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Fixed point networks are dynamic networks that encode stimuli via distinctoutput patterns. Although such networks are omnipresent in neural systems,their structures are typically unknown or poorly characterized. It is thereforevaluable to use a supervised approach for resolving how a network encodesdistinct inputs of interest, and the superposition of those inputs from sampledmultiple node time series. In this paper we show that accomplishing such a taskinvolves finding a low-dimensional state space from supervised recordings. Wedemonstrate that standard methods for dimension reduction are unable to providethe desired functionality of optimal separation of the fixed points andtransient trajectories to them. However, the combination of dimension reductionwith selection and optimization can successfully provide such functionality.Specifically, we propose two methods: Exclusive Threshold Reduction (ETR) andOptimal Exclusive Threshold Reduction (OETR) for finding a basis for theclassification state space. We show that the classification space constructedupon combination of dimension reduction optimal separation can directlyfacilitate recognition of stimuli, and classify complex inputs (mixtures) intosimilarity classes. We test our methodology and compare it to standardstate-of-the-art methods on a benchmark dataset - an experimental neuronalnetwork (the olfactory system) that we recorded from to test these methods. Weshow that our methods are capable of providing a basis for the classificationspace in such network, and to perform recognition at a significantly betterrate than previously proposed approaches.

Classification of Fixed Point Network Dynamics From Multiple Node Timeseries Data