Transfer Learning is an effective method of dealing with real-world problems where the training and test data are drawn from different distributions. Transfer learning methods use a labelled source domain to boost the task in a target domain that may be unsupervised or semi-supervised. However, previous transfer learning algorithms use Euclidean distance or Mahalanobis distance formula to represent the relationships between instances and to try and capture the geometry of the manifold. In many real-world scenarios, this is not enough and these functions fail to capture the intrinsic geometry of the manifold that the data exists in. In this paper, we propose a transfer learning framework called Semi-Supervised Metric Transfer Learning with Relative Constraints (SSMTR), that uses distance metric learning with a set of relative distance constraints that capture the similarities and dissimilarities between the source and the target domains better. In SSMTR, instance weights are learned for different domains which are then used to reduce the domain shift while a Relative Distance metric is learnt in parallel. We have developed SSMTR for classification problems as well and have conducted extensive experiments on several real-world datasets, particularly, the PIE Face, Office-Caltech and USPS-MNIST datasets to verify the accuracy of our proposed algorithm when compared to current transfer learning algorithms.

The performance of the supervised learning algorithms such as k-nearest neighbor (k-NN) depends on the labeled data. For some applications (Target Domain), obtaining such labeled data is very expensive and labor-intensive. In a real-world scenario, the possibility of some other related application (Source Domain) is always accompanied by sufficiently labeled data. However, there is a distribution discrepancy between the source domain and the target domain application data as the background of collecting both the domains data is different. Therefore, source domain application with sufficient labeled data cannot be directly utilized for training the target domain classifier. Domain Adaptation (DA) or Transfer learning (TL) provides a way to transfer knowledge from source domain application to target domain application. Existing DA methods may not perform well when there is a much discrepancy between the source and the target domain data, and the data is non-linear separable. Therefore, in this paper, we provide a Kernelized Unified Framework for Domain Adaptation (KUFDA) that minimizes the discrepancy between both the domains on linear or non-linear data-sets and aligns them both geometrically and statistically. The substantial experiments verify that the proposed framework outperforms state-of-the-art Domain Adaptation and the primitive methods (Non-Domain Adaptation) on real-world Office-Caltech and PIE Face data-sets. Our proposed approach (KUFDA) achieved mean accuracies of 86.83% and 74.42% for all possible tasks of Office-Caltech with VGG-Net features and PIE Face data-sets.

This paper deals with the problem of visual domain adaptation in which source domain labeled data is available for training, but the target domain unlabeled data is available for testing. Many recent domain adaptation methods merely concentrate on extracting domain-invariant features via minimizing the distributional and geometrical divergence between domains simultaneously while ignoring within-class and between-class structure properties, especially for the target domain due to the unavailability of labeled data. We propose Linear Discriminant Analysis via Pseudo Labels (LDAPL), a unified framework for visual domain adaptation that can tackle these two issues together. LDAPL is to learn a domain-invariant features across both domains with preserving important properties such as minimizing the shift between domains both statistically and geometrically, retaining the original similarity of data samples, maximizing the target domain variance, and minimizing the within-class and maximizing the between-class properties of both domains. Specifically, LDAPL preserves the target domain discriminative information (or within-class and between-class properties) using pseudo labels, and these pseudo labels are refined until convergence. Extensive experiment on several visual cross-domain benchmarks, including Office+Caltech10 with all three types of features (such as Speeded Up Robust Features (SURF), Deep Convolutional Activation Feature (DeCAF ₆ ), and Visual Geometry Group-Fully Connected layer ( $\text {VGG-FC}_{6}$ ) features), COIL20 (Columbia Object Image Library), digit, and PIE (Pose, Illumination, and Expression), LDAPL achieved average accuracies of 79.11%, 99.72%, 79.0%, and 84.50%, respectively. Comparative results on several visual cross-domain classification tasks verify that LDAPL can significantly outperform the state-of-the-art primitive and domain adaptation methods. Specifically, LDAPL gains over baseline Joint Geometrical and Statistical Alignment (JGSA) method with 6.6%, 5.3%, 6.3%, and 44.93% average accuracies on Office+Caltech10 (SURF, DeCAF ₆ , and $\text {VGG-FC}_{6}$ ), COIL20, digit, and PIE, respectively.