Abstract—Dataset shift from the training data in a source domain to the data in a target domain poses a great challenge for many statistical learning methods. Most algorithms can be viewed as exploiting only the first-order statistics, namely, the empirical mean discrepancy to evaluate the distribution gap. Intuitively, considering only the empirical mean may not be statistically efficient. In this paper, we propose a nonparametric distance metric with a good property which jointly considers the empirical mean (Location) and sample covariance (Scatter) difference. More specifically, we propose an improved symmetric Stein’s loss function which combines the mean and covariance discrepancy into a unified Bregman matrix divergence of which Jensen-Shannon divergence between normal distributions is a particular case. Our target is to find a good feature representation which can reduce the distribution gap between different domains, at the same time, ensure that the new derived representation can encode most discriminative components with respect to the label information. We have conducted extensive experiments on several document classification datasets to demonstrate the effectiveness of our proposed method. Keywords-Domain Adaptation, Feature Extraction I
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