[This post assumes that you know the basics of Google’s TensorFlow library. If you don’t, have a look at my earlier post to get started.] A Self-Organizing Map, or SOM, falls under the rare domain of unsupervised learning in Neural Networks. Its essentially a grid of neurons, each denoting one cluster learned during training. Traditionally speaking, there is no concept of neuron ‘locations’ in ANNs. However, in an SOM, each neuron has a location, and neurons that lie close to each other represent clusters with similar properties. Each neuron has a weightage vector, which is equal to the centroid of its particular cluster.

AI-Junkie’s post does a great job of explaining how an SOM is trained, so I won’t re-invent the wheel.

The Code

Here’s my code for a 2-D version of an SOM. Its written with TensorFlow as its core training architecture: (Its heavily commented, so look at the inline docs if you want to hack/dig around)

import tensorflow as tf
import numpy as np

class SOM(object):
"""
2-D Self-Organizing Map with Gaussian Neighbourhood function
and linearly decreasing learning rate.
"""

#To check if the SOM has been trained
_trained = False

def __init__(self, m, n, dim, n_iterations=100, alpha=None, sigma=None):
"""
Initializes all necessary components of the TensorFlow
Graph.

m X n are the dimensions of the SOM. 'n_iterations' should
should be an integer denoting the number of iterations undergone
while training.
'dim' is the dimensionality of the training inputs.
'alpha' is a number denoting the initial time(iteration no)-based
learning rate. Default value is 0.3
'sigma' is the the initial neighbourhood value, denoting
the radius of influence of the BMU while training. By default, its
taken to be half of max(m, n).
"""

#Assign required variables first
self._m = m
self._n = n
if alpha is None:
alpha = 0.3
else:
alpha = float(alpha)
if sigma is None:
sigma = max(m, n) / 2.0
else:
sigma = float(sigma)
self._n_iterations = abs(int(n_iterations))

##INITIALIZE GRAPH
self._graph = tf.Graph()

##POPULATE GRAPH WITH NECESSARY COMPONENTS
with self._graph.as_default():

##VARIABLES AND CONSTANT OPS FOR DATA STORAGE

#Randomly initialized weightage vectors for all neurons,
#stored together as a matrix Variable of size [m*n, dim]
self._weightage_vects = tf.Variable(tf.random_normal(
[m*n, dim]))

#Matrix of size [m*n, 2] for SOM grid locations
#of neurons
self._location_vects = tf.constant(np.array(
list(self._neuron_locations(m, n))))

##PLACEHOLDERS FOR TRAINING INPUTS
#We need to assign them as attributes to self, since they
#will be fed in during training

#The training vector
self._vect_input = tf.placeholder("float", [dim])
#Iteration number
self._iter_input = tf.placeholder("float")

##CONSTRUCT TRAINING OP PIECE BY PIECE
#Only the final, 'root' training op needs to be assigned as
#an attribute to self, since all the rest will be executed
#automatically during training

#To compute the Best Matching Unit given a vector
#Basically calculates the Euclidean distance between every
#neuron's weightage vector and the input, and returns the
#index of the neuron which gives the least value
bmu_index = tf.argmin(tf.sqrt(tf.reduce_sum(
tf.pow(tf.sub(self._weightage_vects, tf.pack(
[self._vect_input for i in range(m*n)])), 2), 1)),
0)

#This will extract the location of the BMU based on the BMU's
#index
np.array([[0, 1]]))
bmu_loc = tf.reshape(tf.slice(self._location_vects, slice_input,
tf.constant(np.array([1, 2]))),
)

#To compute the alpha and sigma values based on iteration
#number
learning_rate_op = tf.sub(1.0, tf.div(self._iter_input,
self._n_iterations))
_alpha_op = tf.mul(alpha, learning_rate_op)
_sigma_op = tf.mul(sigma, learning_rate_op)

#Construct the op that will generate a vector with learning
#rates for all neurons, based on iteration number and location
#wrt BMU.
bmu_distance_squares = tf.reduce_sum(tf.pow(tf.sub(
self._location_vects, tf.pack(
[bmu_loc for i in range(m*n)])), 2), 1)
neighbourhood_func = tf.exp(tf.neg(tf.div(tf.cast(
bmu_distance_squares, "float32"), tf.pow(_sigma_op, 2))))
learning_rate_op = tf.mul(_alpha_op, neighbourhood_func)

#Finally, the op that will use learning_rate_op to update
#the weightage vectors of all neurons based on a particular
#input
learning_rate_multiplier = tf.pack([tf.tile(tf.slice(
learning_rate_op, np.array([i]), np.array()), [dim])
for i in range(m*n)])
weightage_delta = tf.mul(
learning_rate_multiplier,
tf.sub(tf.pack([self._vect_input for i in range(m*n)]),
self._weightage_vects))
weightage_delta)
self._training_op = tf.assign(self._weightage_vects,
new_weightages_op)

