Learning distance function by coding similarity

Aharon Bar Hillel*, Daphna Weinshall

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

13 Scopus citations


We consider the problem of learning a similarity function from a set of positive equivalence constraints, i.e. 'similar' point pairs. We define the similarity in information theoretic terms, as the gain in coding length when shifting from independent encoding of the pair to joint encoding. Under simple Gaussian assumptions, this formulation leads to a non-Mahalanobis similarity function which is efficient and simple to learn. This function can be viewed as a likelihood ratio test, and we show that the optimal similarity-preserving projection of the data is a variant of Fisher Linear Discriminant. We also show that under some naturally occurring sampling conditions of equivalence constraints, this function converges to a known Mahalanobis distance (RCA). The suggested similarity function exhibits superior performance over alternative Mahalanobis distances learnt from the same data. Its superiority is demonstrated in the context of image retrieval and graph based clustering, using a large number of data sets.

Original languageAmerican English
Number of pages8
StatePublished - 2007
Event24th International Conference on Machine Learning, ICML 2007 - Corvalis, OR, United States
Duration: 20 Jun 200724 Jun 2007


Conference24th International Conference on Machine Learning, ICML 2007
Country/TerritoryUnited States
CityCorvalis, OR


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