  Fixed point networks are dynamic networks that encode stimuli via distinct
output patterns. Although such networks are omnipresent in neural systems,
their structures are typically unknown or poorly characterized. It is therefore
valuable to use a supervised approach for resolving how a network encodes
distinct inputs of interest, and the superposition of those inputs from sampled
multiple node time series. In this paper we show that accomplishing such a task
involves finding a low-dimensional state space from supervised recordings. We
demonstrate that standard methods for dimension reduction are unable to provide
the desired functionality of optimal separation of the fixed points and
transient trajectories to them. However, the combination of dimension reduction
with selection and optimization can successfully provide such functionality.
Specifically, we propose two methods: Exclusive Threshold Reduction (ETR) and
Optimal Exclusive Threshold Reduction (OETR) for finding a basis for the
classification state space. We show that the classification space constructed
upon combination of dimension reduction optimal separation can directly
facilitate recognition of stimuli, and classify complex inputs (mixtures) into
similarity classes. We test our methodology and compare it to standard
state-of-the-art methods on a benchmark dataset - an experimental neuronal
network (the olfactory system) that we recorded from to test these methods. We
show that our methods are capable of providing a basis for the classification
space in such network, and to perform recognition at a significantly better
rate than previously proposed approaches.
