Newton's method for nonparallel plane proximal classifier with unity norm hyperplanes

Ghorai, Santanu; Hossain, Shaikh Jahangir; Mukherjee, Anirban; Dutta, Pranab

doi:10.1016/j.sigpro.2009.05.020

Cited by 28 publications

(18 citation statements)

References 11 publications

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“…We have selected nonparallel plane proximal classifier (NPPC) [45], [46] as a part of the wrapper method. In our previous research work, we have proposed NPPC [45], [46] for binary data classification that provides comparable accuracy with that of SVM classifiers [47], [48], [49] with a lower computational cost. In [45], we have focused on the chronological development of NPPC having its root from SVM.…”

Section: Introductionmentioning

confidence: 99%

“…NPPC combines ideas from the TWSVM and PSVM. NPPC generates two unity norm nonparallel planes [46] by solving two equality-constrained (like PSVM) optimization problems. This idea of nonparallel plane classifier differs from that of the classical SVM, which is based on the margin maximization of two separating parallel hyperplanes [47], [48].…”

Section: Introductionmentioning

confidence: 99%

“…This idea of nonparallel plane classifier differs from that of the classical SVM, which is based on the margin maximization of two separating parallel hyperplanes [47], [48]. But NPPC is computationally more efficient than SVM classifier [46]. The equality constraints accomplish the training task of the NPPC faster than its inequality counterpart in TWSVM.…”

Section: Introductionmentioning

confidence: 99%

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Cancer Classification from Gene Expression Data by NPPC Ensemble

Ghorai

Mukherjee

Sengupta

et al. 2011

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Abstract-The most important application of microarray in gene expression analysis is to classify the unknown tissue samples according to their gene expression levels with the help of known sample expression levels. In this paper, we present a nonparallel plane proximal classifier (NPPC) ensemble that ensures high classification accuracy of test samples in a computer-aided diagnosis (CAD) framework than that of a single NPPC model. For each data set only, a few genes are selected by using a mutual information criterion. Then a genetic algorithm-based simultaneous feature and model selection scheme is used to train a number of NPPC expert models in multiple subspaces by maximizing cross-validation accuracy. The members of the ensemble are selected by the performance of the trained models on a validation set. Besides the usual majority voting method, we have introduced minimum average proximity-based decision combiner for NPPC ensemble. The effectiveness of the NPPC ensemble and the proposed new approach of combining decisions for cancer diagnosis are studied and compared with support vector machine (SVM) classifier in a similar framework. Experimental results on cancer data sets show that the NPPC ensemble offers comparable testing accuracy to that of SVM ensemble with reduced training time on average.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cancer Classification from Gene Expression Data by NPPC Ensemble

Ghorai

Mukherjee

Sengupta

et al. 2011

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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“…It is also generalized to deal with multi-classification problem in [32] and multi-surface classification problem in [33]. Recently, some new results based on it about nonparallel classification hyperplane are reported [34].…”

Section: The Related Models and Their Relationshipsmentioning

confidence: 99%

“…Here we give some plots to compare the M1 and M2 with least squares loss in details. M1 equipped with least squares loss is called LS-SVM [25,30], and M2 equipped with least squares loss is called PSVM [21,32,33,34]. Eight plots with different training data sizes and regularizer paremeters are given in Fig.…”

Section: Drawback Of M1 With the Least Squares Lossmentioning

confidence: 99%

Which is better? Regularization in RKHS vs R^m on Reduced SVMs

Zhou

2013

Stat., optim. inf. comput.

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In SVMs community, the learning results are always a combination of the selected functions. SVMs have two mainly regularization models to find the combination coefficients. The most popular model with m input samples is norm-regularized the classification function in a reproducing kernel Hilbert space(RKHS), and it is converted to an optimization problem in R m by duality or representer theorem. Another important model is generalized support vector machine(GSVM), in which the coefficients of the hypothesis is norm-regularized in the Euclidean space R m . In this work, we analyze the difference between them on computing stability, computational complexity and the efficiency of the Newton type algorithms, especially on the reduced SVMs for large scale training problems. Many typical loss functions are considered. Our studies show that the model of GSVM has more advantages than the other model. Some experiments are given to support our analysis.

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