LEARNING-THEORETIC METHODS IN VECTOR QUANTIZATION

The principal goal of data compression (also known as source coding) is to replace data by a compact representation in such a manner that from this representation the original data can be reconstructed either perfectly, or with high enough accuracy. Generally, the representation is given in the form of a sequence of binary digits (bits) that can be used for efficient digital transmission or storage.

[1]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[2]  Herbert Gish,et al.  Asymptotically efficient quantizing , 1968, IEEE Trans. Inf. Theory.

[3]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[4]  Toby Berger.  Optimum quantizers and permutation codes , 1972, IEEE Trans. Inf. Theory.

[5]  Robert M. Gray,et al.  Quantizer Mismatch , 1975, IEEE Trans. Commun..

[6]  R. Gray,et al.  A Generalization of Ornstein's $\bar d$ Distance with Applications to Information Theory , 1975 .

[7]  S. Szarek.  On the best constants in the Khinchin inequality , 1976 .

[8]  E. Slud.  Distribution Inequalities for the Binomial Law , 1977 .

[9]  R. Dudley.  Central Limit Theorems for Empirical Measures , 1978 .

[10]  Robert M. Gray,et al.  An Algorithm for Vector Quantizer Design , 1980, IEEE Trans. Commun..

[11]  D. Pollard.  Strong Consistency of $K$-Means Clustering , 1981 .

[12]  Gary L. Wise,et al.  On the existence of optimal quantizers , 1982, IEEE Trans. Inf. Theory.

[13]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[14]  D. Pollard.  A Central Limit Theorem for $k$-Means Clustering , 1982 .

[15]  Paul L. Zador,et al.  Asymptotic quantization error of continuous signals and the quantization dimension , 1982, IEEE Trans. Inf. Theory.

[16]  David Pollard,et al.  Quantization and the method of k -means , 1982, IEEE Trans. Inf. Theory.

[17]  G. Wise,et al.  Convergence of Vector Quantizers with Applications to Optimal Quantization , 1984 .

[18]  Robert M. Gray,et al.  Global convergence and empirical consistency of the generalized Lloyd algorithm , 1986, IEEE Trans. Inf. Theory.

[19]  R. Gray.  Source Coding Theory , 1989 .

[20]  Philip A. Chou,et al.  Entropy-constrained vector quantization , 1989, IEEE Trans. Acoust. Speech Signal Process..

[21]  D. Pollard.  Empirical Processes: Theory and Applications , 1990 .

[22]  S. M. Perlmutter,et al.  Training sequence size and vector quantizer performance , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[23]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[24]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

[25]  P. Chou.  The distortion of vector quantizers trained on n vectors decreases to the optimum as O/sub p/(1/n) , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[26]  G. Lugosi,et al.  Rates of convergence in the source coding theorem, in empirical quantizer design, and in universal lossy source coding , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[27]  David A. Cohn,et al.  Theory and Practice of Vector Quantizers Trained on Small Training Sets , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  László Györfi,et al.  A Probabilistic Theory of Pattern Recognition , 1996, Stochastic Modelling and Applied Probability.

[29]  Khalid Sayood,et al.  Introduction to Data Compression , 1996 .

[30]  Neri Merhav,et al.  On the amount of statistical side information required for lossy data compression , 1997, IEEE Trans. Inf. Theory.

[31]  Vahid Tarokh,et al.  Existence of optimal prefix codes for infinite source alphabets , 1997, IEEE Trans. Inf. Theory.

[32]  Tamás Linder,et al.  Empirical quantizer design in the presence of source noise or channel noise , 1997, IEEE Trans. Inf. Theory.

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

[34]  Assaf J. Zeevi.  On the performance of vector quantizers empirically designed from dependent sources , 1998, Proceedings DCC '98 Data Compression Conference (Cat. No.98TB100225).

[35]  David L. Neuhoff,et al.  Quantization , 2022, IEEE Trans. Inf. Theory.

[36]  Tamás Linder,et al.  The minimax distortion redundancy in empirical quantizer design , 1997, Proceedings of IEEE International Symposium on Information Theory.

[37]  P. A. Chou,et al.  When optimal entropy-constrained quantizers have only a finite number of codewords , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[38]  Peter L. Bartlett,et al.  Neural Network Learning - Theoretical Foundations , 1999 .

[39]  R. Ash,et al.  Probability and measure theory , 1999 .

[40]  S. Graf,et al.  Foundations of Quantization for Probability Distributions , 2000 .

[41]  Tamás Linder,et al.  Optimal entropy-constrained scalar quantization of a uniform source , 2000, IEEE Trans. Inf. Theory.

[42]  Tamás Linder.  On the training distortion of vector quantizers , 2000, IEEE Trans. Inf. Theory.

[43]  T. Linder,et al.  On the structure of entropy-constrained scalar quantizers , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[44]  Gábor Lugosi,et al.  Pattern Classification and Learning Theory , 2002 .

[45]  Dudley,et al.  Real Analysis and Probability: Measurability: Borel Isomorphism and Analytic Sets , 2002 .

[46]  Tamás Linder,et al.  A Lagrangian formulation of Zador's entropy-constrained quantization theorem , 2002, IEEE Trans. Inf. Theory.

[47]  Harald Luschgy,et al.  Rates of convergence for the empirical quantization error , 2002 .

[48]  Tamás Linder,et al.  On the structure of optimal entropy-constrained scalar quantizers , 2002, IEEE Trans. Inf. Theory.