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Distances and kernels based
on cumulative distribution
Hongjun Su; Hong Zhang Department of Computer Science and Information Technology, Armstrong State University, Savannah, GA,
Similarity and dissimilarity measures such as kernels and distances are key components of classiication
and clustering algorithms. We propose a novel technique to construct distances and kernel functions
between probability distributions based on cumulative distribution functions. The proposed distance
measures incorporate global discriminating information and can be computed efficiently.
Cumulative distribution function
1 Introduction
A kernel is a similarity measure that is the key component of support vector machine ([ 1 ]) and
other machine learning techniques. More generally, a distance (a metric) is a function that rep-
resents the dissimilarity between objects.
In many patern classiication and clustering applications, it is useful to measure the simil-
arity between probability distributions. Even if the data in an application is not in the form of
a probability distribution, they can often be reformulated into a distribution through a simple
A large number of divergence and affinity measures on distributions have already been
deined in traditional statistics. These measures are typically based on the probability density
functions and are not effective in detecting global changes.
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