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W-shingling
In natural language processing a ''w-shingling'' is a set of ''unique'' ''shingles'' (therefore ''n-grams'') each of which is composed of contiguous subsequences of tokens within a document, which can then be used to ascertain the similarity between documents. The symbol ''w'' denotes the quantity of tokens in each shingle selected, or solved for. The document, "a rose is a rose is a rose" can therefore be maximally tokenized as follows: :(a,rose,is,a,rose,is,a,rose) The set of all contiguous ''sequences of 4 tokens'' (Thus 4=''n'', thus 4-''grams'') is : Which can then be reduced, or maximally shingled in this particular instance to . Resemblance For a given shingle size, the degree to which two documents ''A'' and ''B'' resemble each other can be expressed as the ratio of the magnitudes of their shinglings' intersection and union, or :r(A,B)= where , A, is the size of set A. The resemblance is a number in the range ,1 where 1 indicates that two documents are ident ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bag-of-words Model
The bag-of-words model is a simplifying representation used in natural language processing and information retrieval (IR). In this model, a text (such as a sentence or a document) is represented as the bag (multiset) of its words, disregarding grammar and even word order but keeping multiplicity. The bag-of-words model has also been used for computer vision. The bag-of-words model is commonly used in methods of document classification where the (frequency of) occurrence of each word is used as a feature for training a classifier. An early reference to "bag of words" in a linguistic context can be found in Zellig Harris's 1954 article on ''Distributional Structure''. The Bag-of-words model is one example of a Vector space model. Example implementation The following models a text document using bag-of-words. Here are two simple text documents: (1) John likes to watch movies. Mary likes movies too. (2) Mary also likes to watch football games. Based on these two text d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Space Model
Vector space model or term vector model is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers (such as index terms). It is used in information filtering, information retrieval, indexing and relevancy rankings. Its first use was in the SMART Information Retrieval System. Definitions Documents and queries are represented as vectors. :d_j = ( w_ ,w_ , \dotsc ,w_ ) :q = ( w_ ,w_ , \dotsc ,w_ ) Each dimension corresponds to a separate term. If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, also known as (term) weights, have been developed. One of the best known schemes is tf-idf weighting (see the example below). The definition of ''term'' depends on the application. Typically terms are single words, keywords, or longer phrases. If words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary (the number of dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rolling Hash
A rolling hash (also known as recursive hashing or rolling checksum) is a hash function where the input is hashed in a window that moves through the input. A few hash functions allow a rolling hash to be computed very quickly—the new hash value is rapidly calculated given only the old hash value, the old value removed from the window, and the new value added to the window—similar to the way a moving average function can be computed much more quickly than other low-pass filters. One of the main applications is the Rabin–Karp string search algorithm, which uses the rolling hash described below. Another popular application is the rsync program, which uses a checksum based on Mark Adler's adler-32 as its rolling hash. Low Bandwidth Network Filesystem (LBFS) uses a Rabin fingerprint as its rolling hash. FastCDC (Fast Content-Defined Chunking) uses a compute-efficient Gear fingerprint as its rolling hash. At best, rolling hash values are pairwise independentDaniel Lemire, Owen K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MinHash
In computer science and data mining, MinHash (or the min-wise independent permutations locality sensitive hashing scheme) is a technique for quickly estimating how similar two sets are. The scheme was invented by , and initially used in the AltaVista search engine to detect duplicate web pages and eliminate them from search results.. It has also been applied in large-scale clustering problems, such as clustering documents by the similarity of their sets of words.. Jaccard similarity and minimum hash values The Jaccard similarity coefficient is a commonly used indicator of the similarity between two sets. Let be a set and and be subsets of , then the Jaccard index is defined to be the ratio of the number of elements of their intersection and the number of elements of their union: : J(A,B) = . This value is 0 when the two sets are disjoint, 1 when they are equal, and strictly between 0 and 1 otherwise. Two sets are more similar (i.e. have relatively more members in common) wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jaccard Coefficient
The Jaccard index, also known as the Jaccard similarity coefficient, is a statistic used for gauging the similarity and diversity of sample sets. It was developed by Grove Karl Gilbert in 1884 as his ratio of verification (v) and now is frequently referred to as the Critical Success Index in meteorology. It was later developed independently by Paul Jaccard, originally giving the French name ''coefficient de communauté'', and independently formulated again by T. Tanimoto. Thus, the Tanimoto index or Tanimoto coefficient are also used in some fields. However, they are identical in generally taking the ratio of Intersection over Union. The Jaccard coefficient measures similarity between finite sample sets, and is defined as the size of the intersection divided by the size of the union of the sample sets: : J(A,B) = = . Note that by design, 0\le J(A,B)\le 1. If ''A'' intersection ''B'' is empty, then ''J''(''A'',''B'') = 0. The Jaccard coefficient is widely used in co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rabin Fingerprint
