Linde–Buzo–Gray algorithm: Difference between revisions

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{{one source|date=December 2023}}

The '''Linde–Buzo–Gray algorithm''' (named after its creators Yoseph Linde, Andrés Buzo and [[Robert M. Gray]], who designed it in 1980)<ref>{{Cite journal| doi = 10.1109/TCOM.1980.1094577| issn = 0090-6778| volume = 28| issue = 1| pages = 84–95| last1 = Linde| first1 = Y.| last2 = Buzo| first2 = A.| last3 = Gray| first3 = R.| title = An Algorithm for Vector Quantizer Design| journal = IEEE Transactions on Communications| access-date = 2023-12-28| date = 1980| urls2cid = https://ieeexplore.ieee.org/document/1094577/18530691}}</ref> is an [[Iterative method|iterative]] [[vector quantization]] algorithm to improve a small set of vectors (codebook) to represent a larger set of vectors (training set), such that it will be [[Local optimum|locally optimal]]. It combines [[Lloyd's Algorithm]] with a splitting technique in which larger codebooks are built from smaller codebooks by splitting each code vector in two with [[Lloyd's Algorithm]]. The core idea of the algorithm is that by splitting the codebook such that all code vectors from the previous codebook are present, the new codebook must be as good as the previous one or better. <ref name=gray1992>{{Cite book| edition = 1| publisher = Springer| isbn = 978-1-4613-6612-6| last1 = Gray| first1 = R.| last2 = Gersho| first2 = A.| title = Vector Quantization and Signal Compression| date = 1992| doi = 10.1007/978-1-4615-3626-0| url = https://doi.org/10.1007/978-1-4615-3626-0}}</ref>{{rp|361-362}}

== Description ==

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'''output''': codebook that is twice the size and better or as good as ''old-codebook''

''new-codebook'' &larr;← {}

'''for each''' ''old-codevector'' '''in''' ''old-codebook'' '''do'''

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'''do'''

''previous-codebook'' &larr;← ''codebook''

''clusters'' &larr;← divide ''training'' into |''codebook''| clusters, where each cluster contains all vectors in ''training'' who are best represented by the corresponding vector in ''codebook''

'''for each''' cluster ''cluster'' in ''clusters'' '''do'''

the corresponding code vector in ''codebook'' &larr;← the centroid of all training vectors in ''cluster''

'''while''' the difference in distortionerror representing ''training'' between ''codebook'' and ''previous-codebook'' &gt; {{epsilon}}

'''return''' ''codebook''