Transductive Learning Based on Low-Rank Representation with Convex Constraints

Transductive learning is a problem to predict labels of unlabeled data exploiting both of labeled and unlabeled data. There are various methods for transductive learning, which are often variants of existing machine learning methods. In this paper, we use one of the existing unsupervised methods, row-rank representation (LRR), for transductive learning. The proposed method consists of two phases: clustering and classification. In the clustering phase, we apply a revised LRR to the data set including both of labeled and unlabeled data. Then, we obtain a modification of the data set, which reflects cluster structure behind the data set. In the classification phase, we classify unlabeled data by using the modified data set obtained in the clustering phase. We use a classification method which is inspired by LRR. That is, for each class, we approximate each unlabeled data point by the labeled data set of the class, then classify the point to the class with the smallest approximation error. Finally, we examine performance of the proposed method by numerical experiments.