The Rabin fingerprinting scheme is a method for implementing fingerprints using polynomials over a finite field. It was proposed by Michael O. Rabin. Scheme Given an ''n''-bit message ''m''0,...,''m''n-1, we view it as a polynomial of degree ''n''-1 over the finite field GF(2). : f(x) = m_0 + m_1 x + \ldots + m_ x^ We then pick a random irreducible polynomial of degree ''k'' over GF(2), and we define the fingerprint of the message ''m'' to be the remainder r(x) after division of f(x) by p(x) over GF(2) which can be viewed as a polynomial of degree or as a ''k''-bit number. Applications Many implementations of the Rabin–Karp algorithm internally use Rabin fingerprints. The ''Low Bandwidth Network Filesystem'' (LBFS) from MIT uses Rabin fingerprints to implement variable size shift-resistant blocks.Athicha Muthitacharoen, Benjie Chen, and David Mazières"A Low-bandwidth Network File System"/ref> The basic idea is that the filesystem computes the cryptographic hash of each bl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-mer
In bioinformatics, ''k''-mers are substrings of length k contained within a biological sequence. Primarily used within the context of computational genomics and sequence analysis, in which ''k''-mers are composed of nucleotides (''i.e''. A, T, G, and C), ''k''-mers are capitalized upon to assemble DNA sequences, improve heterologous gene expression, identify species in metagenomic samples, and create attenuated vaccines. Usually, the term ''k''-mer refers to all of a sequence's subsequences of length k, such that the sequence AGAT would have four monomers (A, G, A, and T), three 2-mers (AG, GA, AT), two 3-mers (AGA and GAT) and one 4-mer (AGAT). More generally, a sequence of length L will have L - k + 1 ''k''-mers and n^ total possible ''k''-mers, where n is number of possible monomers (e.g. four in the case of DNA). Introduction ''k''-mers are simply length k subsequences. For example, all the possible ''k''-mers of a DNA sequence are shown below: A method of visualizi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-gram
In the fields of computational linguistics and probability, an ''n''-gram (sometimes also called Q-gram) is a contiguous sequence of ''n'' items from a given sample of text or speech. The items can be phonemes, syllables, letters, words or base pairs according to the application. The ''n''-grams typically are collected from a text or speech corpus. When the items are words, -grams may also be called ''shingles''. Using Latin numerical prefixes, an ''n''-gram of size 1 is referred to as a "unigram"; size 2 is a "bigram" (or, less commonly, a "digram"); size 3 is a "trigram". English cardinal numbers are sometimes used, e.g., "four-gram", "five-gram", and so on. In computational biology, a polymer or oligomer of a known size is called a ''k''-mer instead of an ''n''-gram, with specific names using Greek numerical prefixes such as "monomer", "dimer", "trimer", "tetramer", "pentamer", etc., or English cardinal numbers, "one-mer", "two-mer", "three-mer", etc. Applications ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Language Processing
Natural language processing (NLP) is an interdisciplinary subfield of linguistics, computer science, and artificial intelligence concerned with the interactions between computers and human language, in particular how to program computers to process and analyze large amounts of natural language data. The goal is a computer capable of "understanding" the contents of documents, including the contextual nuances of the language within them. The technology can then accurately extract information and insights contained in the documents as well as categorize and organize the documents themselves. Challenges in natural language processing frequently involve speech recognition, natural-language understanding, and natural-language generation. History Natural language processing has its roots in the 1950s. Already in 1950, Alan Turing published an article titled "Computing Machinery and Intelligence" which proposed what is now called the Turing test as a criterion of intelligence, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-gram
In the fields of computational linguistics and probability, an ''n''-gram (sometimes also called Q-gram) is a contiguous sequence of ''n'' items from a given sample of text or speech. The items can be phonemes, syllables, letters, words or base pairs according to the application. The ''n''-grams typically are collected from a text or speech corpus. When the items are words, -grams may also be called ''shingles''. Using Latin numerical prefixes, an ''n''-gram of size 1 is referred to as a "unigram"; size 2 is a "bigram" (or, less commonly, a "digram"); size 3 is a "trigram". English cardinal numbers are sometimes used, e.g., "four-gram", "five-gram", and so on. In computational biology, a polymer or oligomer of a known size is called a ''k''-mer instead of an ''n''-gram, with specific names using Greek numerical prefixes such as "monomer", "dimer", "trimer", "tetramer", "pentamer", etc., or English cardinal numbers, "one-mer", "two-mer", "three-mer", etc. Applications ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersection (set Theory)
In set theory, the intersection of two sets A and B, denoted by A \cap B, is the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A. Notation and terminology Intersection is written using the symbol "\cap" between the terms; that is, in infix notation. For example: \\cap\=\ \\cap\=\varnothing \Z\cap\N=\N \\cap\N=\ The intersection of more than two sets (generalized intersection) can be written as: \bigcap_^n A_i which is similar to capital-sigma notation. For an explanation of the symbols used in this article, refer to the table of mathematical symbols. Definition The intersection of two sets A and B, denoted by A \cap B, is the set of all objects that are members of both the sets A and B. In symbols: A \cap B = \. That is, x is an element of the intersection A \cap B if and only if x is both an element of A and an element of B. For example: * The intersection of the sets and is . * The number 9 is in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
