Order preserving sparse coding

In this paper, we investigate order-preserving sparse coding for classifying structured data whose atomic features possess ordering relationships. Examples include time sequences where individual frame-wise features are temporally ordered, as well as still images (landscape, street view, etc.) where different regions of the image are spatially ordered. Classification of these structured data is often tackled by first decomposing the input data into individual atomic features, then performing sparse coding or other processing for each atomic feature vector independently, and finally aggregating individual responses to classify the input data. However, this heuristic approach ignores the underlying order of the individual atomic features within the input data, and results in suboptimal discriminative capability. In this work, we introduce an order preserving regularizer which aims to preserve the ordering structure of the reconstruction coefficients within the sparse coding framework. An efficient Nesterov-type smooth approximation method is developed for optimization of the new regularization criterion, with theoretically guaranteed error bound. We perform extensive experiments for time series classification on a synthetic dataset, several machine learning benchmarks, and an RGB-D human activity dataset. We also report experiments for scene classification on a benchmark image dataset. The encoded representation is discriminative and robust, and our classifier outperforms state-of-the-art methods on these tasks.