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 &thetas; 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 &thetas;. We develop an optimization framework to learn parametric dictionaries that vary smoothly with &thetas;. 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 &thetas; 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.