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Prediction by partial matching (PPM) is an adaptive statistical data compression technique based on context modeling and prediction. PPM models use a set of previous symbols in the uncompressed symbol stream to predict the next symbol in the stream. PPM algorithms can also be used to cluster data into predicted groupings in cluster analysis.
Predictions are usually reduced to symbol rankings[ clarification needed ]. Each symbol (a letter, bit or any other amount of data) is ranked before it is compressed, and the ranking system determines the corresponding codeword (and therefore the compression rate). In many compression algorithms, the ranking is equivalent to probability mass function estimation. Given the previous letters (or given a context), each symbol is assigned with a probability. For instance, in arithmetic coding the symbols are ranked by their probabilities to appear after previous symbols, and the whole sequence is compressed into a single fraction that is computed according to these probabilities.
The number of previous symbols, n, determines the order of the PPM model which is denoted as PPM(n). Unbounded variants where the context has no length limitations also exist and are denoted as PPM*. If no prediction can be made based on all n context symbols, a prediction is attempted with n − 1 symbols. This process is repeated until a match is found or no more symbols remain in context. At that point a fixed prediction is made.
Much of the work in optimizing a PPM model is handling inputs that have not already occurred in the input stream. The obvious way to handle them is to create a "never-seen" symbol which triggers the escape sequence [ clarification needed ]. But what probability should be assigned to a symbol that has never been seen? This is called the zero-frequency problem. One variant uses the Laplace estimator, which assigns the "never-seen" symbol a fixed pseudocount of one. A variant called PPMd increments the pseudocount of the "never-seen" symbol every time the "never-seen" symbol is used. (In other words, PPMd estimates the probability of a new symbol as the ratio of the number of unique symbols to the total number of symbols observed).
PPM compression implementations vary greatly in other details. The actual symbol selection is usually recorded using arithmetic coding, though it is also possible to use Huffman encoding or even some type of dictionary coding technique. The underlying model used in most PPM algorithms can also be extended to predict multiple symbols. It is also possible to use non-Markov modeling to either replace or supplement Markov modeling. The symbol size is usually static, typically a single byte, which makes generic handling of any file format easy.
Published research on this family of algorithms can be found as far back as the mid-1980s. Software implementations were not popular until the early 1990s because PPM algorithms require a significant amount of RAM. Recent PPM implementations are among the best-performing lossless compression programs for natural language text.
PPMd is a public domain implementation of PPMII (PPM with information inheritance) by Dmitry Shkarin which has undergone several incompatible revisions. [1] It is used in the RAR file format by default. It is also available in the 7z and zip file formats.
Attempts to improve PPM algorithms led to the PAQ series of data compression algorithms.
A PPM algorithm, rather than being used for compression, is used to increase the efficiency of user input in the alternate input method program Dasher.
In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information. Typically, a device that performs data compression is referred to as an encoder, and one that performs the reversal of the process (decompression) as a decoder.
In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression. The process of finding or using such a code is Huffman coding, an algorithm developed by David A. Huffman while he was a Sc.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes".
Lossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Lossless compression is possible because most real-world data exhibits statistical redundancy. By contrast, lossy compression permits reconstruction only of an approximation of the original data, though usually with greatly improved compression rates.
Range coding is an entropy coding method defined by G. Nigel N. Martin in a 1979 paper, which effectively rediscovered the FIFO arithmetic code first introduced by Richard Clark Pasco in 1976. Given a stream of symbols and their probabilities, a range coder produces a space-efficient stream of bits to represent these symbols and, given the stream and the probabilities, a range decoder reverses the process.
In information theory, an entropy coding is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem, which states that any lossless data compression method must have an expected code length greater than or equal to the entropy of the source.
Arithmetic coding (AC) is a form of entropy encoding used in lossless data compression. Normally, a string of characters is represented using a fixed number of bits per character, as in the ASCII code. When a string is converted to arithmetic encoding, frequently used characters will be stored with fewer bits and not-so-frequently occurring characters will be stored with more bits, resulting in fewer bits used in total. Arithmetic coding differs from other forms of entropy encoding, such as Huffman coding, in that rather than separating the input into component symbols and replacing each with a code, arithmetic coding encodes the entire message into a single number, an arbitrary-precision fraction q, where 0.0 ≤ q < 1.0. It represents the current information as a range, defined by two numbers. A recent family of entropy coders called asymmetric numeral systems allows for faster implementations thanks to directly operating on a single natural number representing the current information.
bzip2 is a free and open-source file compression program that uses the Burrows–Wheeler algorithm. It only compresses single files and is not a file archiver. It relies on separate external utilities for tasks such as handling multiple files, encryption, and archive-splitting.
