Deficits in auditory perception have been widely observed in Parkinson's disease (PD) patients and the literature attributes it, in part, to impaired central auditory processing. Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is a well-established therapeutic option for patients with advanced PD. Analysis of auditory evoked potentials suggested a modulatory effect of DBS on central auditory processing. To better understand the latter, we investigated whether DBS modulates auditory steady state responses (ASSR) in electroencephalography (EEG) recordings of 5 PD patients. ASSRs are neural responses along central auditory pathways phase-locked to an auditory stimulus which can serve to understand the spectral aspects of central auditory processing. In our analyses, we estimate the intensity of ASSRs with a novel method based on canonical correlation analysis (CCA) and compare them in DBS ON and OFF conditions. Our results suggest that DBS effectively reduces ASSR in patients with PD. A comparison to age-matched healthy participants suggests a pathological effect of PD on ASSRs, which is disrupted by DBS. These findings support our hypothesis that DBS suppresses central auditory processing. Further research is required to assess the symptomatic effect of this modulation, as well as which cortical and subcortical generators are most affected. A better understanding of the auditory side-effects of DBS could lead to improved treatment options.

Multiway- or tensor-based decoding techniques for brain-computer interfaces (BCIs) are believed to better account for the multilinear structure of brain signals than conventional vector- or matrix-based ones. However, despite their outlook on significant performance gains, the used parameter optimization approach is often too computationally demanding so that conventional techniques are still preferred. We propose two novel tensor factorizations which we integrate into our block-term tensor regression (BTTR) algorithm and further introduce a marginalization procedure that guarantees robust predictions while reducing the risk of overfitting (generalized regression). BTTR accounts for the underlying (hidden) data structure in a fully automatic and computationally efficient manner, leading to a significant performance gain over conventional vector- or matrix-based techniques in a challenging real-world application. As a challenging real-world application, we apply BTTR to accurately predict single finger movement trajectories from intracranial recordings in human subjects. We compare the obtained performance with that of the state-of-the-art.

We introduce a WaveNet-based model that placed second in the Auditory EEG Challenge on the regression subtask of the ICASSP Signal Processing Grand Challenge 2023. The model achieved the highest score on the held-out subjects test set with 341k trainable parameters. In this paper, we present our network architecture, and training strategies along with a short discussion.

Covert attention has been repeatedly shown to impact on EEG responses after single and repeated practice sessions. Machine learning techniques are increasingly adopted to classify single-trial EEG responses thereby primarily relying on amplitude-based features instead of latency-based features. In this study, we investigated changes in EEG response signatures of nine healthy older subjects when performing 10 sessions of covert attention training. We show that, when we trained classifiers to distinguish recorded EEG patterns between the two experimental conditions (a target stimulus is "present" or "not present"), latency-based classifiers outperform the amplitude-based ones and that classification accuracy improved along with behavioral accuracy, providing supportive evidence of brain plasticity.

We trained two spiking neural networks (SNNs), the cortical spiking network (CSN) and the cortical neuron-astrocyte network (CNAN), using a spike-based unsupervised method, on the MNIST and alpha-digit data sets and achieve an accuracy of 96.1% and 77.35%, respectively. We then connected CNAN to CSN by preserving maximum synchronization between them thanks to the concept of prolate spheroidal wave functions (PSWF). As a result, CSN receives additional information from CNAN without retraining. The important outcome is that CSN reaches 70.57% correct classification rate on capital letters without being trained on them. The overall contribution of transfer is 87.47%. We observed that for CSN the classifying neurons that relate to digits 0-9 of the alpha-digit data set are completely supported by the ones that relate to digits 0-9 of the MNIST data set. This means that CSN recognizes the similarity between the digits of the MNIST and alpha-digit data sets and classifies each digit of both data sets in the same class.

The steady-state visual evoked potential (SSVEP) is an electrophysiological response to visual stimulation at a particular frequency. Despite its widespread adoption, primarily a spectral analysis of the recorded signal is performed, and variations in its temporal dynamics are often neglected or considered undesired. In this manuscript, we describe a method for monitoring the temporal dynamics of the SSVEP, and show its efficacy for detecting modifications of the stimulation profile on a single-trial basis. The anomalies elicited by single stimulus modifications were detected with an accuracy of 88%, demonstrating the reliability of the approach.

