Combining spatial filters for the classification of single-trial EEG in a finger movement task

Brain-computer interface (BCI) is to provide a communication channel that translates human intention reflected by a brain signal such as electroencephalogram (EEG) into a control signal for an output device. In recent years, the event-related desynchronization (ERD) and movement-related potentials (MRPs) are utilized as important features in motor related BCI system, and the common spatial patterns (CSP) algorithm has shown to be very useful for ERD-based classification. However, as MRPs are slow nonoscillatory EEG potential shifts, CSP is not an appropriate approach for MRPs-based classification. Here, another spatial filtering algorithm, discriminative spatial patterns (DSP), is newly introduced for better extraction of the difference in the amplitudes of MRPs, and it is integrated with CSP to extract the features from the EEG signals recorded during voluntary left versus right finger movement tasks. A support vector machines (SVM) based framework is designed as the classifier for the features. The results show that, for MRPs and ERD features, the combined spatial filters can realize the single-trial EEG classification better than anyone of DSP and CSP alone does. Thus, we propose an EEG-based BCI system with the two feature sets, one based on CSP (ERD) and the other based on DSP (MRPs), classified by SVM.     

Massively parallel classification of single-trial EEG signals using a min-max modular neural network

This paper presents a method for classifying single-trial electroencephalogram (EEG) signals using min-max modular neural networks implemented in a massively parallel way. The method has three main steps. First, a large-scale, complex EEG classification problem is simply divided into a reasonable number of two-class subproblems, as small as needed. Second, the two-class subproblems are simply learned by individual smaller network modules in parallel. Finally, all the individual trained network modules are integrated into a hierarchical, parallel, and modular classifier according to two module combination laws. To demonstrate the effectiveness of the method, we perform simulations on fifteen different four-class EEG classification tasks, each of which consists of 1491 training and 636 test data. These EEG classification tasks were created using a set of non-averaged, single-trial hippocampal EEG signals recorded from rats; the features of the EEG signals are extracted using wavelet transform techniques. The experimental results indicate that the proposed method has several attractive features. 1) The method is appreciably faster than the existing approach that is based on conventional multilayer perceptrons. 2) Complete learning of complex EEG classification problems can be easily realized, and better generalization performance can be achieved. 3) The method scales up to large-scale, complex EEG classification problems.     

Spatio-spectral filters for improving the classification of single trial EEG

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.     

Familiar/unfamiliar face classification from EEG signals by utilizing pairwise distant channels and distinctive time interval

The aim of the study is to classify single trial electroencephalogram and to estimate active regions/locations on skull in unfamiliar/familiar face recognition task. For this purpose, electroencephalographic signals were acquired from ten subjects in different sessions. Sixty-one familiar and fifty-nine unfamiliar face stimuli were shown to the subjects in the experiments. Since channel responses are different for familiar and unfamiliar classes, the channels discriminating the classes were investigated. To do so, three distances and four similarity measures were employed to assess the most distant channel pairs between familiar and unfamiliar classes for a 1-s time duration; 0.6 s from the stimulus to 1.6 s in a channel selection process. It is experimentally observed that this time interval is maintaining the greatest distance between two categories. The electroencephalographic signals were classified using the determined channels and time interval to measure accuracy. The best classification accuracy was 81.30% and was obtained with the Pearson correlation as channel selection method. The most discriminative channel pairs were selected from prefrontal regions.     

Multiclass support vector machines for EEG-signals classification.

In this paper, we proposed the multiclass support vector machine (SVM) with the error-correcting output codes for the multiclass electroencephalogram (EEG) signals classification problem. The probabilistic neural network (PNN) and multilayer perceptron neural network were also tested and benchmarked for their performance on the classification of the EEG signals. Decision making was performed in two stages: feature extraction by computing the wavelet coefficients and the Lyapunov exponents and classification using the classifiers trained on the extracted features. The purpose was to determine an optimum classification scheme for this problem and also to infer clues about the extracted features. Our research demonstrated that the wavelet coefficients and the Lyapunov exponents are the features which well represent the EEG signals and the multiclass SVM and PNN trained on these features achieved high classification accuracies.     

Partition-based weighted sum filters for image restoration

We develop the concept of partitioning the observation space to build a general class of filters referred to as partition-based weighted sum (PWS) filters. In the general framework, each observation vector is mapped to one of M partitions comprising the observation space, and each partition has an associated filtering function. We focus on partitioning the observation space utilizing vector quantization and restrict the filtering function within each partition to be linear. In this formulation, a weighted sum of the observation samples forms the estimate, where the weights are allowed to be unique within each partition. The partitions are selected and weights tuned by training on a representative set of data. It is shown that the proposed data adaptive processing allows for greater detail preservation when encountering nonstationarities in the data and yields superior results compared to several previously defined filters. Optimization of the PWS filters is addressed and experimental results are provided illustrating the performance of PWS filters in the restoration of images corrupted by Gaussian noise.     

