### Partitioning the variables for alternating optimization of real-valued scalar fieldsPartitioning the variables for alternating optimization of real-valued scalar fields Access Restriction
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 Author Bezdek, J.C. Sponsorship IEEE Syst., Man & Cybernetics Soc Source IEEE Xplore Digital Library Content type Text Publisher Institute of Electrical and Electronics Engineers, Inc. (IEEE) File Format PDF Copyright Year ©2002 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Special computer methods Subject Keyword Computer science ♦ Input variables ♦ Fuzzy logic ♦ Minimization methods ♦ Clustering algorithms ♦ Iterative algorithms ♦ Vector quantization ♦ Expectation-maximization algorithms ♦ Convergence of numerical methods ♦ Partitioning algorithms Abstract Summary form only given, as follows. Let x be a real-valued scalar field, partitioned into t subsets of non-overlapping variables X/sub i/ (i=1, ..., t). Alternating optimization (AO) is an iterative procedure for minimizing (or maximizing) the function f(x)= f(X/sub 1/, X/sub 2/, ..., X/sub t/) jointly over all variables by alternating restricted minimizations (or maximizations) over the individual subsets of variables X/sub 1/, ..., X/sub t/. AO is the basis for the c-means clustering algorithm (t=2), many forms of vector quantization (t = 2, 3 and 4) and the expectation maximization algorithm (t=4) for normal mixture decomposition. First we review where and how AO fits into the overall optimization landscape. Then we state (without proofs) two new theorems that give very general local and global convergence and rate-of-convergence results which hold for all partitionings of x. Finally, we discuss the important problem of choosing a "best" partitioning of the input variables for the AO approach. We show that the number of possible AO iteration schemes is larger than the number of standard partitions of the input variables. Two numerical examples are given to illustrate that the selection of the t subsets of x has an important effect on the rate of convergence of the corresponding AO algorithm to a solution. Description Author affiliation: Comput. Sci. Dept., Univ. of West Florida, Pensacola, FL, USA (Bezdek, J.C.) ISBN 0780374614 Educational Role Student ♦ Teacher Age Range above 22 year Educational Use Research ♦ Reading Education Level UG and PG Learning Resource Type Article Publisher Date 2002-06-27 Publisher Place USA Rights Holder Institute of Electrical and Electronics Engineers, Inc. (IEEE) Size (in Bytes) 52.45 kB
Source: IEEE Xplore Digital Library