We investigate the effect of word typicality - the degree of membership of a word to its superordinate category - on the N400 event-related potential (ERP) using a single trial detection approach based on spatiotemporal beamforming. Unlike the norm in studies, where mostly concrete categories are used (imaginable objects), we considered a total of 6 basic categories: three abstract and unimaginable (emotion, event, illness), one abstract yet clearly imaginable (color), and two concrete categories, a coherent (mammals) and an incoherent one (furniture). We also investigated the source of the observed N400 ERPs in the brain to detect possible differences between the semantic processing of these categories. Our results show that, independently of word abstractness or concreteness, word typicality has a clear effect on N400 both in terms of amplitude and scalp localization as well as in N400 sources, all of which in turn is indicative of differences in difficulty of word processing.

A multivariate sample entropy metric of signal complexity is applied to EEG data recorded when subjects were viewing four prior-labeled emotion-inducing video clips from a publically available, validated database. Besides emotion category labels, the video clips also came with arousal scores. Our subjects were also asked to provide their own emotion labels. In total 30 subjects with age range 19-70 years participated in our study. Rather than relying on predefined frequency bands, we estimate multivariate sample entropy over multiple data-driven scales using the multivariate empirical mode decomposition (MEMD) technique and show that in this way we can discriminate between five self-reported emotions (p < 0.05). These results could not be obtained by analyzing the relation between arousal scores and video clips, signal complexity and arousal scores, and self-reported emotions and traditional power spectral densities and their hemispheric asymmetries in the theta, alpha, beta, and gamma frequency bands. This shows that multivariate, multiscale sample entropy is a promising technique to discriminate multiple emotional states from EEG recordings.

The linearly-constrained minimum-variance (LCMV) beamformer is traditionally used as a spatial filter for source localization, but here we consider its spatiotemporal extension for P300 classification. We compare two variants and show that the spatiotemporal LCMV beamformer is at par with state-of-the-art P300 classifiers, but several orders of magnitude faster in training the classifier.

In this paper, we introduce a game in which the player navigates an avatar through a maze by using a brain-computer interface (BCI) that analyzes the steady-state visual evoked potential (SSVEP) responses recorded with electroencephalography (EEG) on the player's scalp. The four-command control game, called The Maze, was specifically designed around an SSVEP BCI and validated in several EEG setups when using a traditional electrode cap with relocatable electrodes and a consumer-grade headset with fixed electrodes (Emotiv EPOC). We experimentally derive the parameter values that provide an acceptable tradeoff between accuracy of game control and interactivity, and evaluate the control provided by the BCI during gameplay. As a final step in the validation of the game, a population study on a broad audience was conducted with the EPOC headset in a real-world setting. The study revealed that the majority (85%) of the players enjoyed the game in spite of its intricate control (mean accuracy 80.37%, mean mission time ratio 0.90). We also discuss what to take into account while designing BCI-based games.

Recently developed CMOS-based microprobes contain hundreds of electrodes on a single shaft with inter-electrode distances as small as 30 μm. So far, neuroscientists needed to select electrodes manually from hundreds of electrodes. Here we present an electronic depth control algorithm that allows to select electrodes automatically, hereby allowing to reduce the amount of data and locating those electrodes that are close to neurons. The electrodes are selected according to a new penalized signal-to-noise ratio (PSNR) criterion that demotes electrodes from becoming selected if their signals are redundant with previously selected electrodes. It is shown that, using the PSNR, interneurons generating smaller spikes are also selected. We developed a model that aims to evaluate algorithms for electronic depth control, but also generates benchmark data for testing spike sorting and spike detection algorithms. The model comprises a realistic tufted pyramidal cell, non-tufted pyramidal cells and inhibitory interneurons. All neurons are synaptically activated by hundreds of fibers. This arrangement allows the algorithms to be tested in more realistic conditions, including backgrounds of synaptic potentials, varying spike rates with bursting and spike amplitude attenuation.

We propose a complex-valued multilayer feedforward neural network classifier for decoding of phase-coded information from steady-state visual evoked potentials. To optimize the performance of the classifier we supply it with two filter-based feature selection strategies. The proposed approaches could be used for a phase-coded brain-computer interface, enabling to encode several targets using only one stimulation frequency. The proposed classifier is a multichannel one, which distinguishes our approach from the existing single-channel ones. We show that the proposed approach outperforms others in terms of accuracy and length of the data segments used for decoding. We show that the decoding based on one optimally selected channel yields an inferior performance compared to the one based on several features, which supports our argument for a multichannel approach.