Adaptive filtering in subbands using a weighted criterion

Transform-domain adaptive algorithms have been proposed to reduce the eigenvalue spread of the matrix governing their convergence, thus improving the convergence rate. However, a classical problem arises from the conflicting requirements between algorithm improvement requiring rather long transforms and the need to keep the input/output delay as small as possible, thus imposing short transforms. This dilemma has been alleviated by the so-called “short-block transform domain algorithms” but is still apparent. This paper proposes an adaptive algorithm compatible with the use of rectangular orthogonal transforms (e.g., critically subsampled, lossless, perfect reconstruction filter banks), thus allowing better tradeoffs between algorithm improvement, arithmetic complexity, and input/output delay. The method proposed makes a direct connection between the minimization of a specific weighted least squares criterion and the convergence rate of the corresponding stochastic gradient algorithm. This method leads to improvements in the convergence rate compared with both LMS and classical frequency domain algorithms     

采用最小成对误码率设计准则的MISO干扰信道波束形成

本文针对MISO干扰信道的瞬时波束形成的设计问题开展研究.现有的研究都是基于最大速率和准则,没有考虑通信质量.本文以通信质量优先为出发点,基于最小成对误码率准则设计MISO干扰信道的瞬时波束形成向量,建立了问题模型并推导了求解方法.通过仿真实验对两种设计准则下的最优波束形成向量进行了比较,结果表明两种方法得到的最优波束...     

Classifying single-trial EEG during motor imagery by iterative spatio-spectral patterns learning (ISSPL)

In most current motor-imagery-based brain-computer interfaces (BCIs), machine learning is carried out in two consecutive stages: feature extraction and feature classification. Feature extraction has focused on automatic learning of spatial filters, with little or no attention being paid to optimization of parameters for temporal filters that still require time-consuming, ad hoc manual tuning. In this paper, we present a new algorithm termed iterative spatio-spectral patterns learning (ISSPL) that employs statistical learning theory to perform automatic learning of spatio-spectral filters. In ISSPL, spectral filters and the classifier are simultaneously parameterized for optimization to achieve good generalization performance. A detailed derivation and theoretical analysis of ISSPL are given. Experimental results on two datasets show that the proposed algorithm can correctly identify the discriminative frequency bands, demonstrating the algorithm's superiority over contemporary approaches in classification performance.     

Boosting bit rates in noninvasive EEG single-trial classifications by feature combination and multiclass paradigms

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 pre-movement 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.     

Nonparametric weighted feature extraction for classification

In this paper, a new nonparametric feature extraction method is proposed for high-dimensional multiclass pattern recognition problems. It is based on a nonparametric extension of scatter matrices. There are at least two advantages to using the proposed nonparametric scatter matrices. First, they are generally of full rank. This provides the ability to specify the number of extracted features desired and to reduce the effect of the singularity problem. This is in contrast to parametric discriminant analysis, which usually only can extract L-1 (number of classes minus one) features. In a real situation, this may not be enough. Second, the nonparametric nature of scatter matrices reduces the effects of outliers and works well even for nonnormal datasets. The new method provides greater weight to samples near the expected decision boundary. This tends to provide for increased classification accuracy.     

Optimizing Spatial filters for Robust EEG Single-Trial Analysis

Due to the volume conduction multichannel electroencephalogram (EEG) recordings give a rather blurred image of brain activity. Therefore spatial filters are extremely useful in single-trial analysis in order to improve the signal-to-noise ratio. There are powerful methods from machine learning and signal processing that permit the optimization of spatio-temporal filters for each subject in a data dependent fashion beyond the fixed filters based on the sensor geometry, e.g., Laplacians. Here we elucidate the theoretical background of the common spatial pattern (CSP) algorithm, a popular method in brain-computer interface (BCD research. Apart from reviewing several variants of the basic algorithm, we reveal tricks of the trade for achieving a powerful CSP performance, briefly elaborate on theoretical aspects of CSP, and demonstrate the application of CSP-type preprocessing in our studies of the Berlin BCI (BBCI) project.     

A stability criterion for N-dimensional zero-phase recursive digital filters

This paper presents an extension of the work of Pistor to N dimensions. The stability of an N-dimensional recursive digital filter is shown to be related to the properties of its cepstrum. A procedure is also given for the decomposition of unstable recursive digital filters having a nonzero nonimaginary frequency response into a set of stable single-quadrant recursive filters.     

