Bernal S D_2010.pdf - University of Plymouth

6.1. ANALYSIS OF RESULTS
The graph in Figure 5.10 suggests that the optimum v;iluc for Kc\groi.p is approximately 10.
while the graph in Figure 5.\ 1 suggests [hat the optimum value for Kcigroup 's approximately
15. If there are not enough CI features per group, some inpul spalia] arrangements of SI nodes
will not be captured, decreasing Ihe categorization performance. Similarly, if there are too
many C \ features per group, it is more likely that high values will be obtained in all the groups,
thus reducing the informative value of the node. The number of features per group is therefore
crucial for the feedforward recognition process and should provide a compromise between the
two opposed effects described above.
Another factor that has proven crucial for successful categorization is the number of non-zero
elements in the S2-C2 weight matrix, which can be considered equivalent to the sparseness of
the matrix. There is evidence suggesting synaptic connectivity is sparse in feedforward conical
circuits and thai firing patterns of cortical neurons exhibit sparse distrihuled representations, in
which only a few of a large population of neurons are active (Quiroga et al. 2005, Murray and
Kreutz-Delgado 2007, Karklin and Lewicki 200.1. Olshausen 2(H)3). Sparse coding strategies
have proven to be essential to make eflicient use of overcomplete representations, such as those
found in VI, making it easier to lind higher order correlations, increasing the signal-to-noise
ratio and increasing the storage capacity of associative memories (Murray and Kreutz-Delgado
2007). Furthermore, they can improve pattern matching, since they lower the probability of
false matches among elements of a pattern (Oishausen 2003).
The model results shown in Figures 5.12, 5.13. 5.14 and 5.15 indicate that sparse S2-C2 weight
matrices, with < 10% of active connections, improve feedforward categorization. An example
of one such sparse connectivity matrix is shown in Figure 4.11. As ex]>ected. the optimum
number of non-zero elements is proportional to the S2 RF size, l-or S2 RF size=4x4, the op­
timum value of non-zero elements is one. while for higher S2 RF sizes the value lies between
four and eight. As previously staled, sparse coding strategies account for this phenomenon, as
more sparse S2-C2 connections make it less hkely for two different objects to yield the same
C2 response pattern (false positive), thus increasing selectivity. However, when the number of
non-zero elements is too low, the distorted versions of the same object might be categorized as
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