We present a hybrid neural network architecture that supports the estimation of binocular disparity in a cyclopean, head-centric coordinate system without explicitly establishing retinal correspondences. Instead the responses of binocular energy neurons are gain-modulated by oculomotor signals. The network can handle the full six degrees of freedom of binocular gaze and operates directly on image pairs of possibly varying contrast. Furthermore, we show that in the absence of an oculomotor signal the same architecture is capable of estimating the epipolar geometry directly from the population response. The increased complexity of the scenarios considered in this work provides an important step towards the application of computational models centered on gain modulation mechanisms in real-world robotic applications. The proposed network is shown to outperform a standard computer vision technique on a disparity estimation task involving real-world stereo images.

Low-level computer vision algorithms have extreme computational requirements. In this work, we compare two real-time architectures developed using FPGA and GPU devices for the computation of phase-based optical flow, stereo, and local image features (energy, orientation, and phase). The presented approach requires a massive degree of parallelism to achieve real-time performance and allows us to compare FPGA and GPU design strategies and trade-offs in a much more complex scenario than previous contributions. Based on this analysis, we provide suggestions to real-time system designers for selecting the most suitable technology, and for optimizing system development on this platform, for a number of diverse applications.

To offer increased security and comfort, advanced driver-assistance systems (ADASs) should consider individual driving styles. Here, we present a system that learns a human's basic driving behavior and demonstrate its use as ADAS by issuing alerts when detecting inconsistent driving behavior. In contrast to much other work in this area, which is based on or obtained from simulation, our system is implemented as a multithreaded parallel central processing unit (CPU)/graphics processing unit (GPU) architecture in a real car and trained with real driving data to generate steering and acceleration control for road following. It also implements a method for detecting independently moving objects (IMOs) for spotting obstacles. Both learning and IMO detection algorithms are data driven and thus improve above the limitations of model-based approaches. The system's ability to imitate the teacher's behavior is analyzed on known and unknown streets, and results suggest its use for steering assistance but limit the use of the acceleration signal to curve negotiation. We propose that this ability to adapt to the driver can lead to better acceptance of ADAS, which is an important sales argument.

A novel complex echo state network (ESN), utilizing full second-order statistical information in the complex domain, is introduced. This is achieved through the use of the so-called augmented complex statistics, thus making complex ESNs suitable for processing the generality of complex-valued signals, both second-order circular (proper) and noncircular (improper). Next, in order to deal with nonstationary processes with large nonlinear dynamics, a nonlinear readout layer is introduced and is further equipped with an adaptive amplitude of the nonlinearity. This combination of augmented complex statistics and enhanced adaptivity within ESNs also facilitates the processing of bivariate signals with strong component correlations. Simulations in the prediction setting on both circular and noncircular synthetic benchmark processes and real-world noncircular and nonstationary wind signals support the analysis.

We present two neural models for vergence angle control of a robotic head, a simplified and a more complex one. Both models work in a closed-loop manner and do not rely on explicitly computed disparity, but extract the desired vergence angle from the post-processed response of a population of disparity tuned complex cells, the actual gaze direction and the actual vergence angle. The first model assumes that the gaze direction of the robotic head is orthogonal to its baseline and the stimulus is a frontoparallel plane orthogonal to the gaze direction. The second model goes beyond these assumptions, and operates reliably in the general case where all restrictions on the orientation of the gaze, as well as the stimulus position, type and orientation, are dropped.

We propose an invasive brain-machine interface (BMI) that decodes the orientation of a visual grating from spike train recordings made with a 96 microelectrodes array chronically implanted into the prelunate gyrus (area V4) of a rhesus monkey. The orientation is decoded irrespective of the grating's spatial frequency. Since pyramidal cells are less prominent in visual areas, compared to (pre)motor areas, the recordings contain spikes with smaller amplitudes, compared to the noise level. Hence, rather than performing spike decoding, feature selection algorithms are applied to extract the required information for the decoder. Two types of feature selection procedures are compared, filter and wrapper. The wrapper is combined with a linear discriminant analysis classifier, and the filter is followed by a radial-basis function support vector machine classifier. In addition, since we have a multiclass classification problen, different methods for combining pairwise classifiers are compared.

