Multimodal Dimensionality Reduction via Transfer Learning

Abstract

The standard machine learning methods often assume that the training (source domain) and test (target domain) data follow the same distribution and the same feature space. However, many real-world applications suffer from a limited number of training labeled data and therefore benefit from the related available labeled datasets to train the model. In this way, since there is the distribution difference across the source and target domains (domain shift problem), the learned classifier on the training set might perform poorly on the test set. To address the shift problem, domain adaptation provides variety of solutions to learn robust classifiers to deal with distribution mismatch across the source and target domains. In this thesis, we put forward four novel frameworks to solve domain shift problem. First, we introduce a novel domain adaptation approach, referred to as Cross- and multiple- domains transfer learning via Iterative Fischer linear Discriminant Analysis (CIDA) that transfers source and target domains into a shared low dimensional FLDA-based subspace in an unsupervised manner. CIDA benefits joint FLDA and domain adaptation criterions to reduce distribution mismatch across the training and test sets. Moreover, CIDA employs an adaptive classifier to build a robust model against distribution drift across different domains. Also, CIDA generates intermediate pseudo target labels to utilize the target data in training process. CIDA refines the pseudo labels using an iterative manner to converge the model. The second proposed domain adaptation framework is entitled as robust unsupervised learning via Local and Global Adaptation (LGA), which is inspired from two main insights, local and global adaptation capability. The first insight (local adaptation capability) is to maximize the gaps between various classes of the source and target domains and also minimize the gaps between various samples of the same classes of the source and target domains. The second insight (global adaptation capability) is to minimize the conditional and marginal distribution differences between domains. Moreover, we address unsupervised domain shift problem where the difference between the marginal and conditional distributions across domains is too much. We put forward a novel framework entitled as "Joint Distribution Adaptation via Feature and Model Matching", where the difference between both marginal and conditional distributions is reduced, simultaneously. In fact, JDAFMM projects the source and target domains into a shared low dimensional subspace based on Principal Component Analyses (PCA), and then employs the nonparametric Maximum Mean Discrepancy (MMD) to measure the difference between the marginal and conditional distributions across domains. Moreover, JDAFMM learns an adaptive classifier in order to minimize the empirical risk of the prediction function on the source domain and maximizes the rate of consistency among the prediction function and the geometric data structure. At the end, we propose a unified framework that minimizes the shift between the source and target domains both geometrically and statistically, referred to as common and Domain specific feature representation to geometrical and Distributional Adaptation (DDA). Specifically, DDA finds couple of feature transformations to map the source and target domains into separate spaces where the geometrical and distributional divergences between domains are minimized. To this end, the following objectives are satisfied: (1) the marginal and conditional distribution shifts minimization, (2) the between-class scatter maximization of both source and target domains, (3) the within-class scatter minimization of both source and target domains, (4) the subspace shift minimization between domains, and (5) the target variance maximization. The performance of the proposed frameworks are evaluated on different types of benchmark domain adaptation datasets. Our comprehensive experiments demonstrate that the proposed approaches outperform other state-of-the-art domain adaptation and dimensionality reduction methods in most cases.

Key Words: Machine learning, Transfer learning, Domain shift, Fisher linear discriminant analysis, Feature- and model-based domain adaptation, Feature transformation, Model matching, Geometrical and distributional divergences.