A framework for semi-supervised metric transfer learning on manifolds

A common assumption of statistical learning theory is that the training and testing data are drawn from the same distribution. However, in many real-world applications, this assumption does not hold true. Hence, a realistic strategy, Cross Domain Adaptation (DA) or Transfer Learning (TA), can be used to employ previously labelled source domain data to boost the task in the new target domain. Previously, Cross Domain Adaptation methods have been focused on re-weighting the instances or aligning the cross-domain distributions. However, these methods have two significant challenges: (1) There is no proper consideration of the unlabelled data of target task as in the real-world, an abundant amount of unlabelled data is available, (2) The use of normal Euclidean distance function fails to capture the appropriate similarity or dissimilarity between samples. To deal with this issue, we have proposed a Semi-Supervised Metric Transfer Learning framework called SSMT that reduces the distribution between domains both statistically and geometrically by learning the instance weights, while a regularized distance metric is learned to minimize the within-class co-variance and maximize the between-class co-variance simultaneously for the target domain. Compared with the previous works where Mahalanobis distance metric and instance weights are learned by using the labelled data or in a pipelined framework that leads to a decrease in the performance, our proposed SSMT attempts to learn a regularized distance metric and instance weights by considering unlabelled data in a parallel framework. Experimental evaluation on three cross-domain visual data sets, e.g., PIE Face, Handwriting Digit Recognition on MNIST-USPS and Object Recognition, demonstrates the effectiveness of our designed approach on facilitating the unlabelled target task learning, compared to current state-of-the-art domain adaptation approaches. (C) 2019 Elsevier B.V. All rights reserved.