By Guandong Xu

ISBN-10: 1299704433

ISBN-13: 9781299704435

ISBN-10: 1466585838

ISBN-13: 9781466585836

ISBN-10: 1466585846

ISBN-13: 9781466585843

Info mining has witnessed giant advances in fresh a long time. New study questions and sensible demanding situations have arisen from rising components and functions in the a variety of fields heavily regarding human way of life, e.g. social media and social networking. This e-book goals to bridge the space among conventional facts mining and the most recent advances in newly rising details companies. It explores theRead more...

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Formally, the Mahalanobis distance of a multivariate vector x = (x1, x2, x3, · · · , xN)T from a group of values with mean µ = (µ1, µ2, µ3, · · · , µN)T and covariance matrix S is defined as: DM(x) = T −1 μ ). 12) Mahalanobis distance can also be defined as a dissimilarity measure between two random vectors x and y of the same distribution with the covariance matrix S: Mathematical Foundations 33 d ( x, y ) = ( x − y )T S −1 ( x − y ). 13) If the covariance matrix is the identity matrix, the Mahalanobis distance reduces to the Euclidean distance.

If |U| = |V |, that is, if the two subsets have equal cardinality, then G is called a Balanced Bipartite graph. Also, scientists have established the Vicsek model to describe swarm behavior. A swarm is modeled in this graph by a collection of particles that move with a constant speed but respond to a random perturbation by adopting at each time increment the average direction of motion of the other particles in their local neighborhood. Vicsek model predicts that swarming animals share certain properties at the group level, regardless of the type of animals in the swarm.

3) In words, it is the average of the logarithmic difference between the probabilities P and Q, where the average is taken using the probabilities P. The KL divergence is only defined if P and Q both sum up to 1 and if Q(i) > 0 for any i is such that P(i) > 0. If the quantity 0 ln 0 appears in the formula, it is interpreted as zero. 4) where p and q denote the densities of P and Q. 5) DKL(P ÃÃ Q) = ∫X In dQ dP, dP 36 Applied Data Mining dQ is the Radon-Nikodym derivative of Q with respect to P, and dp provided the expression on the right-hand side exists.

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