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In this paper, we present a new algorithm for semi-supervised representationlearning. In this algorithm, we first find a vector representation for thelabels of the data points based on their local positions in the space. Then, wemap the data to lower-dimensional space using a linear transformation such thatthe dependency between the transformed data and the assigned labels ismaximized. In fact, we try to find a mapping that is as discriminative aspossible. The approach will use Hilber-Schmidt Independence Criterion (HSIC) asthe dependence measure. We also present a kernelized version of the algorithm,which allows non-linear transformations and provides more flexibility infinding the appropriate mapping. Use of unlabeled data for learning newrepresentation is not always beneficial and there is no algorithm that candeterministically guarantee the improvement of the performance by exploitingunlabeled data. Therefore, we also propose a bound on the performance of thealgorithm, which can be used to determine the effectiveness of using theunlabeled data in the algorithm. We demonstrate the ability of the algorithm infinding the transformation using both toy examples and real-world datasets.

Semi-Supervised Representation Learning based on Probabilistic Labeling