python-som

Implementation of the 2D self-organizing map, with support for NumPy arrays and Pandas DataFrames. Most features were implemented using NumPy, with Scikit-learn for standardization and PCA operations.

Features

• Stepwise and batch training
• Random weight initialization
• Random sampling weight initialization
• Linear weight initialization (with PCA)
• Automatic selection of map size ratio (with PCA)
• Support for cyclic arrays, for toroidal or spherical maps
• Gaussian, Bubble and Mexican hat neighborhood functions
• Support for custom decay functions
• Support for visualization (U-matrix, activation matrix)
• Support for supervised learning (label map)
• Support for NumPy arrays, Pandas DataFrames and regular lists of values

Usage

In the following code excerpt (also available in test.py) is an example of instantiation and training of a SOM with the Iris dataset:

# Import python_som
import python_som
# Import NumPy and Pandas for storing data
import numpy as np
import pandas as pd
# Import libraries for plotting results
import matplotlib.pyplot as plt
import seaborn as sns

# Load Iris dataset and columns of features and labels
iris = sns.load_dataset('iris')
target = iris.iloc[:, -1].to_numpy()
iris = iris.iloc[:, :-1].to_numpy()
# Transform labels into numeric codes for plotting
tg = np.zeros(len(target), dtype=int)
tg[target == 'setosa'] = 0
tg[target == 'versicolor'] = 1
tg[target == 'virginica'] = 2

# Instantiate SOM from  python_som
# Selecting shape automatically (providing dataset for constructor)
# Using default decay and distance functions
# Using gaussian neighborhood function
# Using cyclic arrays in the vertical and horizontal directions
som = python_som.SOM(x=20, y=None, input_len=iris.shape[1], learning_rate=0.5, neighborhood_radius=1.0,
        neighborhood_function='gaussian', cyclic_x=True, cyclic_y=True, data=iris)

# Initialize weights of the SOM with linear initialization
som.weight_initialization(mode='linear', data=iris)

# Training SOM with default number of iterations
# Using batch learning process
som.train(data=iris, n_iteration=len(iris), mode='batch', verbose=True)

# Calculating distance matrix for plotting
umatrix = som.distance_matrix().T

# Plotting U-matrix with seaborn/matplotlib
plt.figure(figsize=som.get_shape())
plt.pcolor(umatrix, cmap='bone_r')

markers = ['o', 's', 'D']
colors = ['C0', 'C1', 'C2']
for cnt, xx in enumerate(iris):
    w = som.winner(xx)  # getting the winner
    plt.plot(w[0] + .5, w[1] + .5, markers[tg[cnt]], markerfacecolor='None',
             markeredgecolor=colors[tg[cnt]], markersize=12, markeredgewidth=2)
plt.axis([0, som.get_shape()[0], 0, som.get_shape()[1]])
plt.show()

Test output

The following image is generated from the previous test code, with the U-matrix of the trained SOM, and the distribution of the instances from the Iris dataset. In this graph, the instances are mapped to the self-organizing map, with color codes for each different label:

• Setosa: blue circle
• Versicolor: orange square
• Virginica: green diamond

Public methods and functions

The following are lists of public methods and functions currently available in the SOM class. The full documentation of each method can be found in the source code:

Utility functions

• _asymptotic_decay
• _linear_decay
• _exponential_decay
• _inverse_decay
• _euclidean_distance

SOM public methods

• SOM
• SOM.get_shape
• SOM.get_weights
• SOM.set_learning_rate
• SOM.set_neighborhood_radius
• SOM.activate
• SOM.winner
• SOM.quantization
• SOM.quantization_error
• SOM.distance_matrix
• SOM.activation_matrix
• SOM.winner_map
• SOM.label_map
• SOM.train
• SOM.weight_initialization

Neighborhood functions

The neighborhood_function parameter selects how the winner's correction is spread over the grid. All three are functions of the distance between two nodes in the grid, sqdist(c, i) in Eq. (5) of Kohonen (2013):

The mexican hat takes negative values, so it cannot be used with mode='batch': the batch update of Kohonen (2013), Eq. (8), is a weighted mean whose denominator Σⱼ nⱼ·hⱼᵢ is not sign-definite for a signed neighborhood function. Use mode='random' or mode='sequential' instead; passing mode='batch' raises a ValueError.

References

This implemetation was based on the following paper, by Professor Teuvo Kohonen:

Teuvo Kohonen, Essentials of the self-organizing map, Neural Networks, Volume 37, 2013, Pages 52-65, ISSN 0893-6080, https://doi.org/10.1016/j.neunet.2012.09.018.

The mexican hat neighborhood function follows the lateral-interaction formulation in:

O. J. Vrieze, Kohonen network, in: Artificial Neural Networks: An Introduction to ANN Theory and Practice, Lecture Notes in Computer Science, Volume 931, Springer, Berlin, Heidelberg, 1995, Pages 83-100, https://doi.org/10.1007/BFb0027024.