components of the principal component analysis decomposition
(here, acting as a filter) of the data set
within the training region. A network of three neurons
was trained repeatedly on multiple examples until a
minimal error was achieved. Following training, the
network was presented with the data set collected on
the whole area shown in Figure 7c and it correctly
identified both of the bacterial species. Interestingly,
other topographical features, distinct from the substrate,
were classified as background, which identifies
them as non-bacterial debris. However, a small relatively
flat region (right upper corner in Figure 7c) was
classified as M. lysodeikticus, implying that this region
could be covered in a membrane of lysed bacteria of
that species. Thus, supervised learning presents a powerful
image recognition tool that can identify objects based
on a small subset of information provided in the training
set. Even though successful neural network operation
requires extensive training for accuracy, the computational
cost during operation is infinitesimal. The illustrated
example was computed on a typical user desktop
without additional high-end components or computational
clusters. Similarly, neural network approaches
can be extended to training on theoretical model outputs,
with the experimental results presented for analysis. Examples
include functional fits to relaxation parameters
[71] or Ising model simulations [72,73].
Deep learning
In this section, we discuss the pathways to establish correspondence
between statistical analysis and a physical