Automatic Registration and Clustering of Time Series

Abstract

Clustering of time series data exhibits a number of challenges not present in other settings, notably the problem of registration (alignment) of observed signals. Typical approaches include preregistration to a user-specified template or time warping approaches which attempt to optimally align series with a minimum of distortion. For many signals obtained from recording or sensing devices, these methods may be unsuitable as a template signal is not available for pre-registration, while the distortion of warping approaches may obscure meaningful temporal information. We propose a new method for automatic time series alignment within a clustering problem. Our approach, Temporal Registration using Optimal Unitary Transformations (TROUT), is based on a novel dissimilarity measure between time series that is easy to compute and automatically identifies optimal alignment between pairs of time series. By embedding our new measure in a optimization formulation, we retain well-known advantages of computational and statistical performance. We provide an efficient algorithm for TROUT-based clustering and demonstrate its superior performance over a range of competitors.

Network Clustering for Latent State and Changepoint Detection

“…Due to the Frobenious loss function, Problem (1) performs based for Gaussian-like (continuous, symmetric) data. By replacing this loss function, this convex clustering framework has been extended to a variety of other structured data types including: histogram-valued data [11], wavelet basis (sparse) data [12], time series data [13], and data drawn from arbitrary exponential families [14]. The major contribution of this paper is to extend the convex clustering framework to situations where each observation is represented by a network, as discussed in more detail below.…”