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...means often converges to poor quality clusters. It is also data-order independent unlike standard k-means where the order of the input data affects the positioning of the cluster centres and Bradley (=-=Bradley et al., 1999-=-) shows that k-medoids provides better class separation than k-means and hence is better suited to a novelty recognition task due to the improved separation capabilities. However, k-means outperforms ...

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...ed), and a model analysis phase. In such an approach, the last objective is “to process the data in order to extract valid, novel, potentially useful, and ultimately understandable structure in data” =-=[22]-=-. of Barrax (Spain). We have used six hyperspectral images acquired with the HyMAP spectrometer during the DAISEX1999 campaign. This instrument provides 128 bands across the reflective solar wavelengt...

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... into what is known as clusters and thus the objective measures how well X can be partitioned into k clusters. The k-median problem has numerous applications, starting from clustering and data mining =-=[3]-=- to assigning efficient sources of supplies to minimize the transportation cost([14, 20]). The difficulty of the k-median problem lies in the hard constraint that only k facilities are allowed to be o...

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...n predict if a customer will make a purchase within a session or not and, thus, classify the customer into “buyer” versus “nonbuyer.” Other classification problems include predicting if a customer will be a repeat visitor or will click on an advertisement, or will follow one of several recommendations. The use of optimization methods for learning optimal discriminant functions can be traced all the way back to the work of Fisher (1936). Many researchers have extended this approach across the last 40 years, and more recent surveys of some of these methods can be found in Mangasarian (1997) and Bradley et al. (1999). We now consider linear, nonlinear, and integer programming methods for building classifiers. 3.5.1. Building Classifiers Using Linear Programming. A linear binary classification problem can be 1336 Management Science/Vol. 49, No. 10, October 2003 PADMANABHAN AND TUZHILIN On the Use of Optimization for Data Mining formulated as follows. Given two sets of points A and B in the n-dimensional real space Rn, the task is to separate them with a hyperplane wx+ ) = 0. The separable case was studied in Mangasarian (1965) in which A and B can be separated by a hyperplane wx+) = 0 so that the condition...

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...en the function f(S, S) achieves its minimum when each point is assigned to its closest cluster center. Therefore, MSSC can be described by the following bilevel programming problem (see for instance =-=[4, 27]-=-). min c1,··· ,ck n� i=1 min{�si − c1� 2 , · · · , �si − ck� 2 }. (1) Geometrically speaking, assigning each point to the nearest center fits into a framework called Voronoi Program, and the resulting...

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...ngst them are the k-nearest neighbor and various mathematical programming methods [2] [3]. Bradley et al. provide a comprehensive review of various mathematical programming approaches for data mining =-=[4]-=-. Various inductive learning approaches have been developed for classification, including decision 2strees, neural networks, support vector machines. More recently, evolutionary computation techniques...