Algorithms for fast vector quantization

This paper shows that if one is willing to relax the requirement of finding the true nearest neighbor, it is possible to achieve significant improvements in running time and at only a very small loss in the performance of the vector quantizer. The authors present three algorithms for nearest neighbor searching: standard and priority k-d tree search algorithms and a neighborhood graph search algorithm in which a directed graph is constructed for the point set and edges join neighboring points.<<ETX>>

[1]  Keinosuke Fukunaga,et al.  A Branch and Bound Algorithm for Computing k-Nearest Neighbors , 1975, IEEE Transactions on Computers.

[2]  Jon Louis Bentley,et al.  Multidimensional binary search trees used for associative searching , 1975, CACM.

[3]  Jon Louis Bentley,et al.  An Algorithm for Finding Best Matches in Logarithmic Expected Time , 1977, TOMS.

[4]  H. Lipkin Where is the ?c? , 1978 .

[5]  Jean Vuillemin,et al.  A data structure for manipulating priority queues , 1978, CACM.

[6]  Godfried T. Toussaint,et al.  The relative neighbourhood graph of a finite planar set , 1980, Pattern Recognit..

[7]  R. Gray,et al.  Speech coding based upon vector quantization , 1980, ICASSP.

[8]  N. J. A. Sloane,et al.  Fast quantizing and decoding and algorithms for lattice quantizers and codes , 1982, IEEE Trans. Inf. Theory.

[9]  Biing-Hwang Juang,et al.  Multiple stage vector quantization for speech coding , 1982, ICASSP.

[10]  R. Gray,et al.  Product code vector quantizers for waveform and voice coding , 1984 .

[11]  Robert M. Gray,et al.  An Improvement of the Minimum Distortion Encoding Algorithm for Vector Quantization , 1985, IEEE Trans. Commun..

[12]  Andrew Chi-Chih Yao,et al.  A general approach to d-dimensional geometric queries , 1985, STOC '85.

[13]  Bjarne Stroustrup,et al.  C++ Programming Language , 1986, IEEE Softw..

[14]  Allen Gersho,et al.  A fast codebook search algorithm for nearest-neighbor pattern matching , 1986, ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[15]  Jerzy W. Jaromczyk,et al.  A note on relative neighborhood graphs , 1987, SCG '87.

[16]  Kenneth L. Clarkson,et al.  A Randomized Algorithm for Closest-Point Queries , 1988, SIAM J. Comput..

[17]  William Equitz,et al.  A new vector quantization clustering algorithm , 1989, IEEE Trans. Acoust. Speech Signal Process..

[18]  Rajiv Laroia,et al.  A Structured Fixed-Rate Vector Quantizer Derived from Variable- Length Encoded Scalar Quantizers , 1990 .

[19]  Jon Louis Bentley,et al.  K-d trees for semidynamic point sets , 1990, SCG '90.

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

[21]  Kuldip K. Paliwal,et al.  Fast K-dimensional tree algorithms for nearest neighbor search with application to vector quantization encoding , 1992, IEEE Trans. Signal Process..

[22]  Dexter Kozen,et al.  The Design and Analysis of Algorithms , 1991, Texts and Monographs in Computer Science.

[23]  Sunil Arya,et al.  Approximate nearest neighbor queries in fixed dimensions , 1993, SODA '93.

[24]  Kenneth L. Clarkson,et al.  An algorithm for approximate closest-point queries , 1994, SCG '94.