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We propose simple and fast methods based on nearest neighbors that order objects from high-dimensional data sets from typical points to untypical points. On the one hand, we show that these easy-to-compute orderings allow us to detect outliers (i.e. very untypical points) with a performance comparable to or better than other often much more sophisticated methods. On the other hand, we show how to use these orderings to detect prototypes (very typical points) which facilitate exploratory data analysis algorithms such as noisy nonlinear dimensionality reduction and clustering. Comprehensive experiments demonstrate the validity of our approach.
A brain-computer interface (BCI) is a system that allows its users to control external devices with brain activity. Although the proof-of-concept was given decades ago, the reliable translation of user intent into device control commands is still a major challenge. Success requires the effective interaction of two adaptive controllers: the user's brain, which produces brain activity that encodes intent, and the BCI system, which translates that activity into device control commands. In order to facilitate this interaction, many laboratories are exploring a variety of signal analysis techniques to improve the adaptation of the BCI system to the user. In the literature, many machine learning and pattern classification algorithms have been reported to give impressive results when applied to BCI data in offline analyses. However, it is more difficult to evaluate their relative value for actual online use. BCI data competitions have been organized to provide objective formal evaluations of alternative methods. Prompted by the great interest in the first two BCI Competitions, we organized the third BCI Competition to address several of the most difficult and important analysis problems in BCI research. The paper describes the data sets that were provided to the competitors and gives an overview of the results.
Combined optimization of spatial and temporal filters for improving brain-computer interfacing
(2006)
Brain-computer interface (BCI) systems create a novel communication channel from the brain to an output de ice by bypassing conventional motor output pathways of nerves and muscles. Therefore they could provide a new communication and control option for paralyzed patients. Modern BCI technology is essentially based on techniques for the classification of single-trial brain signals. Here we present a novel technique that allows the simultaneous optimization of a spatial and a spectral filter enhancing discriminability rates of multichannel EEG single-trials. The evaluation of 60 experiments involving 22 different subjects demonstrates the significant superiority of the proposed algorithm over to its classical counterpart: the median classification error rate was decreased by 11%. Apart from the enhanced classification, the spatial and/or the spectral filter that are determined by the algorithm can also be used for further analysis of the data, e.g., for source localization of the respective brain rhythms.
Phase synchronization is an important phenomenon that occurs in a wide variety of complex oscillatory processes. Measuring phase synchronization can therefore help to gain fundamental insight into nature. In this Letter we point out that synchronization analysis techniques can detect spurious synchronization, if they are fed with a superposition of signals such as in electroencephalography or magnetoencephalography data. We show how techniques from blind source separation can help to nevertheless measure the true synchronization and avoid such pitfalls
A blind separation problem where the sources are not independent, but have variance dependencies is discussed. For this scenario Hyvarinen and Hurri (2004) proposed an algorithm which requires no assumption on distributions of sources and no parametric model of dependencies between components. In this paper, we extend the semiparametric approach of Amari and Cardoso (1997) to variance dependencies and study estimating functions for blind separation of such dependent sources. In particular, we show that many ICA algorithms are applicable to the variance-dependent model as well under mild conditions, although they should in principle not. Our results indicate that separation can be done based only on normalized sources which are adjusted to have stationary variances and is not affected by the dependent activity levels. We also study the asymptotic distribution of the quasi maximum likelihood method and the stability of the natural gradient learning in detail. Simulation results of artificial and realistic examples match well with our theoretical findings
This paper proposes a new independent component analysis (ICA) method which is able to unmix overcomplete mixtures of sparce or structured signals like speech, music or images. Furthermore, the method is designed to be robust against outliers, which is a favorable feature for ICA algorithms since most of them are extremely sensitive to outliers. Our approach is based on a simple outlier index. However, instead of robustifying an existing algorithm by some outlier rejection technique we show how this index can be used directly to solve the ICA problem for super-Gaussian sources. The resulting inlier-based ICA (IBICA) is outlier-robust by construction and can be used for standard ICA as well as for overcomplete ICA (i.e. more source signals than observed signals). (c) 2005 Wiley Periodicals, Inc
Data recorded in electroencephalogram (EEG)-based brain-computer interface experiments is generally very noisy, non-stationary, and contaminated with artifacts that can deteriorate discrimination/classification methods. In this paper, we extend the common spatial pattern (CSP) algorithm with the aim to alleviate these adverse effects. In particular, we suggest an extension of CSP to the state space, which utilizes the method of time delay embedding. As we will show, this allows for individually tuned frequency filters at each electrode position and, thus, yields an improved and more robust machine learning procedure. The advantages of the proposed method over the original CSP method are verified in terms of an improved information transfer rate (bits per trial) on a set of EEG-recordings from experiments of imagined limb movements
Noninvasive electroencephalogram (EEG) recordings provide for easy and safe access to human neocortical processes which can be exploited for a brain-computer interface (BCI). At present, however, the use of BCIs is severely limited by low bit-transfer rates. We systematically analyze and develop two recent concepts, both capable of enhancing the information gain from multichannel scalp EEG recordings: 1) the combination of classifiers, each specifically tailored for different physiological phenomena, e.g., slow cortical potential shifts, such as the premovement Bereitschaftspotential or differences in spatio-spectral distributions of brain activity (i.e., focal event-related desynchronizations) and 2) behavioral paradigms inducing the subjects to generate one out of several brain states (multiclass approach) which all bare a distinctive spatio-temporal signature well discriminable in the standard scalp EEG. We derive information-theoretic predictions and demonstrate their relevance in experimental data. We will show that a suitably arranged interaction between these concepts can significantly boost BCI performances
A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non- orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorithm's efficiency stems from the special approximation of the cost function resulting in a sparse, block-diagonal Hessian to be used in the computation of the quasi-Newton update step. Extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods. The results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state-of-the-art joint diagonalization algorithms. The practical use of our algorithm is shown for blind source separation problems
Pairwise proximity data, given as similarity or dissimilarity matrix, can violate metricity. This occurs either due to noise, fallible estimates, or due to intrinsic non-metric features such as they arise from human judgments. So far the problem of non-metric pairwise data has been tackled by essentially omitting the negative eigenvalues or shifting the spectrum of the associated (pseudo) covariance matrix for a subsequent embedding. However, little attention has been paid to the negative part of the spectrum itself. In particular no answer was given to whether the directions associated to the negative eigenvalues would at all code variance other than noise related. We show by a simple, exploratory analysis that the negative eigenvalues can code for relevant structure in the data, thus leading to the discovery of new features, which were lost by conventional data analysis techniques. The information hidden in the negative eigenvalue part of the spectrum is illustrated and discussed for three data sets, namely USPS handwritten digits, text-mining and data from cognitive psychology