Minimum Jump Cost dissimilarity measure in Python

This python library implements the Minimum Jump Cost (MJC) dissimilarity measure devised by Joan Serra and Josep Lluis Arcos in 2012. The MJC dissimilarity measure was shown to outperform the Dynamic Time Warp (DTW) dissimilarity measure on several datasets. You can read their paper here: https://www.iiia.csic.es/sites/default/files/4584.pdf.

This library can compute the MJC for timeseries with different sampling rates, arbitrarily spaced data points, and non-overlapping regions.

How to install

pymjc is available from PyPi. Run the following in a command line terminal:
pip install pymjc

How to use

Example:

from pymjc import mjc
import numpy as np

series_1 = np.array([1,2,3,2,1])
series_2 = np.array([0,1,2,1,0])

d_xy, abandoned = mjc(series_1, series_2, show_plot=True)

print(f"The MJC dissimilarity of series 1 and series 2 is {d_xy}")

There are some options for reducing the computational load of this algorithm. They are detailed in the next section.

More detailed information

The time series s1 and s2 are specified as follows:

• They may be python Lists or numpy.ndarrays
• They may be of different length.
• They may or may not have time information.
• If one of the time series has time information, the other must also have it.
• Their datatype may be floats or integers.

A time series with no time information is just a list of values. The first element of the list corresponds to the earliest point in the time series.
Example: s1 = [d₀, d₁, d₂, ...], where dᵢ is the i-th value of the time series.

A time series with time information must be a 2D array of shape (2, n). The data at index 0 are time data, and the data at index 1 is amplitude data.
Example: s1 = [[t₀, t₁, t₂, ...], [d₀, d₁, d₂, ...]], where tᵢ is the time of the i-th measurement. The time values may be integers or floats, and need not begin at 0.

To visualize the algorithm, you may pass the variable show_plot=True. This will generate a plot with the two time series, and arrows signifying the jumps that the algorithm made when calculating the Minimum Jump Cost.

To stop the algorithm early, pass a value for dxy_limit. If the dissimilarity measure exceeds this value during computation, it is abandoned.

Performance

The time series are cast to numpy arrays. The checking and casting lowers execution speed. Therefore, an option to disable this checking and casting has been implemented. If you are certain that the time series s1 and s2 are numpy.ndarrays of the format [[time data],[amplitude data]], you may pass the variable override_checks=True.

The algorithm locates the overlapping region between the two timeseries. This step is skipped if the first and last timestamps are equal between the two timeseries. If your data has no time data, it is skipped if there is the same number of samples in each timeseries.

As part of the calculation of the MJC, the algorithm calculates the standard deviations of the amplitude data, and the average sampling periods of s1 and s2. This lowers execution speed, but is required. However, if you know the standard deviations and/or the average time difference between data points of either (or both) s1 and s2 a-priori, you may pass these as variables. They are named std_s1, std_s2, tavg_s1, and tavg_s2. Any number of these may be passed. The ones which are not passed will be calculated.

mjc() input parameters:

s1              : numpy ndarray | List. Time series 1.
s2              : numpy ndarray | List. Time series 2.
dxy_limit       : Optional float. Early abandoning variable.
beta            : Optional float. Time jump cost. 
show_plot       : Optional bool. If True, displays a plot that visualize the algorithms jump path. Default False.
std_s1          : Optional float. Standard deviation of time series s1.
std_s2          : Optional float. Standard deviation of time series s2.
tavg_s1         : Optional float. Average sampling period of time series 1.
tavg_s2         : Optional float. Average sampling period of time series 2. 
return_args     : Optional bool. If True, returns the values for std_s1, std_s2, tavg_s1, tavg_s2, s1, and s2.
override_checks : Optional bool. Override checking and casting