Single-trial decoding of brain recordings is a real challenge, since it pushes the signal-to-noise ratio issue to the limit. In this paper, we concentrate on the single-trial decoding of stimulus-reward pairing from local field potentials (LFPs) recorded chronically in the visual cortical area V4 of monkeys during a perceptual conditioning task. We developed a set of physiologically meaningful features that can classify and monitor the monkey's training performance. One of these features is based on the recently discovered propagation of waves of LFPs in the visual cortex. Time-frequency features together with spatial features (phase synchrony and wave propagation) yield, after applying a feature selection procedure, an exceptionally good single-trial classification performance, even when using a linear classifier.

The Mind Speller is a Brain-Computer Interface which enables subjects to spell text on a computer screen by detecting P300 Event-Related Potentials in their electroencephalograms. This BCI application is of particular interest for disabled patients who have lost all means of verbal and motor communication. We report on the implementation of a feature extraction procedure on a new ultra low-power 8-channel wireless EEG device. The feature extraction procedure is based on downsampled EEG signal epochs, the Student's t-statistic of the Continuous Wavelet Transform, and the Common Spatial Pattern technique. For classification, we use a linear Least-Squares Support Vector Machine. The results show that subjects are potentially able to communicate a character in less than ten seconds with an accuracy of 94.5%, which is more than twice as fast as the state of the art. In addition since our EEG device is wireless it offers an increased comfort to the subject.

In this paper, we describe a new methodology for defining brain regions-of-interset (ROIs) in functional magnetic resonance imaging (fMRI) data. The ROIs are defined based on their functional connectivity to other ROIs, i.e., ROIs are defined as sets of voxels with similar connectivity patterns to other ROIs. The method relies on 1) a spatially regularized canonical correlation analysis for identifying maximally correlated signals, which are not due to correlated noise; 2) a test for merging ROIs which have similar connectivity patterns to the other ROIs; and 3) a graph-cuts optimization for assigning voxels to ROIs. Since our method is fully connectivity-based, the extracted ROIs and their corresponding time signals are ideally suited for a subsequent brain connectivity analysis.

We introduce a new approach to constrained independent component analysis (ICA) by formulating the original, unconstrained ICA problem as well as the constraints in mutual information terms directly. As an estimate of mutual information, a robust version of the Edgeworth expansion is used, on which gradient descent is performed. As an application, we consider the extraction of both the mother and the fetal antepartum electrocardiograms (ECG) from multielectrode cutaneous recordings on the mother's thorax and abdomen.

A new gradient technique is introduced for linear independent component analysis (ICA) based on the Edgeworth expansion of mutual information, for which the algorithm operates sequentially using fixed-point iterations. In order to address the adverse effect of outliers, a robust version of the Edgeworth expansion is adopted, in terms of robust cumulants, and robust derivatives of the Hermite polynomials are used. Also, a new constrained version of ICA is introduced, based on goal programming of mutual information objectives, which is applied to the extraction of the antepartum fetal electrocardiogram from multielectrode cutaneous recordings on the mother's thorax and abdomen.

A new detection criterion based on the change in the marginal information redundancy is presented. By establishing a link with information theory we are able to give an intuitive interpretation of our criterion. The usefulness of the new criterion is demonstrated for a case study of human movement initiation detection from force and torque signals in activity of daily living tasks. Using the new criterion, we achieve a performance that is more in agreement with expert decisions compared with traditional thresholding techniques and the advanced wavelet-based detector and energy detectors.

A novel stabilization method is introduced that enables the extraction of optic flow from short unstable sequences. Contrary to traditional stabilization techniques that use approximative global motion models to estimate the full camera motion, our method estimates the unstable component of the camera motion only. This allows for the use of even simpler global motion models, while at the same time extending the validity to more diverse environments, such as close scenes containing independently moving objects. The unstable component of the camera motion is derived for each frame by maximizing the temporal constancy of the local velocities over the entire short sequence. The method is embedded within a phase-based optic flow algorithm and tested on complex real-world sequences. The optic flow obtained using our technique is much denser than that extracted directly from the original sequence. The proposed method also compares favorably to a more traditional stabilization technique.

We introduce a new unbiased metric for assessing the quality of density estimation based on gaussian mixtures, called differential log likelihood. As an application, we determine the optimal smoothness and the optimal number of kernels in gaussian mixtures. Furthermore, we suggest a learning strategy for gaussian mixture density estimation and compare its performance with log likelihood maximization for a wide range of real-world data sets.

