Computational Intelligence and Neuroscience / 2009 / Article / Fig 9

Research Article

Unsupervised Learning of Overlapping Image Components Using Divisive Input Modulation

Figure 9

(a) A simple neural network of the type used by all the algorithms described in this article (the symbols are the same as those used in Figure 1). This network has three output nodes which receive input from three error-detecting nodes. All three error-detecting nodes receive equal strength input from three image pixels (i.e., 𝑀 3 2 = 𝑀 3 3 = π‘Ž ). The first output node has weights that are selective to the first two inputs (i.e., π‘Ž > 0 , where π‘Ž while π‘Ž and is thus missing from the diagram), and the third output node represents the last two inputs (i.e., π‘Ž while πš— πš– 𝚏 𝚜 𝚎 𝚚 , where 𝚍 πš’ πš– ). The middle output node has weak weights (equal to 0.25) connecting it to all three error-detecting nodes. Each subfigure in (b) and (c) shows the steady-state activation strength of the three output nodes and the three error-detecting nodes in this simple network calculated using (b) the sequential NMF algorithm, and (c) the divisive input modulation algorithm. The steady-state responses are calculated for different values of 𝑛 = 4 8 (the positive weights targeting the first and third output nodes). In the top row of (b) and (c) 𝛽 equals 0.5, and in the bottom row of (b) and (c) 𝐲 equals 1 (the width of each connection in these subplots is proportional to its strength). Note that there is no stochastic element in the calculation of the neural responses generated by these algorithms, so identical results will be generated each time the network is simulated with these weight values.

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