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Our goal on one hand is to use labels or other forms of ground truth data to guide the tasks of de-noising and dimensionality reduction and balance the objectives of better prediction and better data summarization, on the other hand it is to explicitly model the noise in the feature values. We use a generalization of L2 loss, on which PCA and K-Means are based, to the Bregman family which, as a consequence widens the applicability of the proposed algorithms to cases where the data may be constrained to lie on sets of integers or sets of labels rather than R as in PCA or K-means formulations. This makes it possible to handle different prediction tasks such as classification and regression in an unified way. Two tasks are formulated (i) Transductive Total Bregman Regression (ii) Transductive Bregman PCA.

Transductive De-Noising and Dimensionality Reduction using Total Bregman Regression