Effort-To-Compress in Python

• What is this
  • References
• What can it do
  • Study Haemodynamics, Heart-Rate Variability and Cardiac Aging using ECG/EKG
  • Network Neuroscience, Psychophysics and Scientific Study of Consciousness
  • Genome Complexity Analysis and Classification of Nucleotide Sequences
  • Audio Signal Processing and Denoising
• How to use it
  • Dependencies
  • Installation
  • Updating
  • Usage
  • Testing
  • MATLAB Implementation
• TODO
• License

A Python implementation of the compression-complexity measure called Effort-To-Compress or ETC. ETC captures the compressibility and complexity of discrete symbolic sequences using lossless compression. It has been shown to robustly estimate complexity, comparing favorably for short and noisy time series in comparison with entropy and Lempel-Ziv complexity.

Using ETC, causal information flow between multiple discrete symbolic sequences can be assessed and recently, such a use has been presented, rigorously proven and demonstrated to be an effective model-free measure of causality. Introduced as Compression-Complexity Causality or CCC, this measure is robust to numerous data contaminants, noise sources and pre-processing artifacts. On comparison with Granger Causality and Transfer Entropy, CCC compares favorably and outperforms them on synthetic as well as real world causal interactions. An implementation of CCC is included in this repository.

While any lossless compressor may be used with ETC and subsequently with CCC, a grammar-based lossless compression algorithm called Non-Sequential Recursive Pair Substitution or NSRPS is used presently. NSRPS has been rigorously studied and shown to be an effective tool for data compression and entropy estimation. This repository also contains a fast Cython implementation of NSRPS for use with ETC and CCC.

• Benedetto, Dario, Emanuele Caglioti, and Davide Gabrielli. “Non-Sequential Recursive Pair Substitution: Some Rigorous Results.” Journal of Statistical Mechanics: Theory and Experiment 2006, no. 09 (September 25, 2006): P09011–P09011. https://doi.org/10.1088/1742-5468/2006/09/P09011.
• Balasubramanian, Karthi, Gayathri R. Prabhu, Lakshmipriya V. K. , Maneesha Krishnan, Praveena R. , and Nithin Nagaraj. “Classification of Periodic, Chaotic and Random Sequences Using NSRPS Complexity Measure.” ArXiv:1205.4886 [Nlin], May 22, 2012. http://arxiv.org/abs/1205.4886.
• Nagaraj, Nithin, Karthi Balasubramanian, and Sutirth Dey. “A New Complexity Measure for Time Series Analysis and Classification.” The European Physical Journal Special Topics 222, no. 3–4 (July 2013): 847–60. https://doi.org/10.1140/epjst/e2013-01888-9.
• Nagaraj, Nithin, and Karthi Balasubramanian. “Dynamical Complexity of Short and Noisy Time Series: Compression-Complexity vs. Shannon Entropy.” The European Physical Journal Special Topics 226, no. 10 (July 2017): 2191–2204. https://doi.org/10.1140/epjst/e2016-60397-x.
• Kathpalia, Aditi, and Nithin Nagaraj. “Data-Based Intervention Approach for Complexity-Causality Measure.” PeerJ Computer Science 5 (May 27, 2019): e196. https://doi.org/10.7717/peerj-cs.196.

• Balasubramanian, Karthi, Nithin Nagaraj, and Sandipan Pati. “Chaos or Randomness? Effect of Vagus Nerve Stimulation During Sleep on Heart-Rate Variability.” IETE Journal of Research, June 30, 2020, 1–7. https://doi.org/10.1080/03772063.2020.1780165.
• Srilakshmi, P, Karthi Balasubramanian, Nithin Nagaraj, and Sandipan Pati. “Multiscale Analysis of Heart Rate Variability Using Subsymmetry and Effort-to-Compress Complexity Measures.” In 2018 15th IEEE India Council International Conference (INDICON), 1–5. Coimbatore, India: IEEE, 2018. https://doi.org/10.1109/INDICON45594.2018.8986972.
• Thanaj, Marjola, Andrew J. Chipperfield, and Geraldine F. Clough. “Analysis of Microvascular Blood Flow and Oxygenation: Discrimination between Two Haemodynamic Steady States Using Nonlinear Measures and Multiscale Analysis.” Computers in Biology and Medicine 102 (November 2018): 157–67. https://doi.org/10.1016/j.compbiomed.2018.09.026.
• Balasubramanian, Karthi, K Harikumar, Nithin Nagaraj, and Sandipan Pati. “Vagus Nerve Stimulation Modulates Complexity of Heart Rate Variability Differently during Sleep and Wakefulness.” Annals of Indian Academy of Neurology 20, no. 4 (2017): 403. https://doi.org/10.4103/aian.AIAN_148_17.
• Balasubramanian, Karthi, and Nithin Nagaraj. “Aging and Cardiovascular Complexity: Effect of the Length of RR Tachograms.” PeerJ 4 (2016): e2755. https://doi.org/10.7717/peerj.2755.

