Abstract
We propose a complete characterization of a certain class of aggregation-invariant dissimilarities between row (or column) profiles. This class (for which row and column dispersions coincide) contains the chi-square, ratio, Kullback-Leibler, Hellinger, Cressie-Read dissimilarities, as well as a presumably new “type s” class of dissimilarities. Distinguishing between two forms of Huygens’ principle from Classical Mechanics, we show “type s” dissimilarities to satisfy the weak Huygens’ principle; the strong Huygens’ principle however holds for a single member of the class, namely the chi-square dissimilarity. Extending the concept of dissimilarity to “type s” divergences restores the strong principle.
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© 2000 Springer-Verlag Berlin · Heidelberg
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Bavaud, F. (2000). On a Class of Aggregation-invariant Dissimilarities Obeying the Weak Huygens’ Principle. In: Kiers, H.A.L., Rasson, JP., Groenen, P.J.F., Schader, M. (eds) Data Analysis, Classification, and Related Methods. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59789-3_21
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DOI: https://doi.org/10.1007/978-3-642-59789-3_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67521-1
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