Showing papers by "James C. Bezdek published in 2003"
TL;DR: Under reasonable assumptions, the general AO approach is shown to be locally, q-linearly convergent, and to also exhibit a type of global convergence.
Abstract: Let f : Rs → R be a real-valued function, and let x = (x1,...,xs)T ∈ Rs be partitioned into t subsets of non-overlapping variables as x = (X1,...,Xt)T, with Xi ∈ Rpi for i = 1,...,t, Σi=1tpi = s. Alternating optimization (AO) is an iterative procedure for minimizing f(x) = f(X1, X2,..., Xt) jointly over all variables by alternating restricted minimizations over the individual subsets of variables X1,...., Xt. Alternating optimization has been (more or less) studied and used in a wide variety of areas. Here a self-contained and general convergence theory is presented that is applicable to all partitionings of x. Under reasonable assumptions, the general AO approach is shown to be locally, q-linearly convergent, and to also exhibit a type of global convergence.
383 citations
TL;DR: This work considers two kinds of non-numerical patterns provided by the World Wide Web: document contents such as the text parts of web pages, and sequences of webpages visited by particular users, so-called web logs.
94 citations
TL;DR: The display method introduced here uses images generated from the results of any prototype generator clustering algorithm to do cluster validation.
60 citations
25 May 2003
TL;DR: The proposed approach uses intensity images generated from the results of any prototype generator clustering algorithm as a means for cluster validation.
Abstract: Conventional cluster validity techniques usually represent all the validity information available about a particular clustering by a single number. The display method introduced here is an alternative to standard validity functionals. The proposed approach uses intensity images generated from the results of any prototype generator clustering algorithm as a means for cluster validation. Several numerical examples are given to illustrate the method.
9 citations
01 Jan 2003
TL;DR: For text data, the RACE cluster centers extracted by RACE from internet newsgroup articles serve as keywords for those articles that can be used for automatic document classification.
Abstract: Clustering is used to determine partitions and prototypes from pattern sets. Sets of numerical patterns can be clustered by alternating optimization (AO) of clustering objective functions or by alternating cluster estimation (ACE). Sets of non-numerical patterns can often be represented numerically by (pairwise) relations. For text data, relational data can be automatically computed using the Levenshtein (or edit) distance. These relational data sets can be clustered by relational ACE (RACE). For text data, the RACE cluster centers can be used as keywords. In particular, the cluster centers extracted by RACE from internet newsgroup articles serve as keywords for those articles. These keywords can be used for automatic document classification.
6 citations