Exact Discovery of Length-Range Motifs

Motif discovery is the problem of finding unknown patterns that appear frequently in real valued timeseries. Several approaches have been proposed to solve this problem with no a-priori knowledge of the timeseries or motif characteristics. MK algorithm is the de facto standard exact motif discovery algorithm but it can discover a single motif of a known length. In this paper, we argue that it is not trivial to extend this algorithm to handle multiple motifs of variable lengths when constraints of maximum overlap are to be satisfied which is the case in many real world applications. The paper proposes an extension of the MK algorithm called MK++ to handle these conditions. We compare this extensions with a recently proposed approximate solution and show that it is not only guaranteed to find the exact top pair-motifs but that it is also faster. The proposed algorithm is then applied to several real-world time series.

[1]  Y. Mohammad,et al.  Unsupervised discovery of basic human actions from activity recording datasets , 2012, 2012 IEEE/SICE International Symposium on System Integration (SII).

[2]  Xindong Wu,et al.  Advanced Research in Applied Artificial Intelligence , 2012, Lecture Notes in Computer Science.

[3]  Toyoaki Nishida,et al.  Constrained Motif Discovery in Time Series , 2009, New Generation Computing.

[4]  Irfan A. Essa,et al.  Improving Activity Discovery with Automatic Neighborhood Estimation , 2007, IJCAI.

[5]  Eamonn J. Keogh,et al.  HOT SAX: efficiently finding the most unusual time series subsequence , 2005, Fifth IEEE International Conference on Data Mining (ICDM'05).

[6]  Eamonn J. Keogh,et al.  Probabilistic discovery of time series motifs , 2003, KDD '03.

[7]  Abdullah Mueen.  Enumeration of Time Series Motifs of All Lengths , 2013, ICDM.

[8]  Toyoaki Nishida,et al.  Approximately Recurring Motif Discovery Using Shift Density Estimation , 2013, IEA/AIE.

[9]  Abdullah Mueen,et al.  Enumeration of time series motifs of all lengths , 2013, 2013 IEEE 13th International Conference on Data Mining.

[10]  Toyoaki Nishida,et al.  G-SteX: Greedy Stem Extension for Free-Length Constrained Motif Discovery , 2012, IEA/AIE.

[11]  Jeremy Buhler,et al.  Finding motifs using random projections , 2001, RECOMB.

[12]  Tibor Bosse,et al.  Recent Trends in Applied Artificial Intelligence , 2013, Lecture Notes in Computer Science.

[13]  Johannes Fürnkranz,et al.  Knowledge Discovery in Databases: PKDD 2006, 10th European Conference on Principles and Practice of Knowledge Discovery in Databases, Berlin, Germany, September 18-22, 2006, Proceedings , 2006, PKDD.

[14]  Eamonn J. Keogh,et al.  Exact Discovery of Time Series Motifs , 2009, SDM.

[15]  Michael Kipp,et al.  ANVIL - a generic annotation tool for multimodal dialogue , 2001, INTERSPEECH.

[16]  Toyoaki Nishida,et al.  Learning interaction protocols using Augmented Baysian Networks applied to guided navigation , 2010, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[17]  Tom Armstrong,et al.  Discovering Patterns in Real-Valued Time Series , 2006, PKDD.

[18]  Jessica Lin,et al.  Finding Motifs in Time Series , 2002, KDD 2002.