  Consider traffic data (i.e., triplets in the form of
source-destination-timestamp) that grow over time. Tensors (i.e.,
multi-dimensional arrays) with a time mode are widely used for modeling and
analyzing such multi-aspect data streams. In such tensors, however, new entries
are added only once per period, which is often an hour, a day, or even a year.
This discreteness of tensors has limited their usage for real-time
applications, where new data should be analyzed instantly as it arrives. How
can we analyze time-evolving multi-aspect sparse data 'continuously' using
tensors where time is'discrete'? We propose SLICENSTITCH for continuous
CANDECOMP/PARAFAC (CP) decomposition, which has numerous time-critical
applications, including anomaly detection, recommender systems, and stock
market prediction. SLICENSTITCH changes the starting point of each period
adaptively, based on the current time, and updates factor matrices (i.e.,
outputs of CP decomposition) instantly as new data arrives. We show,
theoretically and experimentally, that SLICENSTITCH is (1) 'Any time': updating
factor matrices immediately without having to wait until the current time
period ends, (2) Fast: with constant-time updates up to 464x faster than online
methods, and (3) Accurate: with fitness comparable (specifically, 72 ~ 100%) to
offline methods.
