single labeled training sample per class. Then, using these feature signs, we extend an initial supervised learning problem into an (almost) unsupervised clustering formulation that can incorporate new data without requiring ground truth labels. Our method works both as a feature selection mechanism and as a fully competitive classifier. It has important properties, low computational cost and excellent accuracy, especially in difficult cases of very limited training data. We experiment on large-scale recognition in video and show superior speed and performance to established feature selection approaches such as AdaBoost, Lasso, greedy forward-backward selection, and powerful classifiers such as SVM.Comment: arXiv admin note: text overlap with arXiv:1411.771