An application of the nearest correlation matrix on web document classification

Previous Article
On saddle points of a class of augmented lagrangian functions
JIMO Home
This Issue
Next Article
Coordination of supply chain with buyer's promotion

October 2007, 3(4): 701-713. doi: 10.3934/jimo.2007.3.701

An application of the nearest correlation matrix on web document classification

Houduo Qi ^1, , ZHonghang Xia ^2, and Guangming Xing ^2,

1.	School of Mathematics, The University of Southampton, Highfield, Southampton SO17 1BJ, UK, Springfield, MO 65801-2604, United States
2.	Department of Computer Science, Western Kentucky University, 1906 College Heights Blvd, Bowling Green, Kentucky 42101, United States, United States

Received October 2006 Revised July 2007 Published October 2007

Abstract
Related Papers

The Web document is organized by a set of textual data according to a predefined logical structure. It has been shown that collecting Web documents with similar structures can improve query efficiency. The XML document has no vectorial representation, which is required in most existing classification algorithms. The kernel method has been applied to represent structural data with pairwise similarity. In this case, a set of Web data can be fed into classification algorithms in the format of a kernel matrix. However, since the distance between a pair of Web documents is usually obtained approximately, the derived distance matrix is not a kernel matrix. In this paper, we propose to use the nearest correlation matrix (of the estimated distance matrix) as the kernel matrix, which can be fast computed by a Newton-type method. Experimental studies show that the classification accuracy can be significantly improved.

Keywords: Semidefinite Programming., Classification, Kernel Matrix, Support vector machines.

Mathematics Subject Classification: Primary: 58F15, 58F1.

Citation: Houduo Qi, ZHonghang Xia, Guangming Xing. An application of the nearest correlation matrix on web document classification. Journal of Industrial & Management Optimization, 2007, 3 (4) : 701-713. doi: 10.3934/jimo.2007.3.701

[1]	Ye Tian, Wei Yang, Gene Lai, Menghan Zhao. Predicting non-life insurer's insolvency using non-kernel fuzzy quadratic surface support vector machines. Journal of Industrial & Management Optimization, 2019, 15 (2) : 985-999. doi: 10.3934/jimo.2018081
[2]	K. Schittkowski. Optimal parameter selection in support vector machines. Journal of Industrial & Management Optimization, 2005, 1 (4) : 465-476. doi: 10.3934/jimo.2005.1.465
[3]	Hong-Gunn Chew, Cheng-Chew Lim. On regularisation parameter transformation of support vector machines. Journal of Industrial & Management Optimization, 2009, 5 (2) : 403-415. doi: 10.3934/jimo.2009.5.403
[4]	Yubo Yuan, Weiguo Fan, Dongmei Pu. Spline function smooth support vector machine for classification. Journal of Industrial & Management Optimization, 2007, 3 (3) : 529-542. doi: 10.3934/jimo.2007.3.529
[5]	Keiji Tatsumi, Masashi Akao, Ryo Kawachi, Tetsuzo Tanino. Performance evaluation of multiobjective multiclass support vector machines maximizing geometric margins. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 151-169. doi: 10.3934/naco.2011.1.151
[6]	Cristian Dobre. Mathematical properties of the regular -representation of matrix $$-algebras with applications to semidefinite programming. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 367-378. doi: 10.3934/naco.2013.3.367
[7]	Fengqiu Liu, Xiaoping Xue. Subgradient-based neural network for nonconvex optimization problems in support vector machines with indefinite kernels. Journal of Industrial & Management Optimization, 2016, 12 (1) : 285-301. doi: 10.3934/jimo.2016.12.285
[8]	Yanfei Lu, Qingfei Yin, Hongyi Li, Hongli Sun, Yunlei Yang, Muzhou Hou. Solving higher order nonlinear ordinary differential equations with least squares support vector machines. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-22. doi: 10.3934/jimo.2019012
[9]	Qinghong Zhang, Gang Chen, Ting Zhang. Duality formulations in semidefinite programming. Journal of Industrial & Management Optimization, 2010, 6 (4) : 881-893. doi: 10.3934/jimo.2010.6.881
[10]	Shouhong Yang. Semidefinite programming via image space analysis. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1187-1197. doi: 10.3934/jimo.2016.12.1187
[11]	Christine Bachoc, Alberto Passuello, Frank Vallentin. Bounds for projective codes from semidefinite programming. Advances in Mathematics of Communications, 2013, 7 (2) : 127-145. doi: 10.3934/amc.2013.7.127
[12]	Jiani Wang, Liwei Zhang. Statistical inference of semidefinite programming with multiple parameters. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-12. doi: 10.3934/jimo.2019015
[13]	Yi Xu, Wenyu Sun. A filter successive linear programming method for nonlinear semidefinite programming problems. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 193-206. doi: 10.3934/naco.2012.2.193
[14]	Pooja Louhan, S. K. Suneja. On fractional vector optimization over cones with support functions. Journal of Industrial & Management Optimization, 2017, 13 (2) : 549-572. doi: 10.3934/jimo.2016031
[15]	Yubo Yuan. Canonical duality solution for alternating support vector machine. Journal of Industrial & Management Optimization, 2012, 8 (3) : 611-621. doi: 10.3934/jimo.2012.8.611
[16]	Siamak RabieniaHaratbar. Support theorem for the Light-Ray transform of vector fields on Minkowski spaces. Inverse Problems & Imaging, 2018, 12 (2) : 293-314. doi: 10.3934/ipi.2018013
[17]	Jian Luo, Shu-Cherng Fang, Yanqin Bai, Zhibin Deng. Fuzzy quadratic surface support vector machine based on fisher discriminant analysis. Journal of Industrial & Management Optimization, 2016, 12 (1) : 357-373. doi: 10.3934/jimo.2016.12.357
[18]	Xin Li, Ziguan Cui, Linhui Sun, Guanming Lu, Debnath Narayan. Research on iterative repair algorithm of Hyperchaotic image based on support vector machine. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1199-1218. doi: 10.3934/dcdss.2019083
[19]	Guoqiang Wang, Zhongchen Wu, Zhongtuan Zheng, Xinzhong Cai. Complexity analysis of primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function with a trigonometric barrier term. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 101-113. doi: 10.3934/naco.2015.5.101
[20]	Yang Li, Yonghong Ren, Yun Wang, Jian Gu. Convergence analysis of a nonlinear Lagrangian method for nonconvex semidefinite programming with subproblem inexactly solved. Journal of Industrial & Management Optimization, 2015, 11 (1) : 65-81. doi: 10.3934/jimo.2015.11.65

2017 Impact Factor: 0.994

American Institute of Mathematical Sciences