In this letter, two batch-map extensions are described for the kernel-based maximum entropy learning rule (kMER). In the first, the weights are iteratively set to weighted component-wise medians, while in the second the generalized median is used, enabling kMER to process symbolic data. Simulations are performed to illustrate the extensions.

A novel, nonlinear algorithm is introduced for the estimation of rigid camera motion from instantaneous velocity measurements in the calibrated case. It is shown that by minimizing an approximation to the image-reprojection error rather than the actual error, as done by the optimal algorithms, the proposed algorithm achieves largely increased robustness to local minima at the cost of a slightly decreased accuracy.

An assessment of the performance of the pipelined recurrent neural network (PRNN) is provided from two aspects, a quantitative one based on the prediction gain and a qualitative one based on examining the changes in the nature of the processed signal. This is achieved by means of the recently introduced 'delay vector variance' (DVV) method for phase space signal characterisation. A comprehensive analysis of this approach on both linear and nonlinear benchmark signals suggests that the PRNN not only outperforms a single recurrent neural network (RNN) in terms of the prediction gain, but also has better or similar performance in terms of preserving the nature of the processed signal.

We introduce a new unsupervised learning algorithm for kernel-based topographic map formation of heteroscedastic gaussian mixtures that allows for a unified account of distortion error (vector quantization), log-likelihood, and Kullback-Leibler divergence.

Instead of increasing the order of the Edgeworth expansion of a single gaussian kernel, we suggest using mixtures of Edgeworth-expanded gaussian kernels of moderate order. We introduce a simple closed-form solution for estimating the kernel parameters based on weighted moment matching. Furthermore, we formulate the extension to the multivariate case, which is not always feasible with algebraic density approximation procedures.

We develop the general, multivariate case of the Edgeworth approximation of differential entropy and show that it can be more accurate than the nearest-neighbor method in the multivariate case and that it scales better with sample size. Furthermore, we introduce mutual information estimation as an application.

We describe a method to model connectivity patterns between words in a document collection. These connectivity patterns may be helpful to gain more insight in the meaning of the document collection as a whole, in the semantics of the field, or they may be used in other applications like information retrieval, query-refinement, question-answering, etc. Structural equation modelling (SEM) has been used as a statistical technique for modelling the connectivities between terms. Furthermore, in order to validate the goodness-of-fit of the models, we adopt a bootstrapping approach since the data encountered in text mining applications are likely to violate the underlying assumptions of SEM and the calculated test statistics often does follow the theoretical distributions. We applied the described method on a corpus of journal articles taken from the neuroscience literature.

A new information-theoretic learning algorithm for kernel-based topographic map formation is introduced. In the one-dimensional case, the algorithm is aimed at uniformizing the cumulative distribution of the kernel mixture densities by maximizing its differential entropy. A nonparametric differential entropy estimator is used on which normalized gradient ascent is performed. Both differentiable and nondifferentiable kernels are in principle supported, such as Gaussian and rectangular (on/off) kernels. The relation is shown with joint entropy maximization of the kernel outputs. The learning algorithm's performance is assessed and compared with the theoretically optimal performance. A fixed-point rule is derived for the case of heterogeneous kernel mixtures. Finally, an extension of the algorithm to the multidimensional case is suggested.

A novel method for determining the set of parameters for a phase space representation of a time series is proposed. Based upon the differential entropy, both the optimal embedding dimension m, and time lag /spl tau/, are simultaneously determined. The choice of these parameters is closely related to the length of the optimal tap input delay line of an adaptive filter or time-delay neural network. The method employs a single criterion - the "entropy ratio" between the phase space representation of a signal and an ensemble of its surrogates - and is first systematically tested on synthetic time series for which the optimal embedding parameters are known, after which it is verified on a number of benchmark real-world time series. The proposed entropy ratio method is shown to consistently outperform some well-established methods.

A comparative study of neural implementations running principal component analysis (PCA) and independent component analysis (ICA) was carried out. Both artificially generated data and real biomedical time series were employed in order to critically evaluate and assess the performance of various algorithms under study. The assumption of independence, even if weak, was proved reach in relevant interferences on brain activity. The ICA algorithms were proved more realistic in terms of neurophysiological relevance as compared to PCA.

