Unsupervised Learning of Overlapping Image Components Using Divisive Input Modulation
(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., ). The first
output node has weights that are selective to the first two inputs (i.e., , where while and is thus
missing from the diagram), and the third output node represents the last two
inputs (i.e., while , where ). 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 (the positive
weights targeting the first and third output nodes). In the top row of (b) and
(c) equals 0.5, and
in the bottom row of (b) and (c) 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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