ccc-coef 0.1.6

The Clustermatch Correlation Coefficient (CCC) is a highly-efficient, next-generation not-only-linear correlation coefficient that can work on numerical and categorical data types.

Clustermatch Correlation Coefficient (CCC)

Overview

The Clustermatch Correlation Coefficient (CCC) is a highly-efficient, next-generation not-only-linear correlation coefficient that can work on numerical and categorical data types. This repository contains the code of CCC and instructions to install and use it. It also has all the scripts/notebooks to run the analyses for the manuscript, where we applied CCC on gene expression data.

Installation

CCC is available as a PyPI (Python) package (ccc-coef). We tested CCC in Python 3.9+, but it should work on prior 3.x versions. You can quickly test it by creating a conda environment and then install it with pip:

# ipython and pandas are used in the following examples, but they are not needed for CCC to work
conda create -y -n ccc-env python=3.9 ipython pandas
conda activate ccc-env
pip install ccc-coef

Usage

Run ipython in your terminal:

$ ipython
Python 3.10.4 (main, Mar 31 2022, 08:41:55) [GCC 7.5.0]
Type 'copyright', 'credits' or 'license' for more information
IPython 8.3.0 -- An enhanced Interactive Python. Type '?' for help.

In [1]: 

When computing the correlation coefficient on a pair of features, CCC supports numpy.array or pandas.Series. This is an example with numerical data (you can copy/paste the entire lines below including In [...]):

In [1]: import numpy as np
In [2]: import pandas as pd
In [3]: from ccc.coef import ccc

In [4]: random_feature1 = np.random.rand(1000)
In [5]: random_feature2 = np.random.rand(1000)
In [6]: ccc(random_feature1, random_feature2)
Out[6]: 0.0018815884476534295

In [7]: random_feature1 = pd.Series(random_feature1)
In [8]: random_feature2 = pd.Series(random_feature2)
In [9]: ccc(random_feature1, random_feature2)
Out[9]: 0.0018815884476534295

CCC always returns a value between zero (no relationship) and one (perfect relationship). As we show in the manuscript, the distribution of CCC values is much more skewed than other coefficients like Pearson's or Spearman's. A comparison between these coefficients should account for that.

You can also mix numerical and categorical data:

In [10]: categories = np.array(["blue", "red", "green", "yellow"])
In [11]: categorical_random_feature1 = np.random.choice(categories, size=1000)
In [12]: categorical_random_feature2 = np.random.choice(categories, size=1000)
In [13]: categorical_random_feature2[:10]
Out[13]: 
array(['yellow', 'red', 'red', 'yellow', 'blue', 'blue', 'red', 'yellow',
       'green', 'blue'], dtype='<U6')

In [14]: ccc(categorical_random_feature1, categorical_random_feature2)
Out[14]: 0.0009263483455638076

In [15]: ccc(random_feature1, categorical_random_feature2)
Out[15]: 0.0015123522641692117

The first argument of ccc could also be a matrix, either as a numpy.array (features are in rows and objects in columns) or as a pandas.DataFrame (objects are in rows and features in columns). In this case, ccc will compute the pairwise correlation across all features:

In [16]: # with a numpy.array
In [17]: data = np.random.rand(10, 1000)
In [18]: c = ccc(data)
In [19]: c.shape
Out[19]: (45,)
In [20]: c[:10]
Out[20]: 
array([0.00404461, 0.00185342, 0.00248847, 0.00232761, 0.00260786,
       0.00121495, 0.00227679, 0.00099051, 0.00313611, 0.00323936])

In [21]: # with a pandas.DataFrame
In [22]: data_df = pd.DataFrame(data.T)
In [23]: c = ccc(data_df)
In [24]: c.shape
Out[24]: (45,)
In [25]: c[:10]
Out[25]: 
array([0.00404461, 0.00185342, 0.00248847, 0.00232761, 0.00260786,
       0.00121495, 0.00227679, 0.00099051, 0.00313611, 0.00323936])

If your data has a mix of numerical and categorical features, it's better to work on a pandas.DataFrame. As an example, we load the Titanic dataset (from seaborn's repository):

In [26]: titanic_url = "https://raw.githubusercontent.com/mwaskom/seaborn-data/master/raw/titanic.csv"
In [27]: titanic_df = pd.read_csv(titanic_url)
In [28]: titanic_df.shape
Out[28]: (891, 11)
In [29]: titanic_df.head()
Out[29]: 
   survived  pclass                                               name     sex   age  sibsp  parch            ticket     fare cabin embarked
0         0       3                            Braund, Mr. Owen Harris    male  22.0      1      0         A/5 21171   7.2500   NaN        S
1         1       1  Cumings, Mrs. John Bradley (Florence Briggs Th...  female  38.0      1      0          PC 17599  71.2833   C85        C
2         1       3                             Heikkinen, Miss. Laina  female  26.0      0      0  STON/O2. 3101282   7.9250   NaN        S
3         1       1       Futrelle, Mrs. Jacques Heath (Lily May Peel)  female  35.0      1      0            113803  53.1000  C123        S
4         0       3                           Allen, Mr. William Henry    male  35.0      0      0            373450   8.0500   NaN        S

