Self-Organizing Maps in Python

Faris — Mon, 04/06/2009 - 00:37

In finding new ways to describe and emulate cognitive microstructure, self-organizing maps (SOM) offer insight into how the visual system might work in a connectionist model of the brain.

For this example, I am going to use len’s examples and code to show how artificial neural networks can be applied to a visual emulation of the brain.

First off, let’s define what this SOM is accomplishing. Remembering that cognitive science studies the input-output function of human behaviour and thought-processes, we have an input: the environment, and an output: the perception of the environment. It’s the stuff in-between the in’s and out’s that we’re going to be looking at in this example.

Feel free to download the files and follow along.

Now, we’re going to try to use an artificial neural network to make a grid of evenly spaced nodes. Each node will space itself evenly from the other. To do this, we will “train” the system with a set of defined points:

def train_step(self):
        if self.epoch >= self.alg.epochs:
            print "Training completed"
            return 1
        radius = self.alg.radius_decay(self.epoch)
        learning_rate = self.alg.learning_rate_decay(self.epoch)
        print 'Epoch %d %0.2f %0.4f' %(self.epoch, radius, learning_rate)
 
        for i in range(self.alg.epoch_iterations):
            v = self.next_sample()
            bmu = self.find_bmu(v)
            self.adjust_nodes(bmu, v, radius, learning_rate)
 
        self.epoch = self.epoch + 1
        return 0

Each iteration will adjust the weight between the nodes to fit with other weights in the nodes:

    def radius_decay(self, t):
        """ returns the radius of influence for current epoch """
        return self.r / 2  * math.exp(-float(t/self.time_constant))
 
    def learning_rate_decay(self, t):
        """ returns the learning rate for current epoch """
        return self.initial_learning_rate * math.exp(-float(t/(self.epochs - t))
)
 
    def distance(self, input, node):
        """ calculates the 'distance' in value space """
        dist = 0
        for i in range(len(input)):
            dist = dist + (input[i] - node[i]) * (input[i] - node[i])
        return dist

By showing the ways in which nodes can organically form maps, SOMs are one more way in which ANNs can provide insight into cognitive processes.

So, after running the program, we will get results similar to the following:

Note that this SOM, even though finished, still has a few mis-aligned nodes. This is typical of SOM: the calculations are implicit. This SOM has completed 100 iterations, try playing around with the code to see what happens with 1,000 iterations.

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