Classification, Clustering, and Data Mining Applications: by Fionn Murtagh (auth.), Dr. David Banks, Dr. Frederick R.

By Fionn Murtagh (auth.), Dr. David Banks, Dr. Frederick R. McMorris, Dr. Phipps Arabie, Prof. Dr. Wolfgang Gaul (eds.)

Modern facts research stands on the interface of records, laptop technology, and discrete arithmetic. This quantity describes new tools during this zone, with distinctive emphasis on type and cluster research. these tools are utilized to difficulties in details retrieval, phylogeny, clinical prognosis, microarrays, and different lively examine areas.

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Additional resources for Classification, Clustering, and Data Mining Applications: Proceedings of the Meeting of the International Federation of Classification Societies (IFCS), Illinois Institute of Technology, Chicago, 15–18 July 2004

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48 Jean-Yves Pin;on and Jean-Paul Rasson As there are two different pruning methods, we have two associated gluing back criteria. 1 The Elbow Gluing-Back Criterion This criterion is easy. We first compute the intraclass inertia for k classes where k decreases from the number of groups after pruning to 1. For each k, we choose the best gluing to have the maximum intraclass inertia after joining two groups. Then, as previously for pruning, we examine the graph that plots the best intraclass inertia against k.

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.

3 Dynamic Clusters Based on Adaptive Lr Distance As before, let Xi = (xL ... , xf) and Xi' = (xL, ... , xf,) be two quantitative feature vectors, representating objects i and i' belonging to class Ck, respectively. We consider the following adaptive Lr distance function, which is parameterized by the weight vector Ak = (Ak,"" A1)), to measure the dissimilarity between Xi and Xi': P d~(Xi'Xi') = LA{(lx{ -xi,lr, r (7) 2: 1. j=l In equation (7), r = 1 and r = 2 give, respectively, adaptive L1 (Diday and Govaert, 1977) and adaptive L2 distances.

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