Unsupervised Tensor based Feature Extraction and Outlier Detection for Multivariate Time Series

Although finding useful feature vector representation is one of crucial tasks as data analysis for multivariate time series, finding useful features is still challenging because both time-wise and variable-wise associations should be taken into account. To overcome this issue, we present an unsupervised feature extraction algorithm for multivariate time series, called UFEKT (Unsupervised Feature Extraction using Kernel Method and Tucker Decomposition). Our algorithm (1) constructs a kernel matrix from subsequences of each time series to account for time-wise association and (2) constructs a single tensor from the kernel matrices and performs Tucker decomposition to account for variable-wise association. Feature representation is obtained as rows of the factor matrix of the decomposed tensor in a fully unsupervised manner, which can be used to subsequent machine learning problems. Our experimental results using synthetic and real-world multivariate time series datasets in the unsupervised outlier detection scenario show that our algorithm improves detection accuracy when it is used as pre-processing for outlier detection algorithms.