By Guandong Xu
Info mining has witnessed titanic advances in fresh a long time. New examine questions and useful demanding situations have arisen from rising parts and purposes in the numerous fields heavily on the topic of human everyday life, e.g. social media and social networking. This publication goals to bridge the space among conventional information mining and the newest advances in newly rising details prone. It explores the extension of well-studied algorithms and techniques into those new study arenas. Read more...
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Mathematical Foundations 29 There are, of course, many reasons for the predominance of the multivariate normal distribution in statistics. These result from some of its most desirable properties as listed below: 1. It represents a natural extension of the univariate normal distribution and provides a suitable model for many real-life problems concerning vector-valued data. 2. 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.
1) We must show that the cosine similarity is indeed a distance measure. We have defined that the angle of two vector is in the range of 0 to 180, no negative similarity value is possible. Two vectors have an angle of zero if and only if they are along the same direction but with possible different length magnitude. Symmetry is obvious: the angle between x and y is the same as the angle between y and x. The triangle inequality is best argued by physical reasoning. One way to rotate from x to y is to rotate to z and thence to y.
The data transformation may be linear, as in principal component analysis (PCA), but many nonlinear dimensionality reduction techniques also exist. 1 Principal Component Analysis Principal component analysis (PCA) is a mathematical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The number of principal components is less than or equal to the number of original variables.