Statistical learning theory was introduced in the late 1960’s. Until the 1990’s it was a purely theoretical analysis of the problem of function estimation from a given collection of data. In the middle of the 1990’s new types of learning algorithms (called support vector machines) based

This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho’s basis pursuit (BP) paradigm can recover the optimal

by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse

signal representation offers the key to addressing this problem. Based on a sparse representation computed by ℓ 1-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature

An iterative method is given for solving Ax ~ffi b and minU Ax- b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable

the algorithms to handle more than thousands of training images. In this paper we develop an extension of the SPM method, by generalizing vector quantization to sparse coding followed by multi-scale spatial max pooling, and propose a linear SPM kernel based on SIFT sparse codes. This new approach remarkably

Sparse coding provides a class of algorithms for finding succinct representations of stimuli; given only unlabeled input data, it discovers basis functions that capture higher-level features in the data. However, finding sparse codes remains a very difficult computational problem. In this paper, we

and graphs, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, and power networks). The collection meets a vital need that artificially-generated matrices cannot meet, and is widely used by the sparse matrix algorithms community

estimation problem. A variant of the algorithm that exploits sparse conditional distributions is also described, and a wide range of other variant algorithms are also seen to be possible. 1. Introduction The Expectation-Maximization (EM) algorithm finds maximum likelihood parameter estimates in problems

In the data stream scenario, input arrives very rapidly and there is limited memory to store the input. Algorithms have to work with one or few passes over the data, space less than linear in the input size or time significantly less than the input size. In the past few years, a new theory has