Piecewise Chebyshev factorization based nearest neighbour classification for time series

In the research field of time series analysis and mining, the nearest neighbour classifier (1NN) based on dynamic time warping distance (DTW) is well known for its high accuracy. However, the high computational complexity of DTW can lead to the expensive time consumption of classification. An effective solution is to compute DTW in the piecewise approximation space (PA-DTW), which transforms the raw data into the feature space based on segmentation, and extracts the discriminatory features for similarity measure. However, most of existing piecewise approximation methods need to fix the segment length, and focus on the simple statistical features, which would influence the precision of PA-DTW. To address this problem, we propose a novel piecewise factorization model for time series, which uses an adaptive segmentation method and factorizes the subsequences with the Chebyshev polynomials. The Chebyshev coefficients are extracted as features for PA-DTW measure (ChebyDTW), which are able to capture the fluctuation information of time series. The comprehensive experimental results show that ChebyDTW can support the accurate and fast 1NN classification.