In this paper, we introduce a methodology for comparing the nonlinearities present in sets of time series using four different nonlinearity measures, one of which, the "delay vector variance" method, is a novel approach to the characterization of a time series. It is then applied to examine the difference in nonlinearity between functional magnetic resonance imaging (fMRI) signals that have been recorded using different contrast agents. Recently, an exogenous contrast agent, monocrystalline iron oxide particle (MION), has been introduced for fMRI, which has been shown to increase the functional sensitivity compared with the traditional blood oxygen level dependent (BOLD) technique. The resulting fMRI signals are influenced by cerebral blood volume, whereas the more traditionally recorded BOLD signals are influenced not only by cerebral blood volume, but also by the cerebral blood flow and the metabolic rate of oxygen. The proposed methodology is applied to address the question whether this difference in the number of physiological variables is reflected in a difference in the degree of nonlinearity. We therefore analyze two sets of fMRI signals, one from a BOLD and the other from a MION monkey study with similar experimental designs. In the neuroimaging context, the proposed nonlinearity analyses are different from those described in the literature, since no a priori model is assumed: rather than pinpointing the source(s) of nonlinearity, nonparametric analyses are performed on BOLD and MION fMRI signals. Furthermore, we introduce a strategy for analyzing a population of fMRI signals, rather than focusing the analysis on one signal, as is traditionally done in the domain of nonlinear signal processing. Our results show that, overall, the BOLD signals are more nonlinear in nature than the MION ones, which is in agreement with current hypotheses.

We introduce a new learning algorithm for kernel-based topographic map formation. The algorithm generates a gaussian mixture density model by individually adapting the gaussian kernels' centers and radii to the assumed gaussian local input densities.

A new learning algorithm for kernel-based topographic map formation is introduced. The kernel parameters are adjusted individually so as to maximize the joint entropy of the kernel outputs. This is done by maximizing the differential entropies of the individual kernel outputs, given that the map's output redundancy, due to the kernel overlap, needs to be minimized. The latter is achieved by minimizing the mutual information between the kernel outputs. As a kernel, the (radial) incomplete gamma distribution is taken since, for a gaussian input density, the differential entropy of the kernel output will be maximal. Since the theoretically optimal joint entropy performance can be derived for the case of nonoverlapping gaussian mixture densities, a new clustering algorithm is suggested that uses this optimum as its "null" distribution. Finally, it is shown that the learning algorithm is similar to one that performs stochastic gradient descent on the Kullback-Leibler divergence for a heteroskedastic gaussian mixture density model.

We introduce a new technique for estimating the optical flow field, starting from image sequences. As suggested by Fleet and Jepson (1990), we track contours of constant phase over time, since these are more robust to variations in lighting conditions and deviations from pure translation than contours of constant amplitude. Our phase-based approach proceeds in three stages. First, the image sequence is spatially filtered using a bank of quadrature pairs of Gabor filters, and the temporal phase gradient is computed, yielding estimates of the velocity component in directions orthogonal to the filter pairs' orientations. Second, a component velocity is rejected if the corresponding filter pair's phase information is not linear over a given time span. Third, the remaining component velocities at a single spatial location are combined and a recurrent neural network is used to derive the full velocity. We test our approach on several image sequences, both synthetic and realistic.

A new unsupervised competitive learning rule is introduced, called the kernel-based Maximum Entropy learning Rule (kMER), for equiprobabilistic topographic map formation. The application envisaged is density-based clustering. An empirical study is conducted to compare the clustering performance of kMER with that of a number of other unsupervised competitive learning rules.

We introduce a new unsupervised competitive learning rule, the kernel-based maximum entropy learning rule (kMER), which performs equiprobabilistic topographic map formation in regular, fixed-topology lattices, for use with nonparametric density estimation as well as nonparametric regression analysis. The receptive fields of the formal neurons are overlapping radially symmetric kernels, compatible with radial basis functions (RBFs); but unlike other learning schemes, the radii of these kernels do not have to be chosen in an ad hoc manner: the radii are adapted to the local input density, together with the weight vectors that define the kernel centers, so as to produce maps of which the neurons have an equal probability to be active (equiprobabilistic maps). Both an "online" and a "batch" version of the learning rule are introduced, which are applied to nonparametric density estimation and regression, respectively. The application envisaged is blind source separation (BSS) from nonlinear, noisy mixtures.

