Topic
Relevance vector machine
About: Relevance vector machine is a research topic. Over the lifetime, 5343 publications have been published within this topic receiving 290471 citations.
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TL;DR: This work shows that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples, and an exponential speedup is obtained.
Abstract: Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases where classical sampling algorithms require polynomial time, an exponential speedup is obtained. At the core of this quantum big data algorithm is a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.
1,078 citations
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24 Jul 1998
TL;DR: Numerical tests on 6 public data sets show that classi ers trained by the concave minimization approach and those trained by a support vector machine have comparable 10fold cross-validation correctness.
Abstract: Computational comparison is made between two feature selection approaches for nding a separating plane that discriminates between two point sets in an n-dimensional feature space that utilizes as few of the n features (dimensions) as possible. In the concave minimization approach [19, 5] a separating plane is generated by minimizing a weighted sum of distances of misclassi ed points to two parallel planes that bound the sets and which determine the separating plane midway between them. Furthermore, the number of dimensions of the space used to determine the plane is minimized. In the support vector machine approach [27, 7, 1, 10, 24, 28], in addition to minimizing the weighted sum of distances of misclassi ed points to the bounding planes, we also maximize the distance between the two bounding planes that generate the separating plane. Computational results show that feature suppression is an indirect consequence of the support vector machine approach when an appropriate norm is used. Numerical tests on 6 public data sets show that classi ers trained by the concave minimization approach and those trained by a support vector machine have comparable 10fold cross-validation correctness. However, in all data sets tested, the classi ers obtained by the concave minimization approach selected fewer problem features than those trained by a support vector machine.
1,074 citations
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27 Dec 2005TL;DR: It is shown that existing SVM software can be used to solve the SVM/LDA formulation and empirical comparisons of the proposed algorithm with SVM and LDA using both synthetic and real world benchmark data are presented.
Abstract: This paper describes a new large margin classifier, named SVM/LDA. This classifier can be viewed as an extension of support vector machine (SVM) by incorporating some global information about the data. The SVM/LDA classifier can be also seen as a generalization of linear discriminant analysis (LDA) by incorporating the idea of (local) margin maximization into standard LDA formulation. We show that existing SVM software can be used to solve the SVM/LDA formulation. We also present empirical comparisons of the proposed algorithm with SVM and LDA using both synthetic and real world benchmark data.
1,030 citations
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26 Oct 1999TL;DR: This book presents architectures for multiclass classification and function approximation problems, as well as evaluation criteria for classifiers and regressors, and discusses kernel methods for improving the generalization ability of neural networks and fuzzy systems.
Abstract: A guide on the use of SVMs in pattern classification, including a rigorous performance comparison of classifiers and regressors. The book presents architectures for multiclass classification and function approximation problems, as well as evaluation criteria for classifiers and regressors. Features: Clarifies the characteristics of two-class SVMs; Discusses kernel methods for improving the generalization ability of neural networks and fuzzy systems; Contains ample illustrations and examples; Includes performance evaluation using publicly available data sets; Examines Mahalanobis kernels, empirical feature space, and the effect of model selection by cross-validation; Covers sparse SVMs, learning using privileged information, semi-supervised learning, multiple classifier systems, and multiple kernel learning; Explores incremental training based batch training and active-set training methods, and decomposition techniques for linear programming SVMs; Discusses variable selection for support vector regressors.
1,002 citations