Higher Order Statistical Information Research Articles

An Improved FastICA Algorithm and its Application in Image Feature Extraction

There are most important features hiding in the higher-order statistics information of the images. They are extracted by classical fast-fixed independent component analysis (FastICA algorithm) which requires a large amount of calculation and it is sensitive on the selection of initial point. To overcome the two shortcomings, an improved FastICA algorithm is proposed and mathematical models are constructed. And they are applied to obtain the basic vectors from the images. Finally, take litchi fruit image in natural environment as an instance and experiment with Matlab software. The results show that there are less computation and stronger stability of the improved FashICA algorithm used to extract image features.

FEATURE EXTRACTION OF MOTOR IMAGERY EEG BASED ON WAVELET TRANSFORM AND HIGHER-ORDER STATISTICS

Feature extraction plays an important role in brain-computer interface (BCI) systems. In order to characterize the motor imagery related rhythm and higher-order statistics information contained within the EEG signals, a novel feature extraction method based on harmonic wavelet transform and bispectrum is developed and applied to the recognition of right and left motor imageries for developing EEG-based BCI systems. The experimental results on the Graz BCI data set have shown that the separability of the two classes features extracted by the proposed method is notable. Its performance was evaluated by a linear discriminant analysis (LDA) classifier. The recognition accuracy of 90% was obtained. The recognition results have demonstrated the effectiveness of the proposed method. This method provides an effective way for EEG feature extraction in BCI system.

GABOR-BASED TENSOR LOCAL DISCRIMINANT EMBEDDING AND ITS APPLICATION ON PALMPRINT RECOGNITION

In this paper, a novel feature extraction method called Gabor-based tensor local discriminant embedding (GTLDE) is proposed. GTLDE first gets the high-order statistic information by using a biologically inspired hierarchical model, and then tensor local discriminant embedding (TLDE) is carried out to extract the discriminant features of the image for recognition task. The method we proposed is not only robust to local translation and scale variations, but also has high distinguishing ability. More importantly, our method can achieve high accuracy with a small number of training samples. Experimental results on PolyU-II palmprint database demonstrate the effectiveness of the method we proposed.

Decomposition and recovery on MA superposition process using ICA

Decomposition and recovery on Moving Average(MA)superposition process contained in multivariable time series were researched in this paper.Firstly,because of the independence of the high-order statistical information,the mixtures were separated by searching a reversible matrix with the Independent Component Analysis(ICA)algorithm-fixed point algorithm.Then an adaptive method was designed to identify MA model based on higher-order cumulant.In every iteration,it estimated the order and the parameters of MA.Finally,the effectiveness of the algorithm was verified by the computer simulation.

EEG/MEG Signal Processing

EEG/MEG Signal Processing

Performance of blind source separation algorithms for fMRI analysis using a group ICA method

Independent component analysis (ICA) is a popular blind source separation technique that has proven to be promising for the analysis of functional magnetic resonance imaging (fMRI) data. A number of ICA approaches have been used for fMRI data analysis, and even more ICA algorithms exist; however, the impact of using different algorithms on the results is largely unexplored. In this paper, we study the performance of four major classes of algorithms for spatial ICA, namely, information maximization, maximization of non-Gaussianity, joint diagonalization of cross-cumulant matrices and second-order correlation-based methods, when they are applied to fMRI data from subjects performing a visuo-motor task. We use a group ICA method to study variability among different ICA algorithms, and we propose several analysis techniques to evaluate their performance. We compare how different ICA algorithms estimate activations in expected neuronal areas. The results demonstrate that the ICA algorithms using higher-order statistical information prove to be quite consistent for fMRI data analysis. Infomax, FastICA and joint approximate diagonalization of eigenmatrices (JADE) all yield reliable results, with each having its strengths in specific areas. Eigenvalue decomposition (EVD), an algorithm using second-order statistics, does not perform reliably for fMRI data. Additionally, for iterative ICA algorithms, it is important to investigate the variability of estimates from different runs. We test the consistency of the iterative algorithms Infomax and FastICA by running the algorithm a number of times with different initializations, and we note that they yield consistent results over these multiple runs. Our results greatly improve our confidence in the consistency of ICA for fMRI data analysis.

