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By Guandong Xu

Info mining has witnessed large advances in contemporary a long time. New examine questions and sensible demanding situations have arisen from rising components and purposes in the numerous fields heavily on the topic of human everyday life, e.g. social media and social networking. This e-book goals to bridge the distance among conventional facts mining and the most recent advances in newly rising details providers. It explores the Read more...

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Mahalanobis’ discovery was prompted by the problem of identifying the similarities of skulls based on measurements. And now, it is widely used in cluster analysis and classification techniques. 1 Cosine Similarity In some applications, the classic vector space model is used generally, such as Relevance rankings of documents in a keyword search. It can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as same kind of vector as the documents.

It is used in information filtering, information retrieval, indexing and relevancy rankings. In vector space model, documents and queries are represented as vectors. Each dimension corresponds to a separate term. 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 distinct words occurring in the corpus). If a term occurs in the document, its value in the vector is non-zero.

Even if in an experiment, the original data cannot be fitted satisfactorily with a multivariate normal distribution (as is the case when the measurements are discrete random vectors), by the central limit theorem, the distribution of the sample mean vector is asymptotically normal. Thus the multivariate normal distribution can be used for approximating the distribution of the same mean vector in the large sample case. 3. The density function of a multivariate normal distribution is uniquely determined by the mean vector and the covariance matrix of the random variable.

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