New direct design method for weighted order statistic filters

The paper describes a new method for the design of optimum weighted order statistic (WOS) filters. WOS filters form a general class of increasing filters which generate an output based on the weighted rank ordering of the samples within the filter window. They include the median, weighted median, stack filters and morphological filters with flat structuring elements. This new design method is applicable to all of these operators. It has the advantage over existing techniques in that the filter weights are calculated directly from the training set observations and require no iteration. The method makes an assumption about the training set observations known as the weight monotonic property. It tests if the training set corruption is suitable for correction with an increasing filter. Where the assumption does not hold then a WOS filter should not be used for that training set. The paper includes two examples to demonstrate the design method and a justification for a training set approach to image restoration problems. Other benefits arising from the new design method are outlined in the paper. These include a method to determine the minimum MAE possible for a given training set and filter window.     

Optimal design of transform-based block digital filters using a quadratic criterion

Block digital filtering is a powerful tool to reduce the computational complexity of digital filtering systems. However, due to their block structure, block digital filters (BDFs) are time-varying linear systems, hence, their design is not easy. The most widely spread approaches to BDF design consist of constraining the BDF to be time-invariant (by restricting the design process to a specific subset of possible solutions) and then using conventional filter synthesis techniques. In this paper, we do not restrict the design process, and we propose a simple and optimal matrix-oriented approach to optimize the BDF coefficients. Furthermore, the proposed approach takes profit of the structure of transform-based BDFs to considerably reduce the computational complexity and memory requirements of the design process. Experimental results confirm that as expected, the obtained global distortion is lower than the distortion obtained with a traditional technique such as overlap-save.     

A simple sufficient criterion for the stability of multidimensional digital filters

In this paper a theorem concerning the absence of zeros of a multivariable polynomial in the closed unit polydisc of a multidimensional complex plane is presented. Using this theorem the stability of a large class of multidimensional digital filters can be tested almost by inspection.     

Quadratic weighted median filters for edge enhancement of noisy images.

Quadratic Volterra filters are effective in image sharpening applications. The linear combination of polynomial terms, however, yields poor performance in noisy environments. Weighted median (WM) filters, in contrast, are well known for their outlier suppression and detail preservation properties. The WM sample selection methodology is naturally extended to the quadratic sample case, yielding a filter structure referred to as quadratic weighted median (QWM) that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers arising in the higher order statistics of environment noise. Through statistical analysis of higher order samples, it is shown that, although the parent Gaussian distribution is light tailed, the higher order terms exhibit heavy-tailed distributions. The optimal combination of terms contributing to a quadratic system, i.e., cross and square, is approached from a maximum likelihood perspective which yields the WM processing of these terms. The proposed QWM filter structure is analyzed through determination of the output variance and breakdown probability. The studies show that the QWM exhibits lower variance and breakdown probability indicating the robustness of the proposed structure. The performance of the QWM filter is tested on constant regions, edges and real images, and compared to its weighted-sum dual, the quadratic Volterra filter. The simulation results show that the proposed method simultaneously suppresses the noise and enhances image details. Compared with the quadratic Volterra sharpener, the QWM filter exhibits superior qualitative and quantitative performance in noisy image sharpening.     

Improved weighted least squares algorithm for the design ofquadrature mirror filters

This paper presents an improved weighted least squares (WLS) algorithm for the design of quadrature mirror filters (QMFs), First, a new term is incorporated into the objective function that effectively prevents an optimization algorithm from producing suboptimal QMFs. These suboptimal QMFs exhibit a transition band anomaly; the frequency responses of the filters have large oscillatory components in the transition band. The new term can be applied to the WLS design of any FIR filter to prevent a similar transition band anomaly. Next, we present an algorithm to obtain the QMF coefficients that minimize the objective function incorporating the new term. The computational requirement of this algorithm is also briefly discussed. Last, we include a set of practical design rules for use with our algorithm. These rules simplify the design process by providing good estimation of the design parameters, such as the minimum filter length, to meet a given set of QMF specifications     

应用于图书馆书籍分类的熵加权聚类算法

目前很多图书馆都更加信息化和数字化,馆藏书籍数量也因此不断提高。如何通过聚类算法做出海量图书类目的精确分类,以便用户更加方便快捷地筛选,成为亟需解决的问题。提出的熵加权聚类改进算法是以传统熵加权聚类算法为基础所设计的新的聚类中心矩阵计算方法。通过选取具有代表性的样本点作为初始聚类中心,降低数据维度和冗余。此外,通过合并策略对信息熵加权隶属表示进行修改,从而避免聚类过程中的局部最优。实验结果表明,提出的聚类方法在处理书籍大数据分类任务时具有较高的精度和稳定度。