Analysis of Classification with a Reject Option

In many classification problems, objects should be rejected when the confidence in their classification is too low. In this paper, we consider a new classification algorithm with a reject option. Based on the majority vote strategy and plug-in rules, we provide error analysis for this algorithm in ideal and realistic settings, respectively. In addition, some discussions of semi-supervised classification are given to demonstrate our theoretical analysis.

[1]  Radu Herbei,et al.  Classification with reject option , 2006 .

[2]  A. Tsybakov,et al.  Optimal aggregation of classifiers in statistical learning , 2003 .

[3]  Philippe Rigollet,et al.  Generalization Error Bounds in Semi-supervised Classification Under the Cluster Assumption , 2006, J. Mach. Learn. Res..

[4]  Chong Zhang,et al.  Estimation of Mental Fatigue Based on Wavelet Packet Parameters and Kernel Learning Algorithms , 2008, Int. J. Wavelets Multiresolution Inf. Process..

[5]  Hong Chen,et al.  Generalization performance of multi-category kernel machines , 2007 .

[6]  Santosh S. Venkatesh,et al.  Learning from a mixture of labeled and unlabeled examples with parametric side information , 1995, COLT '95.

[7]  Ding-Xuan Zhou,et al.  Learning Theory: An Approximation Theory Viewpoint , 2007 .

[8]  M. Wegkamp.  Lasso type classifiers with a reject option , 2007, 0705.2363.

[9]  Jiangtao Peng,et al.  Error bounds of multi-graph regularized semi-supervised classification , 2009, Inf. Sci..

[10]  Hong Chen,et al.  On the rate of convergence for multi-category classification based on convex losses , 2007 .

[11]  S. Prabakaran,et al.  A Wavelet Approach for Classification of microarray Data , 2008, Int. J. Wavelets Multiresolution Inf. Process..

[12]  C. K. Chow,et al.  On optimum recognition error and reject tradeoff , 1970, IEEE Trans. Inf. Theory.

[13]  Peter L. Bartlett,et al.  Classification with a Reject Option using a Hinge Loss , 2008, J. Mach. Learn. Res..

[14]  Brian D. Ripley,et al.  Pattern Recognition and Neural Networks , 1996 .

[15]  Vittorio Castelli,et al.  On the exponential value of labeled samples , 1995, Pattern Recognit. Lett..

[16]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[17]  Felipe Cucker,et al.  On the mathematical foundations of learning , 2001 .

[18]  Vittorio Castelli,et al.  The relative value of labeled and unlabeled samples in pattern recognition with an unknown mixing parameter , 1996, IEEE Trans. Inf. Theory.

[19]  Péter Balázs,et al.  Hilbert-Schmidt Operators and Frames - Classification, Best Approximation by Multipliers and Algorithms , 2006, Int. J. Wavelets Multiresolution Inf. Process..