K-Dimensional Coding Schemes in Hilbert Spaces

被引：63
|
作者：
Maurer, Andreas [1 ]
Pontil, Massimiliano [1 ]
机构：
[1] UCL, Dept Comp Sci, London WC 1E, England
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2010年 / 56卷 / 11期
基金：
英国工程与自然科学研究理事会;
关键词：
Empirical risk minimization; estimation bounds; K-means clustering and vector quantization; statistical learning; GENERALIZATION ERROR; MATRIX;
D O I：
10.1109/TIT.2010.2069250
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This paper presents a general coding method where data in a Hilbert space are represented by finite dimensional coding vectors. The method is based on empirical risk minimization within a certain class of linear operators, which map the set of coding vectors to the Hilbert space. Two results bounding the expected reconstruction error of the method are derived, which highlight the role played by the codebook and the class of linear operators. The results are specialized to some cases of practical importance, including K-means clustering, nonnegative matrix factorization and other sparse coding methods.
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页码：5839 / 5846
页数：8
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