Generalized Time Warping Invariant Dictionary Learning for Time Series Classification and Clustering

Dictionary learning is an effective tool for pattern recognition and classification of time series data. However, real-world time series data often exhibit temporal misalignment due to temporal delay, scaling or other temporal transformations, which poses significant challenges for effective dictionary learning. Dynamic time warping (DTW) is commonly used for dealing with such misalignment issues. Nevertheless, the DTW suffers overfitting or information loss due to its discrete nature in aligning time series data. To address this issue, we propose a generalized time warping invariant dictionary learning algorithm in this paper. Our approach features a generalized time warping operator, which consists of linear combinations of continuous basis functions for facilitating continuous temporal warping. The integration of the proposed operator and the dictionary learning is formulated as an optimization problem, where the block coordinate descent method is employed to jointly optimize warping paths, dictionaries, and sparse coefficients. The optimized results are then used as hyperspace distance measures to feed classification and clustering algorithms. The superiority of the proposed method in terms of dictionary learning, classification, and clustering is validated through ten sets of public datasets in comparison with various benchmark methods.