A locality correlation preserving support vector machine

• Published in: Pattern recognition 2014-09, Vol.47 (9), p.3168-3178
• Main Authors: Zhang, Huaxiang, Cao, Linlin, Gao, Shuang
• Format: Article
• Language: English
• Subjects: Applied sciences; Correlation; Correlation analysis; Exact sciences and technology; Fuzzy membership; Information, signal and communications theory; Kernel methods; Locality correlation preservation; Mathematical models; Maximization; Optimization; Preserving; Scatter; Signal and communications theory; Signal representation. Spectral analysis; Signal, noise; Support vector machine; Support vector machines; Telecommunications and information theory
• ISSN: 0031-3203; 1873-5142
• DOI: 10.1016/j.patcog.2014.04.004

This paper proposes a locality correlation preserving based support vector machine (LCPSVM) by combining the idea of margin maximization between classes and local correlation preservation of class data. It is a Support Vector Machine (SVM) like algorithm, which explicitly considers the locality correlation within each class in the margin and the penalty term of the optimization function. Canonical correlation analysis (CCA) is used to reveal the hidden correlations between two datasets, and a variant of correlation analysis model which implements locality preserving has been proposed by integrating local information into the objective function of CCA. Inspired by the idea used in canonical correlation analysis, we propose a locality correlation preserving within-class scatter matrix to replace the within-class scatter matrix in minimum class variance support machine (MCVSVM). This substitution has the property of keeping the locality correlation of data, and inherits the properties of SVM and other similar modified class of support vector machines. LCPSVM is discussed under linearly separable, small sample size and nonlinearly separable conditions, and experimental results on benchmark datasets demonstrate its effectiveness. •We propose a novel support vector machine like classification algorithm LCPSVM.•LCPSVM combines the idea of margin maximization between classes and local correlation preservation of class data.•It is shown that SVM and other related algorithms can be obtained as special cases of LCPSVM.•Experiments under different conditions are performed, and the results are discussed.