Learning with equivalence constraints and the relation to multiclass learning

Aharon Bar-Hillel*, Daphna Weinshall

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations


We study the problem of learning partitions using equivalence constraints as input. This is a binary classification problem in the product space of pairs of datapoints. The training data includes pairs of datapoints which are labeled as coming from the same class or not. This kind of data appears naturally in applications where explicit labeling of datapoints is hard to get, but relations between datapoints can be more easily obtained, using, for example, Markovian dependency (as in video clips). Our problem is an unlabeled partition problem, and is therefore tightly related to multiclass classification. We show that the solutions of the two problems are related, in the sense that a good solution to the binary classification problem entails the existence of a good solution to the multiclass problem, and vice versa. We also show that bounds on the sample complexity of the two problems are similar, by showing that their relevant 'dimensions' (VC dimension for the binary problem, Natarajan dimension for the multiclass problem) bound each other. Finally, we show the feasibility of solving multiclass learning efficiently by using a solution of the equivalent binary classification problem. In this way advanced techniques developed for binary classification, such as SVM and boosting, can be used directly to enhance multiclass learning.

Original languageAmerican English
Pages (from-to)640-654
Number of pages15
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
StatePublished - 2003
Event16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003 - Washington, DC, United States
Duration: 24 Aug 200327 Aug 2003


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