Biomedical subjects

H T Siegelmann

Publications and source records attributed to H T Siegelmann.

3 recordsLinked to original sources

PubMed2000

Overcoming selective ensemble averaging: unsupervised identification of event-related brain potentials.

We present a novel approach to the problem of event-related potential (ERP) identification, based on a competitive artificial neural network (ANN) structure. Our method uses ensembled electroencephalogram (EEG) data just as used in conventional averaging, however without the need for a priori data subgrouping into distinct categories (e.g., stimulus- or event-related), and thus avoids conventional assumptions on response invariability. The competitive ANN, often described as a winner takes all neural structure, is based on dynamic competition among the net neurons where learning takes place only with the winning neuron. Using a simple single-layered structure, the proposed scheme results in convergence of the actual neural weights to the embedded ERP patterns. The method is applied to real event-related potential data recorded during a common odd-ball type paradigm. For the first time, within-session variable signal patterns are automatically identified, dismissing the strong and limiting requirement of a priori stimulus-related selective grouping of the recorded data. The results present new possibilities in ERP research.

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PubMed2000

Clustering irregular shapes using high-order neurons.

This article introduces a method for clustering irregularly shaped data arrangements using high-order neurons. Complex analytical shapes are modeled by replacing the classic synaptic weight of the neuron by high-order tensors in homogeneous coordinates. In the first- and second-order cases, this neuron corresponds to a classic neuron and to an ellipsoidalmetric neuron. We show how high-order shapes can be formulated to follow the maximum-correlation activation principle and permit simple local Hebbian learning. We also demonstrate decomposition of spatial arrangements of data clusters, including very close and partially overlapping clusters, which are difficult to distinguish using classic neurons. Superior results are obtained for the Iris data.

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PubMed1999

Discontinuities in recurrent neural networks.

This article studies the computational power of various discontinuous real computational models that are based on the classical analog recurrent neural network (ARNN). This ARNN consists of finite number of neurons; each neuron computes a polynomial net function and a sigmoid-like continuous activation function. We introduce arithmetic networks as ARNN augmented with a few simple discontinuous (e.g., threshold or zero test) neurons. We argue that even with weights restricted to polynomial time computable reals, arithmetic networks are able to compute arbitrarily complex recursive functions. We identify many types of neural networks that are at least as powerful as arithmetic nets, some of which are not in fact discontinuous, but they boost other arithmetic operations in the net function (e.g., neurons that can use divisions and polynomial net functions inside sigmoid-like continuous activation functions). These arithmetic networks are equivalent to the Blum-Shub-Smale model, when the latter is restricted to a bounded number of registers. With respect to implementation on digital computers, we show that arithmetic networks with rational weights can be simulated with exponential precision, but even with polynomial-time computable real weights, arithmetic networks are not subject to any fixed precision bounds. This is in contrast with the ARNN that are known to demand precision that is linear in the computation time. When nontrivial periodic functions (e.g., fractional part, sine, tangent) are added to arithmetic networks, the resulting networks are computationally equivalent to a massively parallel machine. Thus, these highly discontinuous networks can solve the presumably intractable class of PSPACE-complete problems in polynomial time.

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