  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 Zoom-SVD,
a fast and memory efficient method for finding latent factors of time series
data in an arbitrary time range. Zoom-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 Zoom-SVD is up to 15x faster, and
requires 15x less space than existing methods. Our case study shows that
Zoom-SVD is useful for capturing past time ranges whose patterns are similar to
a query time range.
