This repository contains the code that we used to find "multipoles", a new class of multivariate relationship patterns in time series data in datasets from climate and neuroscience domain. See [1] for further details.

Instructions to run the code:

1. The code to obtain all the empirical observations discussed in section 4.1 of techincal report can be obtained using empirical_observations.py.

2. Please keep all the codes and data files in the same directory.

3. There are two implementations of COMET algorithm; COMET.py and COMET_ADVANCED.py. The two implementations mainly differ in the choice of algorithm used to solve the clique enumeration problem in one of the intermediate steps. Script COMET.py uses bronk_kerb.py, a python implementation of bronk kerbosch's algorithm (1973), whereas COMET_ADVANCED.py uses the C++ implementation (in quick-cliques folder) provided by authors (available at https://github.com/darrenstrash/quick-cliques). contains the primary module COMET_EXT which can be called to find all multipoles in a given dataset. COMET_EXT takes five inputs:
   CorrMat: Correlation matrix of the entire dataset.
   sigma: minimum threshold on linear dependence of desired multipoles.
   delta: minimum threshold on linear gain of desired multipoles.
   edge_filt: same as parameter \mu of CoMEtExtended (see technical report for further details). Higher values of edge_filt will recover more multipoles but will increase computational time and vice-versa.
   
   group_sz: This code runs in parallel on 20 processors. Each processor examines a group of candidates to find multipoles. group_sz is the desired size of a group. I set it to 10000 on my machine.
   Graph_str(only in the version of COMET_ADVANCED.py): A filename to be given to the text files that store the correlation graphs that are used to find cliques.
   
   In the output, four lists are obtained:
   i) List of all multipoles,
   ii) List of their corresponding least eigenvalues (= 1 - linear dependence),
   iii) List of corresponding linear gains, and
   iv) List of their corresponding sizes.
   

4. Script COMET_fMRI.py was used to find all multipoles in fMRI data (using COMET.py) and also computes statistical significance of all the obtained multipoles.
   

5. Script COMET_Climate.py was used to find all multipoles in SLP data (using COMET.py) and also computes statistical significance of all the obtained multipoles.
   

6. Script COMET_Climate_Multiple_Parameters.py uses COMET_ADVANCED.py to find all multipoles in SLP data (using COMET_ADVANCED.py).
   

7. Script COMET_Climate_Multiple_Parameters.py uses COMET_ADVANCED.py to find all multipoles in fMRI data (using COMET_ADVANCED.py).
   

8. BruteForce_fMRI.py finds all multipoles in fMRI data using a brute-force approach.
   

9. Script BruteForce_Climate.py finds all multipoles in SLP data using a brute-force approach.
   

10. Script compare_with_brute_force.py can be used to compare the output of COMET_EXT with brute force.
    

[1] Technical Report