Editing Vector quantization (section)

=== Use in data compression ===

Vector quantization, also called "block quantization" or "pattern matching quantization" is often used in [[lossy data compression]].  It works by encoding values from a multidimensional [[vector space]] into a finite set of values from a discrete [[linear subspace|subspace]] of lower dimension. A lower-space vector requires less storage space, so the data is compressed.  Due to the density matching property of vector quantization, the compressed data has errors that are inversely proportional to density.

The transformation is usually done by [[projection (mathematics)|projection]] or by using a [[codebook]]. In some cases, a codebook can be also used to [[entropy code]] the discrete value in the same step, by generating a [[prefix code]]d variable-length encoded value as its output.

The set of discrete amplitude levels is quantized jointly rather than each sample being quantized separately.  Consider a ''k''-dimensional vector <math>[x_1,x_2,...,x_k]</math> of amplitude levels.  It is compressed by choosing the nearest matching vector from a set of ''n''-dimensional vectors <math>[y_1,y_2,...,y_n]</math>, with ''n'' < ''k''.

All possible combinations of the ''n''-dimensional vector <math>[y_1,y_2,...,y_n]</math> form the [[vector space]] to which all the quantized vectors belong.
<!--Block Diagram:
A simple vector quantizer is shown below

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Only the index of the codeword in the codebook is sent instead of the quantized values. This conserves space and achieves more compression.

[[TwinVQ#TwinVQ in MPEG-4|Twin vector quantization]] (VQF) is part of the [[MPEG-4]] standard dealing with time domain weighted interleaved vector quantization.