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105 results on '"Chen, Di-Rong"'

101. Shift-invariant spaces of tempered distributions and <f>Lp</f>-functions

Author

Chen, Di-Rong

Subjects
*INVARIANT subspaces, *FOURIER transforms
Abstract

This paper studies the structure of shift-invariant spaces. A characterization for the univariate shift-invariant spaces of tempered distributions is given. In Lp case, an inclusive relation in terms of Fourier transform is established. [Copyright &y& Elsevier]

Published
2003
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102. Local Regularity of L∞∞-Refinable Function Vectors

Author

Chen, Di-Rong

Abstract

This article discusses the local regularity of refinable function vectors associated with a dilation matrix M. Suppose that D is a complete set of representatives of Zs/MZs. Under the assumptions that the self-affine tile T (M,D), associated with dilation matrix M and digit set D, has measure 1 and that the corresponding refinable function vector φ ∈ L∞, we prove that there is a set H ⫅ Rsof full measure such that the restriction φ|Hof φ on H has a positive Hölder exponent α(x) at every x ∈ H. Similar result holds for the derivatives of refinable function vectors provided that the dilation matrix is diagonalizable.

Published
2005
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103. On Linear Independence of Integer Translates of Refinable Vectors

Author

Chen Di-Rong

Subjects
Discrete mathematics, General theory, Symbol (programming), Applied Mathematics, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Linear independence, Stability (probability), Transfer matrix, Analysis, Integer (computer science), Mathematics
Abstract

A refinable vector is a vector with components being compactly supported distributions that satisfies a refinement equation. We characterize, in terms of the symbol associated with the refinement equation, the linear independence and stability of integer translates of the refinable vector. Examples are provided to illustrate the general theory.

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104. Support vector machines regression with l1-regularizer

Author

Tong, Hongzhi, Chen, Di-Rong, and Yang, Fenghong

Subjects
Computer Science::Machine Learning, Error decomposition, Support vector machines regression, Learning rate, Reproducing kernel Hilbert spaces, Coefficient regularization
Abstract

The classical support vector machines regression (SVMR) is known as a regularized learning algorithm in reproducing kernel Hilbert spaces (RKHS) with a ε-insensitive loss function and an RKHS norm regularizer. In this paper, we study a new SVMR algorithm where the regularization term is proportional to l1-norm of the coefficients in the kernel ensembles. We provide an error analysis of this algorithm, an explicit learning rate is then derived under some assumptions.

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