Robust time-series retrieval using adaptive segmental alignment

The problem of time-series retrieval arises in many fields of science and constitutes many important sub-problems including indexing, storage, representation, similarity measurement, etc. The center piece of time-series retrieval is, however, measurement of similarity between the query and the stored sequences in the data-base. Since different time-series sampled from similar phenomena can have variable lengths and/or warping, simple distance metrics such as Euclidean distance are either undefined or do not provide an accurate similarity measure. Therefore, alignment methods such as dynamic time warping have been proposed. They essentially rely on the distance between every sample point of contrasting sequences and recover their alignment using dynamic programming. These algorithms are effective when the sequences are noise-free and causal. In this work we introduce the concept of segmental sequence alignment. We claim that dynamically dividing the contrasting sequences into subsequences and recovering the optimal and monotonic matching between them instead of individual time-points can result in constructing a similarity measure more robust to noise and non-causality. We propose two different approaches and variants of them to accomplish segmental sequence alignment. The first proposed approach is an isotonic extension of Canonical Correlation Analysis (CCA) properly constrained to satisfy the time monotonicity constraint necessary for an alignment algorithm. The second approach is an extension of pair-HMM, which is a probabilistic model for aligning sequences. We have defined a proper observation model and efficient learning and inference algorithms to jointly recover the segmentation and alignment from segmental pair-HMM. We also propose a relaxation to the probabilistic model to increase the computational efficiency. We have shown the utility of our proposed techniques through extensive experiments on both synthetic and real-world data. We have applied our methods to various data sets from EEG signals to human activity. Our methods showed generally significant improvement over traditional models especially in instances when the sequences are corrupted by high levels of noise or are locally non-causal.