Finding recurrent patterns in time series using SAX.

Introduction

For this example I use one of the datasets from The UCR Time Series Classification/Clustering page & collection of test datasets - this one which represents excerpt of two-channel ECG Holter recording. The figure below shows the normalized fragment (from 4779 to 7779) of the heartbeat series:

http://jmotif.googlecode.com/svn/trunk/RCode/motifs/raw_heartbeat.png

The call of SAXFactory.seriesToDiscordsAndMotifs allows to find motifs with JMotif library in a single code line: ``` public static void main(String[args) throws Exception {

Instances tsData = readTSData();

DiscordsAndMotifs dr = SAXFactory.seriesToDiscordsAndMotifs(toDoubleSeries(tsData), windowSize,
    alphabetSize, 2, 2);

System.out.println(dr.toString());

} ```

(The full code to get instances and convert into double is here http://jmotif.googlecode.com/svn-history/r368/trunk/src/edu/hawaii/jmotif/webexample/MotifsDiscordsExample.java MotifsDiscordsExample.java) The output of this code when applied to the plotted segment of heartbeat series is like this: ``` Motifs, as a list [,...,], from last to first: 51 at [122, 123, 124, 422, 423, 570, 571, ... 57 at [106, 107, 108, 109, 110, 257, 258, ...

Discords, as a list , from last to first: 4.214421668509215 at 2305 6.7017497715148995 at 2019 ```

which informs us about two top motifs and two top discords which are highlighted in two figures below:

http://jmotif.googlecode.com/svn/trunk/RCode/motifs/motifs_heartbeat.png

here I highlighted all of the occurrences of the first motif which was observed 57 times at [106, 107, 108, 109, 110, 257, 258, ... . Note that this method reports all of the motif’ occurrences so you might want to perform some reduction, like to reduce 106, 107, 108, 109 & 110 to 106 - the very first occurrence, etc.

http://jmotif.googlecode.com/svn/trunk/RCode/motifs/discord_motifs_heartbeat.png

here I highlighted the first discord occurrence in addition to the first motif occurences.