plot2Dcluster

plot2Dcluster.py is a Python module that visualizes community detection results with the interaction between 2 nominal node attributes.

In the raw data, the 2 attributes are arranged by rows and columns and the communities are denoted by non-negative integers.

Every community will be assigned with a "distinct" enough color (using the HLS-to-RGB conversion).

The rows and columns can be kept as original or rearranged by a majority rule, which includes the following steps:

1. A ranking list of the frequencies of all the communities in the raw data is generated.
2. The majority (most frequent) communities for each row (or column) are recorded.
3. The rows (or columns) with their majority community ranking highest in the list of step 1 will be rearranged first from the top (or from the left for columns).
4. When there are multiple rows (or columns) with their majority community ranking the same in the list of step 1, the one will the highest frequency will be rearranged first.

This project is hosted at: https://github.com/zhenzhu/plot2Dcluster.

MIT License

Copyright (c) 2016 Zhen Zhu

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Table of Contents

• Usage
  • Context
  • Download
  • Input
  • Functions
• Testing
• Reference
• Acknowledgements

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**Packages Required:** - [matplotlib](http://matplotlib.org/) - [numpy](http://www.numpy.org/)

Usage

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Context

Sometimes it is useful to visualize the community detection result with the interaction between 2 nominal node attributes. For example, in our paper, each node of the network has 2 nominal attributes, country and industry.

A typical visualization is based on a community array with the 2 attributes arranged as rows and columns. And each element of the array represents a node in the network and contains a non-negative integer indicating the community which the node belongs to.

You may want to visualize the result using a pre-defined arrangement of rows and columns (e.g. arranging countries by alphabetical order and industry codes by numerical order). But more likely, you want to highlight the largest communities detected (e.g. clustering the rows involving the largest communities on the top).

plot2Dcluster provides such a functionality to visualize the community array either using a pre-defined arrangement or using a majority rule to highlight the most significant communities.

Download

The easiest way is to download the script plot2Dcluster.py directly:

1. Go to the raw version of plot2Dcluster.py.
2. Right click and save it.

Input

plot2Dcluster.py only works with 2-dimension arrays.

The user-supplied lists of row names and column names of the community array (i.e. the 2 nominal node attributes) are also needed.

Finally, the communities (i.e. the elements of the array) need to be denoted as non-negative integers.

Functions

3 functions are available:

1. plot_com_original returns a plot of the community array as it is. The parameters include:

   • com_data: A 2-dimension community array.
   • rownames: A list of strings corresponding to the row names of com_data.
   • colnames: A list of strings corresponding to the column names of com_data.

2. plot_com_order1 returns a plot of the community array and applies the majority rule to rearrange either rows or columns. The parameters include:

   • com_data: A 2-dimension community array.
   • rownames: A list of strings corresponding to the row names of com_data.
   • colnames: A list of strings corresponding to the column names of com_data.
   • row: A logical value. If true, rows will be rearranged according to the majority rule and columns will be fixed. Otherwise, columns will be rearranged and rows will be fixed.

3. plot_com_order2 returns a plot of the community array and applies the majority rule to rearrange both rows and columns. The parameters include:

   • com_data: A 2-dimension community array.
   • rownames: A list of strings corresponding to the row names of com_data.
   • colnames: A list of strings corresponding to the column names of com_data.

Testing

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import random as rd
import numpy as np
import plot2Dcluster as p2c

# Define a function to generate an example community array.
def example_com(n_row,n_col,n_com):
    """
    This function returns a 2-dimension array as an example of community detection
    result. The parameters include:
    n_row: The number of instances of the first node attribute.
    n_col: The number of instances of the second node attribute.
    n_com: The number of communities detected.
    """
    top2 = rd.sample(range(n_com),2) # There will be 2 dominating communities detected.
    
    # The first half of the data.
    prob1 = [(1-0.6)/(n_com-2)]*n_com # All the other communities are assigned with the same probability.
    prob1[top2[0]] = 0.45
    prob1[top2[1]] = 0.15
    data1 = np.random.choice(n_com,(n_row*n_col)/2,p=prob1)
    
    # The second half of the data.
    prob2 = [(1-0.9)/(n_com-2)]*n_com # All the other communities are assigned with the same probability.
    prob2[top2[0]] = 0.7
    prob2[top2[1]] = 0.2
    data2 = np.random.choice(n_com,(n_row*n_col)/2,p=prob2)
    
    # Combine the two halves.
    data = np.concatenate((data1,data2))
    
    # The example will look more "diverse" on the top and more "uniform" on the bottom.
    com_data = data.reshape(n_row,n_col)
    return com_data

# Generate an example community array with 40 rows, 26 columns, and 30 communities.
rd.seed(3)
np.random.seed(3)
example = example_com(40,26,30)

# Generate an example list of column names A-Z.
colnames = []
for i in range(ord('A'),ord('Z')+1):
    colnames.append(chr(i))

# Generate an example list of row names 1-40.
rownames = [str(i) for i in range(1,41)]

# Test 1
rd.seed(3)
p2c.plot_com_original(example,rownames,colnames)

# Test 2
rd.seed(3)
p2c.plot_com_order1(example,rownames,colnames,row=True)

# Test 3
rd.seed(3)
p2c.plot_com_order1(example,rownames,colnames,row=False)

# Test 4
rd.seed(3)
p2c.plot_com_order2(example,rownames,colnames)

The code is working properly if the figures original, order1_row, order1_col, and order2 are generated by Tests 1-4 respectively.

Reference

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If using the code, please cite the publication below:

Cerina F, Zhu Z, Chessa A, Riccaboni M (2015) World Input-Output Network. PLoS ONE 10(7): e0134025. doi:10.1371/journal.pone.0134025

Acknowledgements

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The code is inspired by the figures produced by Federica Cerina in World Input-Output Network.