ARTICLE IN PRESS
Dissimilarity learning for nominal data
Victor Chenga;c, Chun-Hung Lia ;∗, James T. Kwokb, Chi-Kwong Lic
aDepartment of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong
bDepartment of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
cDepartment of Electronic and Information Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong
Received 30 April 2003; accepted 27 December 2003
De.ning a good distance (dissimilarity) measure between patterns is of crucial importance in many classi.cation and
clustering algorithms. While a lot of work has been performed on continuous attributes, nominal attributes are more di0cult to
handle. A popular approach is to use the value di1erence metric (VDM) to de.ne a real-valued distance measure on nominal
values. However, VDM treats the attributes separately and ignores any possible interactions among attributes. In this paper, we
propose the use of adaptive dissimilarity matrices for measuring the dissimilarities between nominal values. These matrices are
learned via optimizing an error function on the training samples. Experimental results show that this approach leads to better
classi.cation performance. Moreover, it also allows easier interpretation of (dis)similarity between di1erent nominal values.
? 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.
Keywords: Nominal attributes; Pattern classi.cation; Dissimilarities; Distance measure; Classi.ers
Many pattern recognition algorithms rely on the use of a
pairwise similarity (e.g., inner product) or dissimilarity (e.g.,
distance) measure between patterns. Examples include the
nearest-neighbor classi.ers, radial basis function networks,
k-means clustering and, more recently, kernel methods [1,2].
For patterns with continuous (quantitative) attributes, a va-
riety of distance metrics have been widely studied. For
example, for tw