#mainTextBox In this example we will train a linear associator to output a 7x30 image of a person's name given their 48x48 facial image as input. A linear associator is a simple linear matrix multiplication from input to output. It is capable of perfectly learning input-output associations when they all are orthogonal to each other. However, even when the pairs are not perfectly orthogonal, learning can still occur.
#subtitleTextBox ArbitrarySynapse
#mainTextBox This is a linear associator network. As mentioned previously, it implements a simple linear matrix multiplication from input to output. A full connection between the 48x48 (2304) input and the 7x30 (210) output would result in 483,840 weights, many more weights than are needed to solve the problem. Therefore, we use the ArbitrarySynapse, shown by the arrow. The ArbitrarySynapse allows the user to choose near, sparse, random or manual connections. Here we use random connections with two connections from every input pixel. Thus, there will be a total of 48x48x2 = 4608 weights. On average, each output will be connected to 4608/210 ~= 22 input pixels.
#subtitleTextBox ImageViewer
#mainTextBox Image viewer probes have been placed at the network's input, output and desired response, and their corresponding windows have been opened at the bottom of your display. They automatically configure themselves to the proper dimension based on the component they are probing. This probe is a powerful way to visualize 2-dimensional data and is an essential tool in image processing. Single-step through the exemplars and observe that the network has yet to learn to associate the pictures with the names.
#subtitleTextBox Training the network
#mainTextBox We have added a bar graph to probe the mean square error. Train the network for 30 exemplars by pushing the "Run" button at right and observe how fast the desired associations converge.
#subtitleTextBox Verifying the training
#mainTextBox Step through the exemplars and observe that the network has learned the desired association.
#subtitleTextBox Summary
#mainTextBox We built a linear associator and saw how the arbitrary synapse can be useful in avoiding an explosion of weights when the number of PEs per layer is large. We also saw that the image viewer is a convenient probe when dealing with images and 2-dimensional data.
