[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 slice_input = tf.pad(tf.reshape(bmu_index, [1]), np.array([[0, 1]])) bmu_loc = tf.reshape(tf.slice(self._location_vects, slice_input, tf.constant(np.array([1, 2]))), [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([1])), [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)) new_weightages_op = tf.add(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[0]].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]) return to_return

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[1], m[0], 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):