Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1171.65043
Wu, Qiang; Ying, Yiming; Zhou, Ding-Xuan
Multi-kernel regularized classifiers. (English)
[J] J. Complexity 23, No. 1, 108-134 (2007). ISSN 0885-064X

Summary: A family of classification algorithms generated from Tikhonov regularization schemes are considered. They involve multi-kernel spaces and general convex loss functions. Our main purpose is to provide satisfactory estimates for the excess misclassification error of these multi-kernel regularized classifiers when the loss functions achieve the zero value. The error analysis consists of two parts: regularization error and sample error. Allowing multi-kernels in the algorithm improves the regularization error and approximation error, which is one advantage of the multi-kernel setting. For a general loss function, we show how to bound the regularization error by the approximation in some weighted $L^{q}$ spaces. For the sample error, we use a projection operator. The projection in connection with the decay of the regularization error enables us to improve convergence rates in the literature even for the one-kernel schemes and special loss functions: least-square loss and hinge loss for support vector machine soft margin classifiers. Existence of the optimization problem for the regularization scheme associated with multi-kernels is verified when the kernel functions are continuous with respect to the index set. Concrete examples, including Gaussian kernels with flexible variances and probability distributions with some noise conditions, are used to illustrate the general theory.

MSC 2000:: *65J20 Improperly posed problems (numerical methods in abstract spaces)

Keywords: classification algorithm; multi-kernel regularization scheme; convex loss function; misclassification error; regularization error; sample error; Tikhonov regularization; convergence rates

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]