What makes a neural microcircuit computationally powerful?

An important aspect of clustering algorithms is whether the partitions constructed on finite samples converge to a useful clustering of the whole data space as the sample size increases. This paper investigates this question for normalized and unnormalized versions of the popular spectral clusteringalgorithm. Surprisingly, the convergence of unnormalized spectral clustering is more difficult to handle than the normalized case. Even though recently some first results on the convergence of normalized spectralclustering have been obtained, for the unnormalized case we have to develop a completely new approach combining tools from numerical integration, spectral and perturbation theory, and probability. It turns out that while in the normalized case, spectral clustering usually converges to a nice partition of the data space, in the unnormalized case the same only holds under strong additional assumptions which are not always satisfied. We conclude that our analysis gives strong evidence for the superiority of normalized spectral clustering. It also provides a basis for future exploration of other Laplacian-based methods.

Dixon describes beats as follows: "much music has as its rhythmic basis a series of pulses, spaced approximately equally in time, relative to which the timing of all musical events can be described. This phenomenon is called the beat, and the individual pulses are also called beats"[1]. Given a piece of recorded music (an MP3 file, for example), we wish to produce a set of beats that correspond to the beats perceived by human listeners. The set of beats of a song can be characterised by the trajectories through time of thetempo and phase offset. Tempo is typically measured in beats per minute (BPM), and describes the frequency of beats.

During the last ten years there has been growing interest in the development ofBrain Computer Interfaces (BCIs). The field has mainly been driven by the needs of completely paralyzed patients to communicate. With a few exceptions, most human BCIs are based on extracranial electroencephalography (EEG).However, reported bit rates are still low. One reason for this is the low signal-to-noise ratio of the EEG [16]. We are currently investigating if BCIs based on electrocorticography (ECoG) are a viable alternative. In this paper we present the method and examples of intracranial EEG recordings of three epilepsy patients with electrode grids placed on the motor cortex. The patients were asked to repeatedly imaginemovements of two kinds, e.g., tongue or finger movements. We analyze the classifiability of the data using Support Vector Machines (SVMs) [18, 21] and Recursive Channel Elimination (RCE) [11].

We propose a gossip-based distributed algorithm for Gaussian mixture learning, Newscast EM. The algorithm operates on network topologies where each node observes a local quantity and can communicate with other nodes in an arbitrary point-to-point fashion. The main difference between Newscast EM and the standard EM algorithm is that the M-step in our case is implemented in a decentralized manner: (random) pairs of nodes repeatedly exchange their local parameter estimates and combine themby (weighted) averaging. We provide theoretical evidence and demonstrate experimentally that, under this protocol, nodes converge exponentially fastto the correct estimates in each M-step of the EM algorithm.

Two neural networks that are trained on their mutual output synchronize to an identical time dependant weight vector. This novel phenomenon can be used for creation of a secure cryptographic secret-key using a public channel. Several models for this cryptographic system have been suggested, and have been tested for their security under different sophisticated attackstrategies. The most promising models are networks that involve chaos synchronization. The synchronization process of mutual learning is described analytically using statistical physics methods.

This paper proposes a method for computing fast approximations to support vectordecision functions in the field of object detection. In the present approach we are building on an existing algorithm where the set of support vectors is replaced by a smaller, so-called reduced set of synthesized inputspace points. In contrast to the existing method that finds the reduced set via unconstrained optimization, we impose a structural constraint on the synthetic points such that the resulting approximations can be evaluated via separable filters. For applications that require scanning largeimages, this decreases the computational complexity by a significant amount.Experimental results show that in face detection, rank deficient approximations are 4 to 6 times faster than unconstrained reduced setsystems.

In this paper we present a framework for using multi-layer perceptron (MLP)networks in nonlinear generative models trained by variational Bayesian learning. The nonlinearity is handled by linearizing it using a Gauss-Hermite quadrature at the hidden neurons. Thisyields an accurate approximation for cases of large posterior variance.The method can be used to derive nonlinear counterparts forlinear algorithms such as factor analysis, independent component/factor analysis and state-space models. This is demonstrated witha nonlinear factor analysis experiment in which even 20 sources can be estimated from a real world speech data set.

Motivated by the particular problems involved in communicating with "locked-in" paralysed patients, we aim to develop a braincomputer interfacethat uses auditory stimuli. We describe a paradigm that allows a user to make a binary decision by focusing attention on one of two concurrent auditory stimulus sequences. Using Support Vector Machine classification and Recursive Channel Eliminationon the independent components of averaged eventrelated potentials,we show that an untrained user's EEG data can be classified with an encouragingly high level of accuracy. This suggests that it is possible for users to modulate EEG signals in a single trial by the conscious direction of attention, well enough to be useful in BCI.

Saliency mechanisms play an important role when visual recognition must be performed in cluttered scenes. We propose a computational definition ofsaliency that deviates from existing models by equating saliency to discrimination. In particular, the salient attributes of a given visual class are defined as the features that enable best discrimination between that class and all other classes of recognition interest. It is shown that this definition leads to saliency algorithms of low complexity, that are scalable to large recognition problems, and is compatible with existing models of early biological vision. Experimental results demonstrating success in the context of challenging recognition problems are also presented.