Download e-book for iPad: Classification, Clustering, and Data Mining Applications by David Banks, Leanna House, Frederick R. McMorris, Phipps

By David Banks, Leanna House, Frederick R. McMorris, Phipps Arabie, Wolfgang Gaul

ISBN-10: 3540220143

ISBN-13: 9783540220145

This quantity describes new tools with particular emphasis on category and cluster research. those equipment are utilized to difficulties in info retrieval, phylogeny, clinical analysis, microarrays, and different energetic learn parts.

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Extra info for Classification, Clustering, and Data Mining Applications

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2 Partitioning We are in the presence of a data set f2 = {Xl, ... ,xn } of objects in lEe, and we look for a partition P = (01 , ... , OK) of f2 that minimizes the intra-classes variance K W(P) = L L Wi IIXi - gk11 2, (1) k=l xiECk where gk is the gravity center or mean vector of class Ok and Wi is the weight of object Xi; in the simplest case, Wi = lin. It is well known that the minimization of W(P) is equivalent to the maximization of the inter-classes variance K B(P) = L JLk Ilgk - g1l2, (2) k=l where JLk = 2: X iE C k Wi is the class weight of Ok, and g = 2:~=1 WiXi is the overall gravity center, since I = W(P) + B(P), I = 2:~=1 Wi IIXi - gl12 is the total variance of f2.

Here Tij (t + 1) = (1 - p)Tij (t) + P 2:~=1 LlmTij (t + 1) where i, j E {l, ... (t + 1) tJ = {Q/Lk if ant rr: uses arc (i,j) in its permutation otherwIse, ° is the amount of pheromone left by ant m, Q being a constant and Lk the length of the cycle constructed by m. For the QAP, there is also a constructive algorithm very similar to the TSP one, with a local heuristic TJih = ddh, where di = 2:;=1 dij and fh = 2:~=1 fhk is the sum of activities flux. There is also a modifying algorithm for QAP (Gambardella et al.

2 First Steps The method developed in Pin;on and Rasson (2003) builds a tree of clusters. We successively split clusters into two sub-clusters on the basis of a single variable. Therefore, finding the cutting criterion is a one-dimensional problem. Afterwards we simplify the structure of the tree by pruning. For the cutting criterion and the pruning methods, this paper just gives the main results. For the development, we refer the reader to the previous article. ). Since we work variable by variable, we can write univariate formulas.

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Classification, Clustering, and Data Mining Applications by David Banks, Leanna House, Frederick R. McMorris, Phipps Arabie, Wolfgang Gaul

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