Download Joining Similarity Measures Using Quasi-Arithmetic Means Etienne Cuvelier , Marie-Aude Aufaure

Joining Similarity Measures Using Quasi-Arithmetic
Means
Etienne Cuvelier1,∗ , Marie-Aude Aufaure2
1. ICHEC, Brussels Management School, Bruxelles, Belgium
2. Ecole Centrale Paris, Paris, France
? Contact author: [email protected]
Keywords: Similarity Measures, Dissimilarity Measures, Combining Measures, Quasi-Arithmetic
Means, Archimedean Generator.
A lot of data analysis methods are based on similarity or dissimilarity measures but, most of the
times, these measures are defined for one type of data (real multidimensional data, interval data,
functional data, nodes in graphs,...). This fact implies that all the techniques of knowledge extraction based on such measures can be performed only on the data type for which they are defined.
But the description and the modelling of real situations require the joint use of several kind of data.
Symbolic Data Analysis deals also with this situation describing concepts using real data, interval
data, histogram data, set data and/or probability distributions. We propose a new technique of
combination of different measures in one single result. The method is based on Quasi-Arithmetics
Means using Archimedean Generators. Quasi-Arithmetic Means with this kind of generators have
several advantages to compute a resulting measure starting from several measures (computed on
different types of data describing the same concept or individual): they allow to choose to emphasize the similarity or the dissimilarity between objects, they have flexible parameters, its possible
to mix similarities and dissimilarities to compute a resulting similarity (or dissimilarity).
The resulting measure (similarity or dissimilarity) can be used in any existing algorithm based on
such measures: clustering, supervised classification...
We will give some examples of use of this method on attributed networks and on symbolic data.
References
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Yang Zhou, Hong Cheng, and Jeffrey Xu Yu (2009). Graph clustering based on structural/attribute
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J. Kim and L. Billard (2013). Dissimilarity measures for histogram-valued observations. Communications in Statistics-Theory and Method , 42, 283 – 303.