Counting the SAX representations of a time series

This section of the chapter presents a utility that counts the SAX representations of a time series. The Python data structure behind the logic of the utility is a dictionary, where the keys are the SAX representations converted into strings and the values are integers.

The code for counting.py is as follows:

#!/usr/bin/env python3
import sys
import pandas as pd
from sax import sax
def main():
     if len(sys.argv) != 5:
           print("TS1 sliding_window cardinality segments")
           print("Suggestion: The window be a power of 2.")
           print("The cardinality SHOULD be a power of 2.")
           sys.exit()
     file = sys.argv[1]
     sliding = int(sys.argv[2])
     cardinality = int(sys.argv[3])
     segments = int(sys.argv[4])
     if sliding % segments != 0:
           print("sliding MODULO segments != 0...")
           sys.exit()
     if sliding <= 0:
           print("Sliding value is not allowed:", sliding)
           sys.exit()
     if cardinality <= 0:
           print("Cardinality Value is not allowed:", cardinality)
           sys.exit()
     ts = pd.read_csv(file, names=['values'], compression='gzip')
     ts_numpy = ts.to_numpy()
     length = len(ts_numpy)
     KEYS = {}
     for i in range(length - sliding + 1):
           t1_temp = ts_numpy[i:i+sliding]
           # Generate SAX for each subsequence
           tempSAXword = sax.createPAA(t1_temp, cardinality, segments)
           tempSAXword = tempSAXword[:-1]
           if KEYS.get(tempSAXword) == None:
                 KEYS[tempSAXword] = 1
           else:
                 KEYS[tempSAXword] = KEYS[tempSAXword] + 1
     for k in KEYS.keys():
           print(k, ":", KEYS[k])
if __name__ == '__main__':
     main()

The for loop splits the time series into subsequences and computes the SAX representation of each subsequence using sax.createPAA(), before updating the relevant counter in the KEYS dictionary. The tempSAXword = tempSAXword[:-1] statement removes an unneeded underscore character from the SAX representation. Finally, we print the content of the KEYS dictionary.

The output of counting.py should be similar to the following:

$ ./counting.py ts1.gz 4 4 2
10_01 : 18
11_00 : 8
01_10 : 14
00_11 : 7

What does this output tell us?

For a time series with 50 elements (ts1.gz) and a sliding window size of 4, there exist 18 subsequences with the 10_01 SAX representation, 8 subsequences with the 11_00 SAX representation, 14 subsequences with the 01_10 SAX representation, and 7 subsequences with the 00_11 SAX representation. For easier comparison, and to be able to use a SAX representation as a key to a dictionary, we convert [01 10] into the 01_10 string, [11 00] into 11_00, and so on.

How many subsequences does a time series have?

Keep in mind that given a time series with n elements and a sliding window size of w, the total number of subsequences is n – w + 1.

counting.py can be used for many practical tasks and will be updated in Chapter 3.

The next section discusses a handy Python package that can help us learn more about processing our time series from a statistical point of view.