Phase transitions in Vector Quantization

We study Winner-Takes-All and rank based Vector Quantization along the lines of the statistical physics of off-line learning. Typical behavior of the system is obtained within a model where high-dimensional training data are drawn from a mixture of Gaussians. The analysis becomes exact in the simplifying limit of high training temperature. Our main findings concern the existence of phase transitions, i.e. a critical or discontinuous dependence of VQ performance on the training set size. We show how the nature and properties of the transition depend on the number of prototypes and the control parameter of rank based cost functions.

Learning Vector Quantization:Generalization ability and dynamics of competing prototypes

Learning Vector Quantization (LVQ) are popular multi-class classification algorithms. Prototypes in an LVQ system represent the typical features of classes in the data. Frequently multiple prototypes are employed for a class to improve the representation of variations within the class and the generalization ability. In this paper, we investigate the dynamics of LVQ in an exact mathematical way, aiming at understanding the influence of the number of prototypes and their assignment to classes. The theory of on-line learning allows a mathematical description of the learning dynamics in model situations. We demonstrate using a system of three prototypes the different behaviors of LVQ systems of multiple prototype and single prototype class representation.

Functional effects of schizophrenia-linked genetic variants on intrinsic single-neuron excitability: A modeling study

Background: Recent genome-wide association studies (GWAS) have identified a large number of genetic risk factors for schizophrenia (SCZ) featuring ion channels and calcium transporters. For some of these risk factors, independent prior investigations have examined the effects of genetic alterations on the cellular electrical excitability and calcium homeostasis. In the present proof-of-concept study, we harnessed these experimental results for modeling of computational properties on layer V cortical pyramidal cell and identify possible common alterations in behavior across SCZ-related genes. Methods: We applied a biophysically detailed multi-compartmental model to study the excitability of a layer V pyramidal cell. We reviewed the literature on functional genomics for variants of genes associated with SCZ, and used changes in neuron model parameters to represent the effects of these variants. Results: We present and apply a framework for examining the effects of subtle single nucleotide polymorphisms in ion channel and Ca2+ transporter-encoding genes on neuron excitability. Our analysis indicates that most of the considered SCZ- related genetic variants affect the spiking behavior and intracellular calcium dynamics resulting from summation of inputs across the dendritic tree. Conclusions: Our results suggest that alteration in the ability of a single neuron to integrate the inputs and scale its excitability may constitute a fundamental mechanistic contributor to mental disease, alongside with the previously proposed deficits in synaptic communication and network behavior