Optimal multi-scale patterns in time series streams

We introduce a method to discover optimal local patterns, which concisely describe the main trends in a time series. Our approach examines the time series at multiple time scales (i.e., window sizes) and efficiently discovers the key patterns in each. We also introduce a criterion to select the best window sizes, which most concisely capture the key oscillatory as well as aperiodic trends. Our key insight lies in learning an optimal orthonormal transform from the data itself, as opposed to using a predetermined basis or approximating function (such as piecewise constant, short-window Fourier or wavelets), which essentially restricts us to a particular family of trends. We go one step further, lifting even that limitation. Furthermore, our method lends itself to fast, incremental estimation in a streaming setting. Experimental evaluation shows that our method can capture meaningful patterns in a variety of settings. Our streaming approach requires order of magnitude less time and space, while still producing concise and informative patterns.