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Sparse approximation

About: Sparse approximation is a research topic. Over the lifetime, 18037 publications have been published within this topic receiving 497739 citations. The topic is also known as: Sparse approximation.


Papers
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Journal ArticleDOI
TL;DR: Two fast sparse approximation schemes for least squares support vector machine (LS-SVM) are presented to overcome the limitation of LS-S VM that it is not applicable to large data sets and to improve test speed.
Abstract: In this paper, we present two fast sparse approximation schemes for least squares support vector machine (LS-SVM), named FSALS-SVM and PFSALS-SVM, to overcome the limitation of LS-SVM that it is not applicable to large data sets and to improve test speed. FSALS-SVM iteratively builds the decision function by adding one basis function from a kernel-based dictionary at one time. The process is terminated by using a flexible and stable epsilon insensitive stopping criterion. A probabilistic speedup scheme is employed to further improve the speed of FSALS-SVM and the resulting classifier is named PFSALS-SVM. Our algorithms are of two compelling features: low complexity and sparse solution. Experiments on benchmark data sets show that our algorithms obtain sparse classifiers at a rather low cost without sacrificing the generalization performance

184 citations

Journal ArticleDOI
TL;DR: An unconstrained version of the $\ell_q$ minimization for the sparse solution of underdetermined linear systems for 0
Abstract: We study an unconstrained version of the $\ell_q$ minimization for the sparse solution of underdetermined linear systems for $0

184 citations

Book ChapterDOI
TL;DR: An overview of these sparse methods for DOA estimation is provided, with a particular highlight on the recently developed gridless sparse methods, e.g., those based on covariance fitting and the atomic norm.
Abstract: Direction-of-arrival (DOA) estimation refers to the process of retrieving the direction information of several electromagnetic waves/sources from the outputs of a number of receiving antennas that form a sensor array. DOA estimation is a major problem in array signal processing and has wide applications in radar, sonar, wireless communications, etc. With the development of sparse representation and compressed sensing, the last decade has witnessed a tremendous advance in this research topic. The purpose of this article is to provide an overview of these sparse methods for DOA estimation, with a particular highlight on the recently developed gridless sparse methods, e.g., those based on covariance fitting and the atomic norm. Several future research directions are also discussed.

184 citations

Journal ArticleDOI
TL;DR: In order to optimize the accuracy of the nearest-neighbor classification rule, a weighted distance is proposed, along with algorithms to automatically learn the corresponding weights, which are specific for each class and feature.
Abstract: In order to optimize the accuracy of the nearest-neighbor classification rule, a weighted distance is proposed, along with algorithms to automatically learn the corresponding weights. These weights may be specific for each class and feature, for each individual prototype, or for both. The learning algorithms are derived by (approximately) minimizing the leaving-one-out classification error of the given training set. The proposed approach is assessed through a series of experiments with UCI/STATLOG corpora, as well as with a more specific task of text classification which entails very sparse data representation and huge dimensionality. In all these experiments, the proposed approach shows a uniformly good behavior, with results comparable to or better than state-of-the-art results published with the same data so far

183 citations

Journal ArticleDOI
TL;DR: This paper presents a novel human activity recognition framework based on recently developed compressed sensing and sparse representation theory using wearable inertial sensors that achieves a maximum recognition rate of 96.1%, which beats conventional methods based on nearest neighbor, naive Bayes, and support vector machine by as much as 6.7%.
Abstract: Human daily activity recognition using mobile personal sensing technology plays a central role in the field of pervasive healthcare. One major challenge lies in the inherent complexity of human body movements and the variety of styles when people perform a certain activity. To tackle this problem, in this paper, we present a novel human activity recognition framework based on recently developed compressed sensing and sparse representation theory using wearable inertial sensors. Our approach represents human activity signals as a sparse linear combination of activity signals from all activity classes in the training set. The class membership of the activity signal is determined by solving a l1 minimization problem. We experimentally validate the effectiveness of our sparse representation-based approach by recognizing nine most common human daily activities performed by 14 subjects. Our approach achieves a maximum recognition rate of 96.1%, which beats conventional methods based on nearest neighbor, naive Bayes, and support vector machine by as much as 6.7%. Furthermore, we demonstrate that by using random projection, the task of looking for “optimal features” to achieve the best activity recognition performance is less important within our framework.

183 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023193
2022454
2021641
2020924
20191,208
20181,371