Support Vector Machines for Classification Problems

2011 ◽  
pp. 3-13
Author(s):  
Yong Shi ◽  
Yingjie Tian ◽  
Gang Kou ◽  
Yi Peng ◽  
Jianping Li
Keyword(s):  
Support Vector Machines ◽  
Support Vector ◽  
Classification Problems ◽  
Vector Machines

scholarly journals Correlation Kernels for Support Vector Machines Classification with Applications in Cancer Data

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Hao Jiang ◽  
Wai-Ki Ching
Keyword(s):  
Support Vector Machines ◽  
Positive Semidefinite ◽  
Superior Performance ◽  
Support Vector ◽  
Svm Classifier ◽  
Classification Problems ◽  
Correlation Kernel ◽  
Cancer Data ◽  
Tumor Tissues ◽  
Vector Machines

High dimensional bioinformatics data sets provide an excellent and challenging research problem in machine learning area. In particular, DNA microarrays generated gene expression data are of high dimension with significant level of noise. Supervised kernel learning with an SVM classifier was successfully applied in biomedical diagnosis such as discriminating different kinds of tumor tissues. Correlation Kernel has been recently applied to classification problems with Support Vector Machines (SVMs). In this paper, we develop a novel and parsimonious positive semidefinite kernel. The proposed kernel is shown experimentally to have better performance when compared to the usual correlation kernel. In addition, we propose a new kernel based on the correlation matrix incorporating techniques dealing with indefinite kernel. The resulting kernel is shown to be positive semidefinite and it exhibits superior performance to the two kernels mentioned above. We then apply the proposed method to some cancer data in discriminating different tumor tissues, providing information for diagnosis of diseases. Numerical experiments indicate that our method outperforms the existing methods such as the decision tree method and KNN method.

scholarly journals Support Vector Machines with Quantum State Discrimination

2021 ◽  
Vol 3 (3) ◽  
pp. 482-499
Author(s):  
Roberto Leporini ◽  
Davide Pastorello
Keyword(s):  
Support Vector Machines ◽  
Quantum State ◽  
Quantum States ◽  
Support Vector ◽  
Classification Algorithms ◽  
Quantum State Discrimination ◽  
Classification Problems ◽  
Density Operators ◽  
State Discrimination ◽  
Vector Machines

We analyze possible connections between quantum-inspired classifications and support vector machines. Quantum state discrimination and optimal quantum measurement are useful tools for classification problems. In order to use these tools, feature vectors have to be encoded in quantum states represented by density operators. Classification algorithms inspired by quantum state discrimination and implemented on classic computers have been recently proposed. We focus on the implementation of a known quantum-inspired classifier based on Helstrom state discrimination showing its connection with support vector machines and how to make the classification more efficient in terms of space and time acting on quantum encoding. In some cases, traditional methods provide better results. Moreover, we discuss the quantum-inspired nearest mean classification.

Support Vector Machines

2011 ◽  
pp. 1518-1523
Author(s):  
Cecilio Angulo ◽  
Luis Gonzalez-Abril
Keyword(s):  
Support Vector Machines ◽  
Text Categorization ◽  
Binary Classification ◽  
Support Vector ◽  
Risk Minimization ◽  
Classification Problems ◽  
Microarray Gene Expression ◽  
Vector Machines ◽  
The Sixties ◽  
Learning Machine

Support Vector Machines -- SVMs -- are learning machines, originally designed for bi-classification problems, implementing the well-known Structural Risk Minimization (SRM) inductive principle to obtain good generalization on a limited number of learning patterns (Vapnik, 1998). The optimization criterion for these machines is maximizing the margin between two classes, i.e. the distance between two parallel hyperplanes that split the vectors of each one of the two classes, since larger is the margin separating classes, smaller is the VC dimension of the learning machine, which theoretically ensures a good generalization performance (Vapnik, 1998), as it has been demonstrated in a number of real applications (Cristianini, 2000). In its formulation is applicable the kernel trick, which improves the capacity of these algorithms, learning not being directly performed in the original space of data but in a new space called feature space; for this reason this algorithm is one of the most representative of the called Kernel Machines (KMs). Main theory was originally developed on the sixties and seventies by V. Vapnik and A. Chervonenkis (Vapnik et al., 1963, Vapnik et al., 1971, Vapnik, 1995, Vapnik, 1998), on the basis of a separable binary classification problem, however generalization in the use of these learning algorithms did not take place until the nineties (Boser et al., 1992). SVMs has been used thoroughly in any kind of learning problems, mainly in classification problems, although also in other problems like regression (Schölkopf et al., 2004) or clustering (Ben-Hur et al., 2001). The fields of Optic Character Recognition (Cortes et al., 1995) and Text Categorization (Sebastiani, 2002) were the most important initial applications where SVMs were used. With the extended application of new kernels, novel applications have taken place in the field of Bioinformatics, concretely many works are related with the classification of data in Genetic Expression (Microarray Gene Expression) (Brown et al., 1997) and detecting structures between proteins and their relationship with the chains of DNA (Jaakkola et al., 2000). Other applications include image identification, voice recognition, prediction in time series, etc. A more extensive list of applications can be found in (Guyon, 2006).

An genetic approach to Support Vector Machines in classification problems

2010 ◽  
Author(s):  
Carlos Alberto de A. Padilha ◽  
Naiyan Hari C. Lima ◽  
Adriao Duarte Doria Neto ◽  
Jorge Dantas de Melo
Keyword(s):  
Support Vector Machines ◽  
Support Vector ◽  
Genetic Approach ◽  
Classification Problems ◽  
Vector Machines
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