##INITIALIZE SESSION
self._sess = tf.Session()

##INITIALIZE VARIABLES
init_op = tf.initialize_all_variables()
self._sess.run(init_op)

def _neuron_locations(self, m, n):
"""
Yields one by one the 2-D locations of the individual neurons
in the SOM.
"""
#Nested iterations over both dimensions
#to generate all 2-D locations in the map
for i in range(m):
for j in range(n):
yield np.array([i, j])

def train(self, input_vects):
"""
Trains the SOM.
'input_vects' should be an iterable of 1-D NumPy arrays with
dimensionality as provided during initialization of this SOM.
Current weightage vectors for all neurons(initially random) are
taken as starting conditions for training.
"""

#Training iterations
for iter_no in range(self._n_iterations):
#Train with each vector one by one
for input_vect in input_vects:
self._sess.run(self._training_op,
feed_dict={self._vect_input: input_vect,
self._iter_input: iter_no})

#Store a centroid grid for easy retrieval later on
centroid_grid = [[] for i in range(self._m)]
self._weightages = list(self._sess.run(self._weightage_vects))
self._locations = list(self._sess.run(self._location_vects))
for i, loc in enumerate(self._locations):
centroid_grid[loc].append(self._weightages[i])
self._centroid_grid = centroid_grid

self._trained = True

def get_centroids(self):
"""
Returns a list of 'm' lists, with each inner list containing
the 'n' corresponding centroid locations as 1-D NumPy arrays.
"""
if not self._trained:
raise ValueError("SOM not trained yet")
return self._centroid_grid

def map_vects(self, input_vects):
"""
Maps each input vector to the relevant neuron in the SOM
grid.
'input_vects' should be an iterable of 1-D NumPy arrays with
dimensionality as provided during initialization of this SOM.
Returns a list of 1-D NumPy arrays containing (row, column)
info for each input vector(in the same order), corresponding
to mapped neuron.
"""

if not self._trained:
raise ValueError("SOM not trained yet")

to_return = []
for vect in input_vects:
min_index = min([i for i in range(len(self._weightages))],
key=lambda x: np.linalg.norm(vect-
self._weightages[x]))
to_return.append(self._locations[min_index])

A few points about the code:

1) Since my post on K-Means Clustering, I have gotten more comfortable with matrix operations in TensorFlow. You need to be comfortable with matrices if you want to work with TensorFlow (or any data flow infrastructure for that matter, even SciPy). You can code pretty much any logic or operational flow with TensorFlow, you just need to be able to build up complex functionality from basic components(ops), and structure the flow of data(tensors/variables) well.

2) It took quite a while for me to build the whole graph in such a way that the entire training functionality could be enclosed in a single op. This op is called during each iteration, for every vector, during training. Such an implementation is more in line with TensorFlow’s way of doing things, than my previous attempt with clustering.

3) I have used a 2-D grid for the SOM, you can use any geometry you wish. You would just have to modify the _neuron_locations method appropriately, and also the method that returns the centroid outputs. You could return a dict that maps neuron location to the corresponding cluster centroid.

4) To keep things simple, I haven’t provided for online training. You could do that by having bounds for the learning rate(s).

Sample Usage

I have used PyMVPA’s example of RGB colours to confirm that the code does work. PyMVPA provides functionality to train SOMs too (along with many other learning techniques).

Here’s how you would do it with my code:

#For plotting the images
from matplotlib import pyplot as plt

#Training inputs for RGBcolors
colors = np.array(
[[0., 0., 0.],
[0., 0., 1.],
[0., 0., 0.5],
[0.125, 0.529, 1.0],
[0.33, 0.4, 0.67],
[0.6, 0.5, 1.0],
[0., 1., 0.],
[1., 0., 0.],
[0., 1., 1.],
[1., 0., 1.],
[1., 1., 0.],
[1., 1., 1.],
[.33, .33, .33],
[.5, .5, .5],
[.66, .66, .66]])
color_names = \
['black', 'blue', 'darkblue', 'skyblue',
'greyblue', 'lilac', 'green', 'red',
'cyan', 'violet', 'yellow', 'white',
'darkgrey', 'mediumgrey', 'lightgrey']

#Train a 20x30 SOM with 400 iterations
som = SOM(20, 30, 3, 400)
som.train(colors)

#Get output grid
image_grid = som.get_centroids()

#Map colours to their closest neurons
mapped = som.map_vects(colors)

#Plot
plt.imshow(image_grid)
plt.title('Color SOM')
for i, m in enumerate(mapped):
plt.text(m, m, color_names[i], ha='center', va='center',
bbox=dict(facecolor='white', alpha=0.5, lw=0))
plt.show()

Here’s a sample of the output you would get (varies each time you train, but the color names should go to the correct locations in the image): 