The projective transformation onto the retina loses the explicit 3D shape description of a moving object. Theoretical studies show that the reconstruction of 3D shape from 2D motion information (shape from motion, SFM) is feasible provided that the first- and second-order directional derivatives of the 2D velocity field are available. Experimental recordings have revealed that the receptive fields of the majority of the cells in macaque area middle temporal (MT) display an antagonistic (suppressive) surround and that a sizable portion of these surrounds are asymmetrical. This has led to the conjecture that these cells provide a local measure for the directional derivatives of the 2D velocity field. In this article, we adopt a nonparametric and biologically plausible approach to modeling the role played by the MT surrounds in the recovery of the orientation in depth (the slant and tilt) of a moving (translating) plane. A three-layered neural network is trained to represent the slant and tilt from the projected motion vectors. The hidden units of the network have speed-tuning characteristics and represent the MT model neurons with their surrounds. We conjecture that the MT surround results from lateral inhibitory connections with other MT cells and that populations of these cells, with different surround types, code linearly for slant and tilt of translating planes.

This article introduces an extremely simple and local learning rule for to pographic map formation. The rule, called the maximum entropy learning rule (MER), maximizes the unconditional entropy of the map's output for any type of input distribution. The aim of this article is to show that MER is a viable strategy for building topographic maps that maximize the average mutual information of the output responses to noiseless input signals when only input noise and noise-added input signals are available.

An unsupervised competitive learning rule, called the vectorial boundary adaptation rule (VBAR), is introduced for topographic map formation. Since VBAR is aimed at producing an equiprobable quantization of the input space, it yields a nonparametric model of the input probability density function. Furthermore, since equiprobable quantization is equivalent to unconditional entropy maximization, we argue that this is a plausible strategy for maximizing mutual information (Shannon information rate) in the case of "online" learning. We use mutual information as a tool for comparing the performance of our rule with Kohonen's self-organizing (feature) map algorithm.

Abstract We present two strategies for the simulation of massive neural networks on message‐passing MIMD machines. In the first strategy all interconnections between neurons are stored explicitly in interconnection matrices. During simulation, every processor is responsible for certain submatrices of these interconnection matrices. The fact that message‐passing MIMD processors do not provide virtual memory seriously limits the size of the networks that can be simulated, since interconnection matrices require huge amounts of memory. An alternative strategy is not to store the connections explicitly, but generate the interconnections as they are needed. This circumvents memory limitations, but because interconnections need to be generated multiple times, it is inherently slower than the first implementation. This yields the connections dilemma: the choice between fast simulation of small networks as against slower simulation of massive networks. We present, analyze and bench‐mark parallel implementations for both strategies. An efficient connection‐look‐up algorithm, which can be used for any network with static interconnections, ensures that simulation times for the second strategy are only marginally longer than for the first strategy. We show that for our users the connections dilemma is no longer a dilemma: by means of our look‐up algorithm the simulation of massive networks becomes possible; furthermore the time to design and construct a network, prior to simulation, is considerably shorter than it is for the matrix version, and in addition this time is independent of network size. Although we have implemented both strategies on a parallel computer, the algorithms presented here can be used on any machine with memory limitations, such as personal computers.

This letter presents a novel unsupervised competitive learning rule called the boundary adaptation rule (BAR), for scalar quantization. It is shown both mathematically and by simulations that BAR converges to equiprobable quantizations of univariate probability density functions and that, in this way, it outperforms other unsupervised competitive learning rules.

A novel unsupervised learning rule, called Boundary Adaptation Rule (BAR), is introduced for scalar quantization. It is shown that the rule maximizes information-theoretic entropy and thus yields equiprobable quantizations of univariate probability density functions. It is shown by simulations that BAR outperforms other unsupervised competitive learning rules in generating equiprobable quantizations. It is also shown that our rule can do better or worse than the Lloyd I algorithm in minimizing average mean square error, depending on the input distribution. Finally, an application to adaptive non-uniform analog to digital (A/D) conversion is considered.

Job-shop scheduling is an np-complete optimization problem subject to precedence and resource constraints. Recently, Foo and Takefuji have introduced a network-based solution procedure for solving job-shop problems formulated as mixed integer linear programming problems. To obtain the solution, the Tank and Hopfield linear programming network was repeatedly used. However, since such a network frequently produces constraint-violating solutions, the reliability of Foo and Takefuji’s approach is doubtful. In this article, it is shown that reliability of the network approach can be greatly improved, by guaranteeing constraint-satisfying solutions, if the original job-shop problem is reformulated as a goal programming problem, before it is mapped onto a goal programming network.