High-dimensional time series clustering: nonparametric trend estimation

Abstract

The era of big data has produced extensive methodologies for extracting features/patterns from complex time series data. From a data science per- spective these methodologies have emerged from multiple disciplines, includ- ing statistics, signal processing/engineering, and computer science. Cluster- ing is a solution for classifying enormous data when there is not any previous knowledge about classes obtaining numerosity reduction for instance. The goal of clustering is to identify structure in an unlabelled data set by organizing data into homogeneous groups where the within-group dissim- ilarity is minimized and the between-group dissimilarity is maximized. Data are called static if all their feature values do not change with time, or the change negligible. The most of clustering analyses has been performed on static data. Just like static data clustering, time series clustering requires a clustering algorithm or procedure to form clusters given a set of unlabelled data objects and the choice of clustering algorithm depends both on the type of data available and on the particular purpose and application. Considering time series as discrete objects, conventional clustering pro- cedures can be used to cluster a set of individual time series with respect to their similarity such that similar time series are grouped into the same clus- ter. From this perspective time series clustering techniques have been devel- oped, most of them critically depend on the choice of distance (i.e., similar- ity) measure. In general, the literature de nes three di erent approaches to cluster time series: (i) Shape-based clustering, clustering is performed based on the shape similarity, where shapes of two time series are matched using a non-linear stretching and contracting of the time axes; (ii) Feature-based clustering, raw time series are transformed into the feature vector of lower di- mension where, for each time series a xed-length and an equal-length feature vector is created (usually a set of statistical characteristics); (iii) Model-based clustering assumes a mathematical model for each cluster and attempts to t the data into the assumed model. ... [edited by Author]