Efficient Time-Series Clustering through Sparse Gaussian Modeling

In this work, we consider the problem of shape-based time-series clustering with the widely used Dynamic Time Warping (DTW) distance. We present a novel two-stage framework based on Sparse Gaussian Modeling. In the first stage, we apply Sparse Gaussian Process Regression and obtain a sparse representation of each time series in the dataset with a logarithmic (in the original length T) number of inducing data points. In the second stage, we apply k-means with DTW Barycentric Averaging (DBA) to the sparsified dataset using a generalization of DTW, which accounts for the fact that each inducing point serves as a representative of many original data points. The asymptotic running time of our Sparse Time-Series Clustering framework is $\Omega (T^2/{\log }^{2}T)$ times faster than the running time of applying k-means to the original dataset because sparsification reduces the running time of DTW from $\Theta \left(T^2\right)$ to $\Theta \left({\log }^{2}T\right)$. Moreover, sparsification tends to smoothen outliers and particularly noisy parts of the original time series. We conduct an extensive experimental evaluation using datasets from the UCR Time-Series Classification Archive, showing that the quality of clustering computed by our Sparse Time-Series Clustering framework is comparable to the clustering computed by the standard k-means algorithm.