Independent component analysis-based penalized discriminant method for tumor classification using gene expression data

Microarrays are capable of determining the expression levels of thousands of genes simultaneously. One important application of gene expression data is classification of samples into categories. In combination with classification methods, this technology can be useful to support clinical management decisions for individual patients, e.g. in oncology. Standard statistic methodologies in classification or prediction do not work well when the number of variables p (genes) far too exceeds the number of samples n. So, modification of existing statistical methodologies or development of new methodologies is needed for the analysis of microarray data. This paper proposes a new method for tumor classification using gene expression data. In this method, we first employ independent component analysis to model the gene expression data, then apply optimal scoring algorithm to classify them. Further speaking, this approach can first make full use of the high-order statistical information contained in the gene expression data. Second, this approach also employs regularized regression models to handle the situation of large numbers of correlated predictor variables. Finally, the predictive models are developed for classifying tumors based on the entire gene expression profile. To show the validity of the proposed method, we apply it to classify four DNA microarray datasets involving various human normal and tumor tissue samples. The experimental results show that the method is efficient and feasible. Matlab scripts are available on request.

Pipeline defects diagnosis based on feature extraction and neural-network fusion

Corrosion, stresses, and mechanical damage of oil and gas pipelines can result in catastrophic failures. So, pipeline-safety nondestructive evaluation is a research hotspot. A pipeline-defect diagnosis approach is proposed to classify detected defects into correct classes that are useful for later defect assessment and repair, effect raw signals are processed by the independent component analysis method, and several independent components are obtained. The residual mutual information matrixes are then constructed. These matrixes that contain useful high-order statistical information are used to train a radial-basis-function fusion network. Laboratory experiments have verified the effectiveness and practicability of this approach. The classification accuracy can reach 92.5%.

Equalisation based on negentropy minimisation

An equalisation method based on negentropy minimisation is introduced and its characteristics are investigated. Negentropy includes higher order statistical information and its error minimisation provides improved convergence and performance. The bit error ratio of the proposed method has similar characteristics to the adaptive minimum bit error rate (AMBER) equaliser. The main advantage of the proposed equaliser is that it needs drastically fewer training iterations than the AMBER and the MMSE equalisers.

In Search of Sensitivity in Network Optimization

This paper concerns the following questions regarding policy synthesis in large queueing networks: (i) It is well known that an understanding of variability is important in the determination of safety stocks to prevent unwanted idleness. Is this the only value of high-order statistical information in policy synthesis? (ii) Will a translation of an optimal policy for the deterministic fluid model (in which there is no variability) lead to an allocation which is approximately optimal for the stochastic network? (iii) What are the sources of highest sensitivity in network control? A sensitivity analysis of an associated fluid-model optimal control problem provides an exact dichotomy in (ii). If an optimal policy for the fluid model is ‘maximally non-idling’, then variability plays a small role in control design. If this condition does not hold, then the ‘gap’ between the fluid and stochastic optimal policies is exactly proportional to system variability. Furthermore, under mild assumptions, we find that the optimal policy for the stochastic model is closely approximated by an affine shift of the fluid optimal solution. However, sensitivity of steady-state performance with respect to perturbations in the policy vanishes with increasing variability.

Blind equalization of MIMO-FIR channels driven by white but higher order colored source signals

The goal of the article is to find a minimal amount of statistical information (or a much weaker condition) about source signals for which blind equalization is possible for multiple-input multiple-output finite-impulse response (MIMO-FIR) channels. First, a sufficiently broad framework is set up within which such a theoretical problem is well posed. Within this framework, it is shown that second-order statistics (SOS) alone are not sufficient for blind equalization when the source signals are white. Additional higher order statistics (HOS) are needed. Then we show that the only additional higher order statistical information needed is spatial fourth-order cumulants. Though it has not yet been proved to be minimal, it is interesting to note that this is the same as the weakest known condition on the source signals even for an instantaneous mixture. We then show a necessary and sufficient condition for blind equalization when the source signals are white and spatially fourth-order uncorrelated. Based on this condition, criterion (A) for blind equalization of MIMO-FIR channels is developed by exploiting the temporal fourth-order statistics. Finally, based on this criterion, a new necessary and sufficient condition in terms of cumulants for the blind equalization of MIMO-FIR channels is obtained.

