Results 1 
5 of
5
Multicategory Support Vector Machines, theory, and application to the classification of microarray data and satellite radiance data
 Journal of the American Statistical Association
, 2004
"... Twocategory support vector machines (SVM) have been very popular in the machine learning community for classi � cation problems. Solving multicategory problems by a series of binary classi � ers is quite common in the SVM paradigm; however, this approach may fail under various circumstances. We pro ..."
Abstract

Cited by 261 (25 self)
 Add to MetaCart
Twocategory support vector machines (SVM) have been very popular in the machine learning community for classi � cation problems. Solving multicategory problems by a series of binary classi � ers is quite common in the SVM paradigm; however, this approach may fail under various circumstances. We propose the multicategory support vector machine (MSVM), which extends the binary SVM to the multicategory case and has good theoretical properties. The proposed method provides a unifying framework when there are either equal or unequal misclassi � cation costs. As a tuning criterion for the MSVM, an approximate leaveoneout crossvalidation function, called Generalized Approximate Cross Validation, is derived, analogous to the binary case. The effectiveness of the MSVM is demonstrated through the applications to cancer classi � cation using microarray data and cloud classi � cation with satellite radiance pro � les.
2002. Classi� cation of multiple cancer types by multicategory support vector machines using gene expression data
"... Monitoring gene expression proles is a novel approach in cancer diagnosis. Several studies showed that prediction of cancer types using gene expression data is promising and very informative. The Support Vector Machine (SVM) is one of the classication methods successfully applied to the cancer dia ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Monitoring gene expression proles is a novel approach in cancer diagnosis. Several studies showed that prediction of cancer types using gene expression data is promising and very informative. The Support Vector Machine (SVM) is one of the classication methods successfully applied to the cancer diagnosis problems using gene expression data. However, its optimal extension to more than two classes was not obvious, which might impose limitations in its application to multiple tumor types. In this paper, we analyze a couple of published multiple cancer types data sets by the multicategory SVM, which is a recently proposed extension of the binary SVM. 1
Estimating the Costs Associated with Worthwhile Predictions of Poor Air Quality
"... In this study we investigate the eect of varying the ratio of falsepositive and falsenegative misclassi cation costs on the sensitivity and selectivity of binary predictions of exceedences of atmospheric pollutants. This allows us to determine a window of values for this ratio for which it is ..."
Abstract
 Add to MetaCart
(Show Context)
In this study we investigate the eect of varying the ratio of falsepositive and falsenegative misclassi cation costs on the sensitivity and selectivity of binary predictions of exceedences of atmospheric pollutants. This allows us to determine a window of values for this ratio for which it is worthwhile making denite rather than probabilistic predictions. The support vector machine provides a suitable statistical pattern recognition method for this work. 1
Theory, and Application to the Classication of Microarray Data and Satellite Radiance Data
, 2002
"... Two category Support Vector Machines (SVM) have been very popular in the machine learning community for the classication problem. Solving multicategory problems by a series of binary classiers is quite common in the SVM paradigm. However, this approach may fail under a variety of circumstances. We h ..."
Abstract
 Add to MetaCart
Two category Support Vector Machines (SVM) have been very popular in the machine learning community for the classication problem. Solving multicategory problems by a series of binary classiers is quite common in the SVM paradigm. However, this approach may fail under a variety of circumstances. We have proposed the Multicategory Support Vector Machine (MSVM), which extends the binary SVM to the multicategory case, and has good theoretical properties. The proposed method provides a unifying framework when there are either equal or unequal misclassication costs. As a tuning criterion for the MSVM, an approximate leavingoutone cross validation function, called Generalized Approximate Cross Validation (GACV) is derived, analogous to the binary case. The eectiveness of the MSVM is demonstrated through the applications to cancer classication using microarray data and cloud classication with satellite radiance proles. Key words: nonparametric classication method, reproducing kernel Hilbert space, regular
1IEICE Transactions on Information and Systems, vol.E97D, no.7, pp.1822{1829, 2014. Constrained LeastSquares DensityDifference Estimation
"... We address the problem of estimating the difference between two probability densities. A naive approach is a twostep procedure that rst estimates two densities separately and then computes their difference. However, such a twostep procedure does not necessarily work well because the rst step is p ..."
Abstract
 Add to MetaCart
(Show Context)
We address the problem of estimating the difference between two probability densities. A naive approach is a twostep procedure that rst estimates two densities separately and then computes their difference. However, such a twostep procedure does not necessarily work well because the rst step is performed without regard to the second step and thus a small error in the rst stage can cause a big error in the second stage. Recently, a singleshot method called the leastsquares densitydifference (LSDD) estimator has been proposed. LSDD directly estimates the density difference without separately estimating two densities, and it was demonstrated to outperform the twostep approach. In this paper, we propose a variation of LSDD called the constrained leastsquares densitydifference (CLSDD) estimator, and theoretically prove that CLSDD improves the accuracy of density difference estimation for correctly specied parametric models. The usefulness of the proposed method is also demonstrated experimentally.