Mining Approximate Motifs in Time Series

Abstract

The problem of discovering previously unknown frequent patterns in time series, also called motifs, has been recently introduced. A motif is a subseries pattern that appears a significant number of times. Results demonstrate that motifs may provide valuable insights about the data and have a wide range of applications in data mining tasks. The main motivation for this study was the need to mine time series data from protein folding/unfolding simulations. We propose an algorithm that extracts approximate motifs, i.e. motifs that capture portions of time series with a similar and eventually symmetric behavior. Preliminary results on the analysis of protein unfolding data support this proposal as a valuable tool. Additional experiments demonstrate that the application of utility of our algorithm is not limited to this particular problem. Rather it can be an interesting tool to be applied in many real world problems.

A disk-aware algorithm for time series motif discovery

“…Many of the methods for time series motif discovery are based on searching a discrete approximation of the time series, inspired by and leveraging off the rich literature of motif discovery in discrete data such as DNA sequences (Chiu et al 2003;Patel et al 2002;Ferreira et al 2006;Minnen et al 2007a;Yoshiki et al 2005;Simona and Giorgio 2004). Discrete representations of the real-valued data must introduce some level of approximation in the motifs discovered by these methods.…”

“…Motifs are defined and categorized using their support, distance, cardinality, length, dimension, underlying similarity measure, etc. Motifs may be restricted to have a minimum count of participating similar subsequences (Chiu et al 2003;Ferreira et al 2006) or may only be a single closest pair (Mueen et al 2009). Motifs may also be restricted to have a distance lower than a threshold (Chiu et al 2003;Ferreira et al 2006;Yankov et al 2007), or restricted to have a minimum density (Minnen et al 2007b).…”

“…Motifs may be restricted to have a minimum count of participating similar subsequences (Chiu et al 2003;Ferreira et al 2006) or may only be a single closest pair (Mueen et al 2009). Motifs may also be restricted to have a distance lower than a threshold (Chiu et al 2003;Ferreira et al 2006;Yankov et al 2007), or restricted to have a minimum density (Minnen et al 2007b). Most of the methods find fixed length motifs (Chiu et al 2003;Ferreira et al 2006;Mueen et al 2009;Yankov et al 2007), while there are a handful of methods for variable length motifs (Minnen et al 2007b;Yoshiki et al 2005;Tang and Liao 2008).…”

“…Motifs may also be restricted to have a distance lower than a threshold (Chiu et al 2003;Ferreira et al 2006;Yankov et al 2007), or restricted to have a minimum density (Minnen et al 2007b). Most of the methods find fixed length motifs (Chiu et al 2003;Ferreira et al 2006;Mueen et al 2009;Yankov et al 2007), while there are a handful of methods for variable length motifs (Minnen et al 2007b;Yoshiki et al 2005;Tang and Liao 2008). Multidimensional motifs and subdimensional motifs are defined (Minnen et al 2007a) and heuristic methods to find them are explored in (Minnen et al 2007a,b;Yoshiki et al 2005).…”

“…In spite of extensive research in recent years (Chiu et al 2003;Ferreira et al 2006;Mueen et al 2009;Yankov et al 2007), finding time series motifs exactly in massive databases is an open problem. Previous efforts either found approximate motifs or considered relatively small datasets residing in main memory (or in most cases, both).…”