Parametric Dictionaries and Feature Augmentation for Continuous Domain Adaptation

In this paper, we study methods for learning classifiers for the case when there is a variation introduced by an underlying continuous parameter θ representing transformations like blur, pose, time, etc. First, we consider the task of learning dictionary-based representation for such cases. Sparse representations driven by data-derived dictionaries have produced state-of-the-art results in various image restoration and classification tasks. While significant advances have been made in this direction, most techniques have focused on learning a single dictionary to represent all variations in the data. In this paper, we show that dictionary learning can be significantly improved by explicitly parameterizing the dictionaries for θ. We develop an optimization framework to learn parametric dictionaries that vary smoothly with θ. We propose two optimization approaches, (a) least squares approach, and (b) the regularized K-SVD approach. Furthermore, we analyze the variations in data induced by θ from a different yet related perspective of feature augmentation. Specifically, we extend the feature augmentation technique proposed for adaptation of discretely separable domains to continuously varying domains, and propose a Mercer kernel to account for such changes. We present experimental validation of the proposed techniques using both synthetic and real datasets.