Building an accurate training database is challenging in supervised classification. For instance, in medical imaging, radiologists often delineate malignant and benign tissues without access to the histological ground...
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Building an accurate training database is challenging in supervised classification. For instance, in medical imaging, radiologists often delineate malignant and benign tissues without access to the histological ground truth, leading to uncertain data sets. This paper addresses the pattern classification problem arising when available target data include some uncertainty information. Target data considered here are both qualitative (a class label) or quantitative (an estimation of the posterior probability). In this context, usual discriminative methods, such as the support vector machine (SVM), fail either to learn a robust classifier or to predict accurate probability estimates. We generalize the regular SVM by introducing a new formulation of the learning problem to take into account class labels as well as class probability estimates. This original reformulation into a probabilistic SVM (P-SVM) can be efficiently solved by adapting existing flexible SVM solvers. Furthermore, this framework allows deriving a unique learned prediction function for both decision and posterior probability estimation providing qualitative and quantitative predictions. The method is first tested on synthetic data sets to evaluate its properties as compared with the classical SVM and fuzzy-SVM. It is then evaluated on a clinical data set of multiparametric prostate magnetic resonance images to assess its performances in discriminating benign from malignant tissues. P-SVM is shown to outperform classical SVM as well as the fuzzy-SVM in terms of probability predictions and classification performances, and demonstrates its potential for the design of an efficient computer-aided decision system for prostate cancer diagnosis based on multiparametric magnetic resonance (MR) imaging.
This paper addresses the pattern classification problem arising when available target data include some uncertainty information. Target data considered here is either qualitative (a class label) or quantitative (an es...
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ISBN:
(纸本)9781457705700
This paper addresses the pattern classification problem arising when available target data include some uncertainty information. Target data considered here is either qualitative (a class label) or quantitative (an estimation of the posterior probability). Our main contribution is a SVM inspired formulation of this problem allowing to take into account class label through a hinge loss as well as probability estimates using epsilon-insensitive cost function together with a minimum norm (maximum margin) objective. This formulation shows a dual form leading to a quadratic problem and allows the use of a representer theorem and associated kernel. The solution provided can be used for both decision and posterior probability estimation. Based on empirical evidence our method outperforms regular SVM in terms of probability predictions and classification performances.
The aim of this paper is to learn a linear principal component using the nature of support vector machines (SVMs). To this end, a complete SVM-like framework of linear PCA (SVPCA) for deciding the projection direction...
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The aim of this paper is to learn a linear principal component using the nature of support vector machines (SVMs). To this end, a complete SVM-like framework of linear PCA (SVPCA) for deciding the projection direction is constructed, where new expected risk and margin are introduced. Within this framework, a new semi-definite programming problem for maximizing the margin is formulated and a new definition of support vectors is established. As a weighted case of regular PCA, our SVPCA coincides with the regular PCA if all the samples play the same part in data compression. Theoretical explanation indicates that SVPCA is based on a margin-based generalization bound and thus good prediction ability is ensured. Furthermore, the robust form of SVPCA with a interpretable parameter is achieved using the soft idea in SVMs. The great advantage lies in the fact that SVPCA is a learning algorithm without local minima because of the convexity of the semi-definite optimization problems. To validate the performance of SVPCA, several experiments are conducted and numerical results have demonstrated that their generalization ability is better than that of regular PCA. Finally, some existing problems are also discussed. (c) 2007 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.
The ideas from fuzzy neural networks and support vector machine (SVM) are incorporated to make SVM classifiers perform better. The influence of the samples with high uncertainty can be decreased by employing the fuzzy...
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The ideas from fuzzy neural networks and support vector machine (SVM) are incorporated to make SVM classifiers perform better. The influence of the samples with high uncertainty can be decreased by employing the fuzzy membership to weigh the margin of each training vector. The linear separability, fuzzy margin, optimal hyperplane, generalization and soft fuzzy marginalgorithms are discussed. A new optimization problem is obtained and SVM is then completely reformulated into a new fuzzy support vector machine (NFSVM). Moreover, the generation bound of NFSVM can be described. We also introduce the membership function in fuzzy neural networks to do some experiments. The results demonstrate that the proposed NFSVM can produce better results than regular SVM and Fuzzy Kernel Perceptron (FKP) in some real cases.
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