In the problem of classification （or pattern recognition）, given a set of n samples, we attempt to construct a classifier gn with a small misclassification error. It is important to study the convergence rates of th...In the problem of classification （or pattern recognition）, given a set of n samples, we attempt to construct a classifier gn with a small misclassification error. It is important to study the convergence rates of the misclassification error as n tends to infinity. It is known that such a rate can＇t exist for the set of all distributions. In this paper we obtain the optimal convergence rates for a class of distributions L^（λ,ω） in multicategory classification and nonstandard binary classification.展开更多
In this paper,we propose a new algorithm to extend support vector machine(SVM)for binary classification to multicategory classification.The proposed method is based on a sequential binary classification algorithm.We f...In this paper,we propose a new algorithm to extend support vector machine(SVM)for binary classification to multicategory classification.The proposed method is based on a sequential binary classification algorithm.We first classify a target class by excluding the possibility of labeling as any other classes using a forward step of sequential SVM;we then exclude the already classified classes and repeat the same procedure for the remaining classes in a backward step.The proposed algorithm relies on SVM for each binary classification and utilizes only feasible data in each step;therefore,the method guarantees convergence and entails light computational burden.We prove Fisher consistency of the proposed forward–backward SVM(FB-SVM)and obtain a stochastic bound for the predicted misclassification rate.We conduct extensive simulations and analyze real-world data to demonstrate the superior performance of FB-SVM,for example,FB-SVM achieves a classification accuracy much higher than the current standard for predicting conversion from mild cognitive impairment to Alzheimer’s disease.展开更多
基金Research supported in part by NSF of China under Grants 10571010 and 10171007The work was partially done while the first author was visiting the Institute for Mathematical Sciences, National University of Singapore in 2003The visit was supported by the Institute
文摘In the problem of classification （or pattern recognition）, given a set of n samples, we attempt to construct a classifier gn with a small misclassification error. It is important to study the convergence rates of the misclassification error as n tends to infinity. It is known that such a rate can＇t exist for the set of all distributions. In this paper we obtain the optimal convergence rates for a class of distributions L^（λ,ω） in multicategory classification and nonstandard binary classification.
基金This work is supported by NIH Grants R01GM124104,NS073671,NS082062,NUL1 RR025747Alzheimer’s Disease Neuroimaging Initiative(ADNI)(U01 AG024904,DOD ADNI,W81XWH-12-2-0012),and a pilot award from the Gillings Innovation Lab at the University of North Carolina.The authors acknowledge the investigators within the ADNI who contributed to the design and implementation of ADNI.
文摘In this paper,we propose a new algorithm to extend support vector machine(SVM)for binary classification to multicategory classification.The proposed method is based on a sequential binary classification algorithm.We first classify a target class by excluding the possibility of labeling as any other classes using a forward step of sequential SVM;we then exclude the already classified classes and repeat the same procedure for the remaining classes in a backward step.The proposed algorithm relies on SVM for each binary classification and utilizes only feasible data in each step;therefore,the method guarantees convergence and entails light computational burden.We prove Fisher consistency of the proposed forward–backward SVM(FB-SVM)and obtain a stochastic bound for the predicted misclassification rate.We conduct extensive simulations and analyze real-world data to demonstrate the superior performance of FB-SVM,for example,FB-SVM achieves a classification accuracy much higher than the current standard for predicting conversion from mild cognitive impairment to Alzheimer’s disease.