The Titanic dataset has missing values:

In [30]: titanic_df.isna().sum()
Out[30]: 
survived      0
pclass        0
name          0
sex           0
age         177
sibsp         0
parch         0
ticket        0
fare          0
cabin       687
embarked      2
dtype: int64

So we need some kind of preprocessing before moving on:

In [31]: titanic_df = titanic_df.dropna(subset=["embarked"]).dropna(axis=1)
In [32]: titanic_df.shape
Out[32]: (889, 9)

Now we can run CCC on the dataset and get a correlation matrix across features:

In [33]: ccc_corrs = ccc(titanic_df)

In [34]: from scipy.spatial.distance import squareform
In [35]: ccc_corrs = squareform(ccc_corrs)
In [36]: np.fill_diagonal(ccc_corrs, 1.0)
In [37]: ccc_corrs = pd.DataFrame(ccc_corrs, index=titanic_df.columns.tolist(), columns=titanic_df.columns.tolist())
In [38]: ccc_corrs.shape
Out[38]: (9, 9)
In [39]: with pd.option_context('display.float_format', '{:,.2f}'.format):
     ...:     display(ccc_corrs)
          survived  pclass  name  sex  sibsp  parch  ticket  fare  embarked
survived      1.00    0.12  0.00 0.32   0.04   0.05    0.00  0.07      0.05
pclass        0.12    1.00  0.00 0.04   0.02   0.01    0.00  0.33      0.01
name          0.00    0.00  1.00 0.00   0.00   0.00    0.00  0.00      0.00
sex           0.32    0.04  0.00 1.00   0.08   0.11    0.00  0.04      0.04
sibsp         0.04    0.02  0.00 0.08   1.00   0.29    0.00  0.23      0.00
parch         0.05    0.01  0.00 0.11   0.29   1.00    0.00  0.14      0.00
ticket        0.00    0.00  0.00 0.00   0.00   0.00    1.00  0.02      0.00
fare          0.07    0.33  0.00 0.04   0.23   0.14    0.02  1.00      0.03
embarked      0.05    0.01  0.00 0.04   0.00   0.00    0.00  0.03      1.00

The ccc function also has a n_jobs parameter that allows to control the number of CPU cores used. Below we compute the pairwise correlation between 20 features across 1000 objects:

In [40]: data = np.random.rand(20, 1000)

In [41]: %timeit ccc(data, n_jobs=1)
1.32 s ± 45.8 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

In [42]: %timeit ccc(data, n_jobs=2)
771 ms ± 11 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

Reproducible research

Below we provide the steps to reproduce all the analyses in the CCC manuscript.

Setup

To prepare the environment to run the analyses in the manuscript, follow the steps in environment. After completing those steps, you'll have the source code in this repository, a Python environment (either using a Docker image or creating your own conda environment) and the necessary data to run the analyses.

Running code

All the analyses are written as Jupyter notebooks and stored in the folder nbs/. All notebooks are organized by directories, such as 01_preprocessing, with file names that indicate the order in which they should be run (if they share the prefix, then it means they can be run in parallel). You can run the analyses either using the JupyterLab server and your browser, or from the command line using papermill.

Using the browser. For example, let's say you want to run the preprocessing notebooks. If you want to use your browser, you first need to start the JupyterLab server:

bash scripts/run_nbs_server.sh

and then go to http://127.0.0.1:8893/ and browse to nbs/05_preprocessing. Then you need to run each notebook in order.

If you use the Docker image, the steps are very similar for any command, but you need to prepend the scripts/run_docker.sh script.

bash scripts/run_docker.sh \
  bash scripts/run_nbs_server.sh --container-mode

Note that the port is different: http://127.0.0.1:8888/

Using the command-line. You can also run the notebooks using the command-line with papermill instead of going to the browser. Using as example the same preprocessing notebooks, you can pick one of these commands to run all the preprocessing notebooks in order:

# using your own conda environment:
#   requires GNU Parallel: https://www.gnu.org/software/parallel/
#   To install in Ubuntu: apt install parallel
parallel \
  -k \
  --lb \
  --halt 2 \
  -j1 \
  'bash nbs/run_nbs.sh {}' ::: nbs/05_preprocessing/*.ipynb

# using the Docker image:
bash scripts/run_docker.sh \
  parallel \
    -k \
    --lb \
    --halt 2 \
    -j1 \
    'bash nbs/run_nbs.sh {}' ::: nbs/05_preprocessing/*.ipynb