Vector quantization: Difference between revisions

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{{Technical|date=October 2023}}

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'''Vector quantization''' ('''VQ''') is a classical [[Quantization (signal processing)|quantization]] technique from [[signal processing]] that allows the modeling of [[probability density functions]] by the distribution of prototype vectors. ItDeveloped in the early 1980s by [[Robert M. Gray]], it was originally used for [[data compression]]. It works by dividing a large set of points ([[coordinate vector|vector]]s) into groups having approximately the same number of points closest to them. Each group is represented by its [[centroid]] point, as in [[k-means]] and some other [[Cluster analysis|clustering]] algorithms. In simpler terms, vector quantization chooses a set of points to represent a larger set of points.

The density matching property of vector quantization is powerful, especially for identifying the density of large and high-dimensional data. Since data points are represented by the index of their closest centroid, commonly occurring data have low error, and rare data high error. This is why VQ is suitable for [[lossy data compression]]. It can also be used for lossy data correction and [[density estimation]].

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* [[Cinepak]]

* [[Daala]] is transform-based but uses [[pyramid vector quantization]] on transformed coefficients<ref>{{cite IETF |title= Pyramid Vector Quantization for Video Coding | first1= JM. |last1= Valin | draft=draft-valin-videocodec-pvq-00 | date=October 2012 |publisher=[[Internet Engineering Task Force|IETF]] |access-date=2013-12-17 |url=httphttps://tools.ietf.org/html/draft-valin-videocodec-pvq-00}} See also arXiv:1602.05209</ref>

* [[Digital Video Interactive]]: Production-Level Video and Real-Time Video

* [[Indeo]]

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| publisher = Xiph.org

| date = 2007-03-09

| url = httphttps://xiph.org/vorbis/doc/Vorbis_I_spec.html

| access-date = 2007-03-09 }}

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=== Use as clustering algorithm ===

As VQ is seeking for centroids as density points of nearby lying samples, it can be also directly used as a prototype-based clustering method: each centroid is then associated with one prototype.

By aiming to minimize the expected squared quantization error<ref>{{cite journal|last=Gray|first=R.M.|title=Vector Quantization|journal=IEEE ASSP Magazine|year=1984|volume=1|issue=2|pages=4–29|doi=10.1109/massp.1984.1162229|hdl=2060/19890012969|hdl-access=free}}</ref> and introducing a decreasing learning gain fulfilling the Robbins-Monro conditions, multiple iterations over the whole data set with a concrete but fixed number of prototypes converges to the solution of [[k-means]] clustering algorithm in an incremental manner.

=== Generative Adversarial Networks (GAN) ===

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==External links==

* http://www.data-compression.com/vq.html {{Webarchive|url=https://web.archive.org/web/20171210201342/http://www.data-compression.com/vq.html |date=2017-12-10 }}

* [httphttps://qccpack.sourceforge.net QccPack — Quantization, Compression, and Coding Library (open source)]

* [https://dl.acm.org/citation.cfm?id=1535126 VQ Indexes Compression and Information Hiding Using Hybrid Lossless Index Coding], Wen-Jan Chen and Wen-Tsung Huang