Learning with Equivalence Constraints and the Relation to Multiclass Learning

Abstract. 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 ...

• Type: Conference
• Year: 2003
• Where: COLT
• Authors: Aharon Bar-Hillel, Daphna Weinshall
• Keywords: Binary Classification Problem, COLT 2003, Multiclass Problem, Unlabeled Partition Problem