Entropy encoding
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In information theory an entropy encoding is a data compression scheme that assigns codes to symbols so as to match code lengths with the probabilities of the symbols. Typically, entropy encoders are used to compress data by replacing symbols represented by equal-length codes with symbols represented by codes where the length of each codeword is proportional to the negative logarithm of the probability. Therefore, the most common symbols use the shortest codes.
According to Shannon's source coding theorem, the optimal code length for a symbol is −logbP, where b is the number of symbols used to make output codes and P is the probability of the input symbol.
Two of the most common entropy encoding techniques are Huffman coding and arithmetic coding. If the approximate entropy characteristics of a data stream are known in advance (especially for signal compression), a simpler static code such as unary coding, Elias gamma coding, Fibonacci coding, Golomb coding, or Rice coding may be useful.
[edit] Entropy as a measure of Similarity
Besides using entropy encoding as a way to compress (and losslessly recover) digital data, an entropy encoder can also be used to measure the amount of similarity between streams of data. This is done by generating an entropy coder/compressor for each class of data; unknown data is then classified by feeding the uncompressed data to each compressor and seeing which compressor yields the highest compression. The coder with the best compression is probably the coder trained on the data that was most similar to the unknown data.
[edit] See also
[edit] External links
- On-line textbook: Information Theory, Inference, and Learning Algorithms, by David MacKay - gives an accessible introduction to Shannon theory and data compression, including the Huffman coding and arithmetic coding.
- Spam Filtering using Statistical Data Compression Models by Andrej Bratko, Gordon V. Cormack, Bogdan Filipic, Thomas R. Lynam and Blaz Zupan, Journal of Machine Learning Research, Vol 7(Dec), 2006.
- Anatomy of Range Encoder
An earlier (open content) version of the above article was posted on PlanetMath.
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