Hierarchical Clustering from ICA Mixtures - On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling - page 99

(a) (b)

sky + cone

stairs +
roof, persons

roof,
persons

cone

stairs

sky

Fig. 4.11 Image segmentation. a Image divided in nine zones, b hierarchical representation of
the zones of the image. Two broad groups of zones are shown

Figure 4.12 (left) shows a mixed image that includes two subimages: a natural
image (a frog) and a text image. There are clear differences in the borders of each
subimage, which are indicated in the distances at which these subimages are
merged at the penultimate level of the hierarchy (Fig. 4.12 (right)). Thus, the
segmentation of the image into the two different subimages has been found.

4.6 Conclusions

A method for agglomerative hierarchical clustering based on an underlying ICA
mixture model has been proposed. The new algorithm uses the ICAMM param-
eters estimated at the bottom of the hierarchy to create higher levels by grouping
clusters. It is based on the symmetric Kullback-Leibler divergence between the
clusters using the ICA parameters assuming non-parametric kernel-based source
densities. Different structures of classification can be derived at the different levels
of the bottom-up merging. A stopping criterion to estimate an optimum cluster
partition was applied using the partition and partition entropy coefficients.
The method has been tested by means of simulations and real data analyses.
The simulations showed the capability of the method to generalize from close data
densities and to detect outliers. This was compared with the traditional single
linkage method that is based on distance between data objects. The proposed
methods showed more suitable groupings than the single linkage method (since not
only the distance between the data objects is taken into account, but also the kinds
of distributions).
The results demonstrated the suitability of the proposed method to process
image data. Image content similarity between objects based on ICA basis functions
allow an organization of objects in higher levels of abstraction to be learned. In