Linde–Buzo–Gray algorithm

The Linde–Buzo–Gray algorithm (introduced by Yoseph Linde, Andrés Buzo and Robert M. Gray in 1980) is a vector quantization algorithm to derive a good codebook.

It is similar to the k-means method in data clustering.

The algorithm

At each iteration, each vector is split into two new vectors.

  • A initial state: centroid of the training sequence;
  • B initial estimation #1: code book of size 2;
  • C final estimation after LGA: Optimal code book with 2 vectors;
  • D initial estimation #2: code book of size 4;
  • E final estimation after LGA: Optimal code book with 4 vectors;

The final two code vectors are splitted into four and the process is repeated until the desired number of code vector is obtained.

References
  • The original paper describing the algorithm, as an extension to Lloyd's algorithm:
    • Linde, Y.; Buzo, A.; Gray, R. (1980). "An Algorithm for Vector Quantizer Design". IEEE Transactions on Communications. 28: 84–95. doi:10.1109/TCOM.1980.1094577.
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