Higher-order-statistics-based detection of vehicles in still images.

We present a statistical pattern recognition scheme for detecting vehicles in still images. The methodology involves pattern classification using higher-order statistics (HOS) in a clustering framework. The proposed method approximately models the unknown distribution of the image patterns of vehicles by learning HOS information about the vehicle class from sample images. Given a test image, statistical information about the background is learned "on the fly." An HOS-based decision measure derived from a series expansion of the multivariate probability density function in terms of the Gaussian function and Hermite polynomials is used to classify test patterns as vehicles or otherwise. Experimental results on real images with cluttered background are given to demonstrate the performance of the proposed method. When tested on real aerial images, the method gives good results, even for complicated scenes. The detection rate is found to be quite good, while the false alarms are very few. The method can serve as an important step toward building an automated traffic monitoring system.

Jitter-based delay-boundary prediction of wide-area networks

The delay-boundary prediction algorithms currently implemented by transport protocols are lowpass filters based on autoregressive and moving average (ARMA) models. However, previous studies have revealed a fractal-like structure of delay sequences, which may not be well suited to ARMA models. We propose a novel delay-boundary prediction algorithm based on a deviation-lag function (DLF) to characterize the end-to-end delay variations. Compared to conventional algorithms derived from ARMA models, the new algorithm can adapt to delay variations more rapidly and share the delay's robust high-order statistical information (jitter deviation) among competing connections along a common network path. Preliminary experiments show that it outperforms Jacobson's (1988) algorithm, which is based on an ARMA model, by significantly reducing the prediction error rate. To show the practical feasibility of the DLF algorithm, we also propose a skeleton implementation model.

Identification of MA processes using cumulants: several sets of linear equations

Several new sets of linear equations relating the coefficients of a moving average (MA) system with its (k – 1)th- and kth-order polyspectra, with k>2 are presented. These equations are used to identify the nonminimum phase MA model parameters from the statistics of the noisy output. The system is driven by an (unobservable) independent and identically distributed nongaussian process and the noise is additive and coloured gaussian with unknown power spectrum. Four estimators based on the method of least-squares using linear relations between third- and fourth-order statistics are proposed and discussed. These methods make use of more higher order statistics information than other linear methods do, and the uniqueness of the solutions can normally be guaranteed by the linearity of the equations. Results from computer simulations confirm the expected theoretical advantages of the proposed methods in coloured noise environments and allow one to draw a comparison among proposed and other published linear methods.

Bounds for effective thermal, electrical, and magnetic properties of heterogeneous materials using high order statistical information

Bounds have been developed for the effective thermal, electrical, and magnetic properties (K*) of a two phase statistically homogeneous and isotropic material. These bounds came in terms of the ratio of the properties of the two phases, volume fractions, and the constants G, G2, G3, M1, and M2. Bounds on the values of these constants are obtained. It is shown that the constants G, G2, and G3 are geometric parameters. They are calculated in the general case of spheroidal inclusions in terms of the axial ratio A. The constants M1 and M2 are packing parameters. General expressions of these constants in terms of packing information are obtained. It is found that certain combinations of the constants M1 and M2 for spheres and plates give exact solutions for the effective property K*. The exact solutions were shown in some cases to be equal to Miller's upper bound and in other cases to Miller's lower bound. A self-consistent scheme for the case of spheres is carried out. The corresponding values of M1 and M2 were identified and used to plot the bounds. The bounds for plates are also calculated. It is found that these bounds introduce a great improvement over Miller's bounds. The small perturbation limit was considered. It is found that our bounds coincide to order η5 and all values of v (η = K1/K2− 1, Ki is the property of material i). Moreover, they include Miller's bounds to order η3 and Hashin bounds to order η2.