• Ashley J. Funkhouser. "The Role of Action in Affordance Perception Using Virtual Reality" 2020. Honors College Thesis with Dr. Alen Hajnal, Department of Psychology, The University of Southwestern Mississipi. https://aquila.usm.edu/honors_theses/714/
• Agarwal, Nikita, Aditi Kathpalia, and Nithin Nagaraj. “Distinguishing Different Levels of Consciousness Using a Novel Network Causal Activity Measure.” In 2019 Global Conference for Advancement in Technology (GCAT), 1–5. BANGALURU, India: IEEE, 2019. https://doi.org/10.1109/GCAT47503.2019.8978424.
• Virmani, Mohit, and Nithin Nagaraj. “A Novel Perturbation Based Compression Complexity Measure for Networks.” Heliyon 5, no. 2 (February 2019): e01181. https://doi.org/10.1016/j.heliyon.2019.e01181.
• Kondo, Fumika. “Can Alterations in the Temporal Structure of Spontaneous Brain Activity Serve as a Disease-Specific Biomarker for Schizophrenia? A Multi Cohort FMRI Study,” 2017. https://doi.org/10.20381/RUOR-20801.
• Kimiskidis, Vasilios K., Christos Koutlis, Alkiviadis Tsimpiris, Reetta Kälviäinen, Philippe Ryvlin, and Dimitris Kugiumtzis. “Transcranial Magnetic Stimulation Combined with EEG Reveals Covert States of Elevated Excitability in the Human Epileptic Brain.” International Journal of Neural Systems 25, no. 05 (August 2015): 1550018. https://doi.org/10.1142/S0129065715500185.

• Balasubramanian, Karthi, and Nithin Nagaraj. “Automatic Identification of SARS Coronavirus Using Compression-Complexity Measures.” Preprint. Bioinformatics, March 27, 2020. https://doi.org/10.1101/2020.03.24.006007.

• Kiefer, Chris, Overholt, Dan and Eldridge, Alice (2020) Shaping the behaviour of feedback instruments with complexity-controlled gain dynamics. New Interfaces for Musical Expression, Birmingham, UK, 21-25 July 2020. Published in: Proceedings of the International Conference on New Interfaces for Musical Expression. 343-348. NIME, Birmingham, UK. ISSN 2220-4806. https://sro.sussex.ac.uk/id/eprint/91009/
• Li, Guohui, Qianru Guan, and Hong Yang. “Noise Reduction Method of Underwater Acoustic Signals Based on CEEMDAN, Effort-To-Compress Complexity, Refined Composite Multiscale Dispersion Entropy and Wavelet Threshold Denoising.” Entropy 21, no. 1 (December 24, 2018): 11. https://doi.org/10.3390/e21010011.

The simplest way right now is to use pip to clone this repository and install locally inside a conda or a virtualenv environment. This way several functions implemented in Cython will be automatically compiled natively on the host system. Instructions below.

While the repository is called ETCPy, the package namespsace available for use is ETC. All functionality is available through the ETC namespace.

For running tests (strongly recommended), additional packages need to be installed.

• GNU/Linux-based distributions (tested on Ubuntu 16.04, 18.04, 20.04)
• Currently does not work out of the box on Windows. Cython and C/C++ build toolchain need to be setup properly for compilation on Windows to work. It may work with some gymnastics using MinGW + Visual Studio Build Tools, currently untested. Although does work on WSL!

For core functionality:

• numpy
• pandas
• joblib
• cython
  • Note: Cython needs a working C/C++ compiler such as GCC/Clang and associated build-utils/toolchain. While it should work out of the box on any modern Linux distribution, ensure a proper installation as instructed in the official documentation..

For tests:

• pytest
• hypothesis

Skip the first step if an environment is already available:

1. Create a fresh conda or pip/virtualenv-based environment with numpy and cython packages. Choose an appropriate name instead of myenv.

   $ conda create -n myenv python numpy pandas joblib cython

2. Activate environment using conda activate myenv or virtualenv equivalent.

   If git is not installed, then:

   • either install it at a system level directly from the official website or via prefereed package manager
   • or install it within the newly created conda environment using conda install git

3. Use pip* to install directly from GitHub using the git VCS backend

   $ python -m pip install git+https://github.com/pranaysy/ETCPy.git

4. Done! Open a Python shell, execute import ETC and proceed to the demo

*mixing pip and conda is not a generally advised but can be used based on certain recommendations

Use the -U flag with pip for updating to the most current version available from this repository:

$ python -m pip install -U git+https://github.com/pranaysy/ETCPy.git

This will rebuild the compiled Cython functions as well.

Please check out demo.py to see ETC in action. Functions for dealing with NumPy arrays are also available. In addition to the core functionality of ETC, a brief demo of Compression-Complexity Causality (CCC) is also included for uncoupled as well as coupled first-order auto-regressive processes.

The implementations of ETC as well as CCC include multicore parallelization (using joblib) and can benefit from more available CPU cores for multiple sequences.

Most of the tests are property-based or behavior-based, and are implemented using the awesome hypothesis framework. Make sure dependencies are satisfied within the working environment:

$ python -m pip install -U pytest hypothesis

Grab a copy of this repository using git and enter the local directory:

$ git clone https://github.com/pranaysy/ETCPy.git
$ cd ETCPy

Run tests:

$ pytest ETC/

• The original ETC implementation in MATLAB can be found here: https://sites.google.com/site/nithinnagaraj2/journal/etc

• Hyperparameter optimization for CCC
• Add performance metrics
• Automated tests with tox
• Better packaging: pip vs conda
• Visualizations
• Improve test coverage
• Documentation using Sphinx/MkDocs
• Windows support

Copyright 2021 Pranay S. Yadav and Nithin Nagaraj

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

   http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.