Skin Lesion Classification - Biomedical Signal Analysis: Contemporary Methods and Applications - page 331

12.3 Classification Using Independent Base Images

In tasks such as image classification, much of the important information
may be contained in the higher-order correlations among the image
pixels. As PCA is based on second-order statistics only, it does not
take into account higher-order statistical dependencies which can be
addressed by ICA. Thus not only decorrelation, but also statistical
independence of the signals, can be achieved, thereby allowing us to
extract relevant information which is coded in higher-order statistics.
By analogy to the eigenimages of the previous section, here we
separate images across space and thus extract a set of statistically
independent base images which may capture some independent features
of the corresponding ensemble.

Statistically independent base images

By analogy to the eigenimages in the previous section, assume all
fluorescence images X =[ x 1 ,..., x m ] with x i =[ x i (1) ,...,x i ( N 2 )]
to be a linear combination ( mixture )of m source images S according
to the image synthesis model in figure 12.4. As the mixing matrix A
is unknown, these source images, have to be recovered by a matrix
W I which produces statistically independent output according to Y =
W I X . As already mentioned, these base images Y can be considered
an ensemble of independent (localized) features in the images and the
coecients for the linear combinations of the independent base images
Y , which comprise each image x i , are represented by the matrix A =
W − I .
In order to be able to control the number of recovered source images
extracted by an ICA algorithm, learning is performed on the first m
principal component eigenimages, which are calculated as in the previous
section. Thus let U =[ u 1 ,..., u m ]denotethe N 2 × m matrix containing

the first m eigenimages u i =[ u i (1) ,...,u i ( N 2 )] in its columns.
After a random initialization of the weight matrix W , the input data
are sphered, using a sphering matrix W z ; thus the unmixing matrix is
given by W I = WW z .ICAisthenperformedon U (i. e. , at each step
m pixels at the same location in the different eigenimages are presented
to the network). Thereby the Infomax learning rule with the natural