Classification of Weakly-Labeled Data with Partial Equivalence Relations

In many vision problems, instead of having fully labeled training data it is easier to obtain the input in small groups, where the data in each group is constrained to be from the same class but the actual class label is not known. Such constraints give rise to partial equivalence relations. The absence of class labels prevents the use of standard discriminative methods in this scenario. On the other hand, the state-of-the-art techniques that use partial equivalence relations, e.g., relevant component analysis, learn projections that are optimal for data representation, but not discrimination. We show that this leads to poor performance in several real-world applications, especially those with high-dimensional data. In this paper, we present a novel discriminative technique for the classification of weakly-labeled data which exploits the null-space of data scatter matrices to achieve good classification accuracy. We demonstrate the superior performance of both linear and nonlinear versions of our approach on face recognition, clustering, and image retrieval tasks. Results are reported on standard datasets as well as real-world images and videos from the Web.