Bernal S D_2010.pdf - University of Plymouth

4.3. LEARNING
4.3.4 S2-C2CPTS
The weights between each C2 node and its afferent S2 nodes are learned using the same
methodology described for the SI -CI layers, i.e. k-means clustering to obtain the most com­
mon arrangements of S2 units. In this case the algorithm extracts Kci^roup clusters of size
^ci 'X Nc2 X Niinndi for each C2 group or S2 state. The parameter Nj,a„ds represents the number
of S2 bands being pooled from, and varies for the different architectures presented.
The resulting weight matrices, learned from the training dalasel of 60 object silhouettes follow­
ing the clustering procedure are shown in Figure 4.11 for a value of Kc2gniup - 10- Note that
each C2 node receives input from Ihe S2 nodes of up to 8 scale bands.
The weight matrices shown in Figure 4,11 are converted to one CPT per each S2 node using an
equivalent procedure to that described for the Sl-Cl CPTs.
4.3.5 C2-S3CPTS
The weights between each S3 node and its afferent C2 nodes are learned in a supervised manner
for each of the KST, — 60 training images. For the 3-layer architecture, the A(C2) response
for each training image becomes the prototype weight matrix. The CPT /'(C2|53) containing
Kcii- 10000) X Ks•^{= 60) elements can be easily obtained in ihis manner, by normalizing the
weight matrices for each prototype. In other words, the prototype of each input image is learned
as a function of the X{C2) response and converted to a CPT relating C2 and S3, as shown in
Figure 4.11.
In the case of Ihe allemalive 3-layer architecture where there are 9 C2 nodes and 4 S3 nodes, the
learning method is also supervised but the size and number of proiotypcs varies. The size of the
S3 prototypes is now AA'y^ x A^'s•.l — 2 x 2 C2 units; and these are learned from the 4 possible
locations within the C2 units (see lop of Figure 4.5), leading lo Ks^ = 60 objects • 4 locations -
^Caption for Figure 4,11. Weighl matricej, bulween a C.2 node and its afferent S2 nodes. These are learned
from the training datasei of 60 object silhuaeties following the clustering pnicedun; described, and represent the
fCc2gniup = 10 mt>sl common arrangemeni of CI nodes for each C2 group and scale hand. Note that each C2 node
receives inpui from the S2 niiden of up lo K scale bands, where, tor each scale band, the pooling range, ANcj. is
differeni. .Similarly, the weighl matrices are divideU according Ui the S2 RF' sizes, as the S2 response maps for
S2 Rl- siK, have differeni sizes and yield different S2-C2 wcighls. For purpio.ses of clarity, a single C2 feature is
highlighted using a red dolled ellipse.
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