By Gintautas Dzemyda

ISBN-10: 1441902368

ISBN-13: 9781441902368

The objective of this e-book is to offer a number of equipment used in multidimensional info visualization. The emphasis is put on new study effects and traits during this box, together with optimization, synthetic neural networks, mixtures of algorithms, parallel computing, various proximity measures, nonlinear manifold studying, and extra. the various functions awarded let us realize the most obvious merits of visible info mining--it is way more straightforward for a choice maker to become aware of or extract precious info from graphical illustration of knowledge than from uncooked numbers.The basic notion of visualization is to supply info in a few visible shape that we could people comprehend them, achieve perception into the knowledge, draw conclusions, and at once impact the method of determination making. visible info mining is a box the place human participation is built-in within the facts research approach; it covers information visualization and graphical presentation of knowledge. Multidimensional info Visualization is meant for scientists and researchers in any box of analysis the place advanced and multidimensional info needs to be visually represented. it could possibly additionally function an invaluable study complement for PhD scholars in operations study, computing device technological know-how, quite a few fields of engineering, in addition to usual and social sciences. learn more... Multidimensional info and the concept that of Visualization -- thoughts for Multidimensional facts Visualization -- Optimization-Based Visualization -- Combining Multidimensional Scaling with man made Neural Networks -- purposes of Visualization

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**Sample text**

2 K¨onig’s Topology Preservation Measure The measure is introduced by K¨onig [122]. It was successfully applied in [59, 111, 128]. K¨onig’s topology preservation measure assesses the preservation of neighborhoods of points, while Spearman’s coefficient assesses the preservation of interpoint distance order for all the points in n-dimensional and d-dimensional spaces. K¨onig’s measure has two parameters—sizes of neighborhoods: μ and ν (μ < ν ). Assume that: • Xi j , j = 1, . . , μ , are μ nearest neighbors of the n-dimensional point Xi , where Xi j ∈ {X1 , X2 , .

Actually, (yi1 , yi2 ) is a linear transformation of the point Xi to the coordinate system (y1 , y2 ). If the aim is to reduce the dimensionality, the point Yi can be comprised of less coordinates, for example, d = 1, Yi = (yi1 ). In this case, we get a transformation of the point Xi to the one-dimensional space. A nonlinear transformation may be described as follows: Y = f (X), where f is a nonlinear function and Y = {Y1 ,Y2 , . . ,Ym } = {yi j , i = 1, . . , m, j = 1, . . , n}. The nonlinear transformation is more complicated than the linear one and requires more time-consuming computations.

A linear transformation may be described by linear equations Yi = Xi A. e. Yi = (yi1 , yi2 , . . , yin ) and Xi = (xi1 , xi2 , . . , xin ), then A is a square matrix, consisting of n rows and n columns. The matrix A is called a transformation matrix. If a linear transformation is used for dimensionality reduction, then d < n, Yi = (yi1 , yi2 , . . , yid ), i = 1, . . , m, and A is a matrix, consisting of n rows and d columns. Let us analyze a simple case of the linear transformation, if n = d = 2.

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