TR-SVD: Fast and Memory Efficient Method for Time Ranged Singular Value Decomposition

Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many data mining applications including dimensionality reduction, principal component analysis, recommender systems, etc. Along with its static version, incremental SVD has been used to deal with multiple semi-infinite time series data and to identify patterns of the data. However, existing SVD methods for the multiple time series data analysis do not provide functionality for detecting patterns of data in an arbitrary time range: standard SVD requires data for all intervals corresponding to a time range query, and incremental SVD does not consider an arbitrary time range. In this paper, we propose TR-SVD (Time Ranged Singular Value Decomposition), a fast and memory efficient method for finding latent factors of time series data in an arbitrary time range. TR-SVD incrementally compresses multiple time series data block by block to reduce the space cost in storage phase, and efficiently computes singular value decomposition (SVD) for a given time range query in query phase by carefully stitching stored SVD results. Through extensive experiments, we demonstrate that TR-SVD is up to 15 x faster, and requires 15 x less space than existing methods. Our case study shows that TR-SVD is useful for capturing past time ranges whose patterns are similar to a query time range.