other components can be seen as an indication of the degree
of purely ferroelectric switching in those regions, as
opposed to other components that appear to result from
dominating influences by surface charges, polar nanoregions,
or field-induced phase transformations. For instance,
the first component appears largest in the top-left
corner of the region studied (Figure 6a), and the coercive
fields for this component are much lower, possibly due to
the increased propensity of field-induced phase transformations
(likely rhombohedral to tetragonal [67]) in this
area. Thus, ICA is a highly useful method for blind source
separation and provides a powerful method accompanying
PCA to de-mix signals where the number of constituent
components is either known from physics or can be
postulated.
Supervised learning
Functional recognition imaging is an example of the supervised
learning approach that employs artificial neural
networks. The process of recognition obviates the need
for sophisticated analytical models, instead relying on
statistical analysis of the complex spectroscopic data
sets. Nikiforov et al. [68] describe functional recognition
imaging of bacterial samples containing live Micrococcus
lysodeikticus and Pseudomonas fluorescens on a poly-Llysine-
coated mica substrate. These bacteria differ in
shape and therefore present a good modeling system for
creating training data sets. The spectroscopic data were
provided by the band excitation PFM method [69,70] in
the form of the electromechanical response vs. excitation