SMF: Drift-Aware Matrix Factorization with Seasonal Patterns

Consider a stream of time-stamped events, such as taxi rides, where we record the start and end locations of each ride. How do we learn a matrix factorization model which takes into account seasonal patterns (such as: rides toward office areas occur more frequently in the morning), and use it to forecast taxi rides tomorrow? Also, how can we model drift (such as population growth), and detect sudden changes (or anomalies)? Existing matrix factorization algorithms do not take seasonal patterns into account. We propose SMF (Seasonal Matrix Factorization), a matrix factorization model for seasonal data, and a streaming algorithm for fitting it. SMF is (a) accurate in forecasting: outperforming baselines by 13% to 60% in RMSE; (b) online: requiring fixed memory even as more data is received over time, and scaling linearly; (c) effective: providing interpretable results. In addition, we propose SMF-A, an algorithm which detects anomalies in a computationally feasible way, without forecasting every observation in the matrix.