Multicategory Classification by Support Vector Machines

Bredensteiner, Erin J.; Bennett, Kristin P.

doi:10.1007/978-1-4615-5197-3_5

Cited by 143 publications

(145 citation statements)

References 13 publications

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“…The idea of keeping the α's constant to compute D J can be extended to the multi-class problem (Bredensteiner, 1999) other kernel methods such as KPCA (Schölkopf, 1998), non-classification problems such as regression, density estimation (see e.g. Vapnik, 1998) and clustering (Ben-Hur, 2000).…”

Section: Generalization Of Svm Rfe To the Non-linear Case And Other Kmentioning

confidence: 99%

Untitled

Guyon¹,

Weston²,

Barnhill³

et al. 2002

Machine Learning

7,437

1,327

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Abstract. DNA micro-arrays now permit scientists to screen thousands of genes simultaneously and determine whether those genes are active, hyperactive or silent in normal or cancerous tissue. Because these new micro-array devices generate bewildering amounts of raw data, new analytical methods must be developed to sort out whether cancer tissues have distinctive signatures of gene expression over normal tissues or other types of cancer tissues.In this paper, we address the problem of selection of a small subset of genes from broad patterns of gene expression data, recorded on DNA micro-arrays. Using available training examples from cancer and normal patients, we build a classifier suitable for genetic diagnosis, as well as drug discovery. Previous attempts to address this problem select genes with correlation techniques. We propose a new method of gene selection utilizing Support Vector Machine methods based on Recursive Feature Elimination (RFE). We demonstrate experimentally that the genes selected by our techniques yield better classification performance and are biologically relevant to cancer.In contrast with the baseline method, our method eliminates gene redundancy automatically and yields better and more compact gene subsets. In patients with leukemia our method discovered 2 genes that yield zero leaveone-out error, while 64 genes are necessary for the baseline method to get the best result (one leave-one-out error). In the colon cancer database, using only 4 genes our method is 98% accurate, while the baseline method is only 86% accurate.

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Section: Generalization Of Svm Rfe To the Non-linear Case And Other Kmentioning

confidence: 99%

Untitled

Guyon¹,

Weston²,

Barnhill³

et al. 2002

Machine Learning

7,437

1,327

View full text Add to dashboard Cite

show abstract

“…In contrast, other one-from-the-rest and SVM k-class classifiers (Bottou et al, 1994;Bennett & Mangasarian, 1993;Bredensteiner & Bennett, 1999) require the solution of either a large single or k smaller quadratic or linear programs that need specialized optimization codes such as CPLEX (1992). On the other hand, obtaining a linear or nonlinear PSVM classifier as we propose here, requires nothing more sophisticated than solving k systems of linear equations.…”

Section: Introductionmentioning

confidence: 99%

Multicategory Proximal Support Vector Machine Classifiers

2005

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Abstract. Given a dataset, each element of which labeled by one of k labels, we construct by a very fast algorithm, a k-category proximal support vector machine (PSVM) classifier. Proximal support vector machines and related approaches (Fung & Mangasarian, 2001; can be interpreted as ridge regression applied to classification problems (Evgeniou, Pontil, & Poggio, 2000). Extensive computational results have shown the effectiveness of PSVM for two-class classification problems where the separating plane is constructed in time that can be as little as two orders of magnitude shorter than that of conventional support vector machines. When PSVM is applied to problems with more than two classes, the well known one-from-the-rest approach is a natural choice in order to take advantage of its fast performance. However, there is a drawback associated with this one-from-the-rest approach. The resulting two-class problems are often very unbalanced, leading in some cases to poor performance. We propose balancing the k classes and a novel Newton refinement modification to PSVM in order to deal with this problem. Computational results indicate that these two modifications preserve the speed of PSVM while often leading to significant test set improvement over a plain PSVM one-from-the-rest application. The modified approach is considerably faster than other one-from-the-rest methods that use conventional SVM formulations, while still giving comparable test set correctness.

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“…As was pointed out in Section 2.2, it was independently introduced by other researchers under various forms (see for instance Vapnik, 1998;Bredensteiner and Bennett, 1999). If we reformulate its learning problem as an instance of Problem 2, then the corresponding loss function WW is given by:…”

Section: Characterization Of the Four Main M-svmsmentioning

confidence: 99%

A generic model of multi-class support vector machine

Guermeur

2012

IJIIDS

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Multicategory Classification by Support Vector Machines

Cited by 143 publications

References 13 publications

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Multicategory Proximal Support Vector Machine Classifiers

A generic model of multi-class support vector machine

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