density estimation, the area/volume that is closer to a particular centroid than to any other is inversely proportional to the density (due to the density matching property of the algorithm). 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 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 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 coded 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 of amplitude levels. It is compressed by choosing the nearest matching vector from a set of n-dimensional vectors , with n < k. All possible combinations of the n-dimensional vector form the vector space to which all the quantized vectors belong. Only the index of the codeword in the codebook is sent instead of the quantized values. This conserves space and achieves more compression. Twin vector quantization (VQF) is part of the MPEG-4 standard dealing with time domain weighted interleaved vector quantization. Video codecs based on vector quantization Bink video Cinepak Daala is transform-based but uses pyramid vector quantization on transformed coefficients Digital Video Interactive: Production-Level Video and Real-Time Video Indeo Microsoft Video 1 QuickTime: Apple Video (RPZA) and Graphics Codec (SMC) Sorenson SVQ1 and SVQ3 Smacker video VQA format, used in many games The usage of video codecs based on vector quantization has declined significantly in favor of those based on motion compensated prediction combined with transform coding, e.g. those defined in MPEG standards, as the low decoding complexity of vector quantization has become less relevant. Audio codecs based on vector quantization AMR-WB+ CELP Codec 2 DTS G.729 iLBC Ogg Vorbis Opus is transform-based but uses pyramid vector quantization on transformed coefficients TwinVQ Use in pattern recognition VQ was also used in the eighties for speech and speaker recognition. Recently it has also been used for efficient nearest neighbor search and