The Lempel–Ziv–Markov chain algorithm (LZMA) is an algorithm used to perform lossless data compression. It has been under development since either 1996 or 1998 by Igor Pavlov and was first used in the 7z format of the 7-Zip archiver. This algorithm uses a dictionary compression scheme somewhat similar to the LZ77 algorithm published by Abraham Lempel and Jacob Ziv in 1977 and features a high compression ratio and a variable compression-dictionary size, while still maintaining decompression speed similar to other commonly used compression algorithms.
7z is a compressed archive file format that supports several different data compression, encryption and pre-processing algorithms. The 7z format initially appeared as implemented by the 7-Zip archiver. The 7-Zip program is publicly available under the terms of the GNU Lesser General Public License. The LZMA SDK 4.62 was placed in the public domain in December 2008. The latest stable version of 7-Zip and LZMA SDK is version 24.05.
PAQ is a series of lossless data compression archivers that have gone through collaborative development to top rankings on several benchmarks measuring compression ratio. Specialized versions of PAQ have won the Hutter Prize and the Calgary Challenge. PAQ is free software distributed under the GNU General Public License.
Context mixing is a type of data compression algorithm in which the next-symbol predictions of two or more statistical models are combined to yield a prediction that is often more accurate than any of the individual predictions. For example, one simple method is to average the probabilities assigned by each model. The random forest is another method: it outputs the prediction that is the mode of the predictions output by individual models. Combining models is an active area of research in machine learning.
In bioinformatics, GLIMMER (Gene Locator and Interpolated Markov ModelER) is used to find genes in prokaryotic DNA. "It is effective at finding genes in bacteria, archea, viruses, typically finding 98-99% of all relatively long protein coding genes". GLIMMER was the first system that used the interpolated Markov model to identify coding regions. The GLIMMER software is open source and is maintained by Steven Salzberg, Art Delcher, and their colleagues at the Center for Computational Biology at Johns Hopkins University. The original GLIMMER algorithms and software were designed by Art Delcher, Simon Kasif and Steven Salzberg and applied to bacterial genome annotation in collaboration with Owen White.
Grammar-based codes or Grammar-based compression are compression algorithms based on the idea of constructing a context-free grammar (CFG) for the string to be compressed. Examples include universal lossless data compression algorithms. To compress a data sequence , a grammar-based code transforms into a context-free grammar . The problem of finding a smallest grammar for an input sequence is known to be NP-hard, so many grammar-transform algorithms are proposed from theoretical and practical viewpoints. Generally, the produced grammar is further compressed by statistical encoders like arithmetic coding.
Lossless JPEG is a 1993 addition to JPEG standard by the Joint Photographic Experts Group to enable lossless compression. However, the term may also be used to refer to all lossless compression schemes developed by the group, including JPEG 2000, JPEG-LS, and JPEG XL.
In the mathematical theory of stochastic processes, variable-order Markov (VOM) models are an important class of models that extend the well known Markov chain models. In contrast to the Markov chain models, where each random variable in a sequence with a Markov property depends on a fixed number of random variables, in VOM models this number of conditioning random variables may vary based on the specific observed realization.
Dynamic Markov compression (DMC) is a lossless data compression algorithm developed by Gordon Cormack and Nigel Horspool. It uses predictive arithmetic coding similar to prediction by partial matching (PPM), except that the input is predicted one bit at a time. DMC has a good compression ratio and moderate speed, similar to PPM, but requires somewhat more memory and is not widely implemented. Some recent implementations include the experimental compression programs hook by Nania Francesco Antonio, ocamyd by Frank Schwellinger, and as a submodel in paq8l by Matt Mahoney. These are based on the 1993 implementation in C by Gordon Cormack.
Context-adaptive binary arithmetic coding (CABAC) is a form of entropy encoding used in the H.264/MPEG-4 AVC and High Efficiency Video Coding (HEVC) standards. It is a lossless compression technique, although the video coding standards in which it is used are typically for lossy compression applications. CABAC is notable for providing much better compression than most other entropy encoding algorithms used in video encoding, and it is one of the key elements that provides the H.264/AVC encoding scheme with better compression capability than its predecessors.
ZPAQ is an open source command line archiver for Windows and Linux. It uses a journaling or append-only format which can be rolled back to an earlier state to retrieve older versions of files and directories. It supports fast incremental update by adding only files whose last-modified date has changed since the previous update. It compresses using deduplication and several algorithms depending on the data type and the selected compression level. To preserve forward and backward compatibility between versions as the compression algorithm is improved, it stores the decompression algorithm in the archive. The ZPAQ source code includes a public domain API, libzpaq, which provides compression and decompression services to C++ applications. The format is believed to be unencumbered by patents.
Asymmetric numeral systems (ANS) is a family of entropy encoding methods introduced by Jarosław (Jarek) Duda from Jagiellonian University, used in data compression since 2014 due to improved performance compared to previous methods. ANS combines the compression ratio of arithmetic coding, with a processing cost similar to that of Huffman coding. In the tabled ANS (tANS) variant, this is achieved by constructing a finite-state machine to operate on a large alphabet without using multiplication.
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