Single-trial event-related potential analysis for brain-computer interfaces

Abstract. Different types of mental activity are utilised as an input in Brain-Computer Interface (BCI) systems. One such activity type is based on Event-Related Potentials (ERPs). The characteristics of ERPs are not visible in single-trials, thus averaging over a number of trials is necessary before the signals become usable. An improvement in ERP-based BCI operation and system usability could be obtained if the use of single-trial ERP data was possible. The method of Independent Component Analysis (ICA) can be utilised to separate single-trial recordings of ERP data into components that correspond to ERP characteristics, background electroencephalogram (EEG) activity and other components with non- cerebral origin. Choice of specific components and their use to reconstruct “denoised” single-trial data could improve the signal quality, thus allowing the successful use of single-trial data without the need for averaging. This paper assesses single-trial ERP signals reconstructed using a selection of estimated components from the application of ICA on the raw ERP data. Signal improvement is measured using Contrast-To-Noise measures. It was found that such analysis improves the signal quality in all single-trials.

Detection of neural correlates of self-paced motor activity using empirical mode decomposition phase locking analysis

Transient episodes of synchronisation of neuronal activity in particular frequency ranges are thought to underlie cognition. Empirical mode decomposition phase locking (EMDPL) analysis is a method for determining the frequency and timing of phase synchrony that is adaptive to intrinsic oscillations within data, alleviating the need for arbitrary bandpass filter cut-off selection. It is extended here to address the choice of reference electrode and removal of spurious synchrony resulting from volume conduction. Spline Laplacian transformation and independent component analysis (ICA) are performed as pre-processing steps, and preservation of phase synchrony between synthetic signals. combined using a simple forward model, is demonstrated. The method is contrasted with use of bandpass filtering following the same preprocessing steps, and filter cut-offs are shown to influence synchrony detection markedly. Furthermore, an approach to the assessment of multiple EEG trials using the method is introduced, and the assessment of statistical significance of phase locking episodes is extended to render it adaptive to local phase synchrony levels. EMDPL is validated in the analysis of real EEG data, during finger tapping. The time course of event-related (de)synchronisation (ERD/ERS) is shown to differ from that of longer range phase locking episodes, implying different roles for these different types of synchronisation. It is suggested that the increase in phase locking which occurs just prior to movement, coinciding with a reduction in power (or ERD) may result from selection of the neural assembly relevant to the particular movement. (C) 2009 Elsevier B.V. All rights reserved.

Constrained principal component analysis reveals functionally connected load-dependent networks involved in multiple stages of working memory

Constrained principal component analysis (CPCA) with a finite impulse response (FIR) basis set was used to reveal functionally connected networks and their temporal progression over a multistage verbal working memory trial in which memory load was varied. Four components were extracted, and all showed statistically significant sensitivity to the memory load manipulation. Additionally, two of the four components sustained this peak activity, both for approximately 3 s (Components 1 and 4). The functional networks that showed sustained activity were characterized by increased activations in the dorsal anterior cingulate cortex, right dorsolateral prefrontal cortex, and left supramarginal gyrus, and decreased activations in the primary auditory cortex and "default network" regions. The functional networks that did not show sustained activity were instead dominated by increased activation in occipital cortex, dorsal anterior cingulate cortex, sensori-motor cortical regions, and superior parietal cortex. The response shapes suggest that although all four components appear to be invoked at encoding, the two sustained-peak components are likely to be additionally involved in the delay period. Our investigation provides a unique view of the contributions made by a network of brain regions over the course of a multiple-stage working memory trial.

Analysis of diffusion tensor magnetic resonance imaging data using principal component analysis

An analysis method for diffusion tensor (DT) magnetic resonance imaging data is described, which, contrary to the standard method (multivariate fitting), does not require a specific functional model for diffusion-weighted (DW) signals. The method uses principal component analysis (PCA) under the assumption of a single fibre per pixel. PCA and the standard method were compared using simulations and human brain data. The two methods were equivalent in determining fibre orientation. PCA-derived fractional anisotropy and DT relative anisotropy had similar signal-to-noise ratio (SNR) and dependence on fibre shape. PCA-derived mean diffusivity had similar SNR to the respective DT scalar, and it depended on fibre anisotropy. Appropriate scaling of the PCA measures resulted in very good agreement between PCA and DT maps. In conclusion, the assumption of a specific functional model for DW signals is not necessary for characterization of anisotropic diffusion in a single fibre.

Sparse density estimation on multinomial manifold combining local component analysis

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion combining local component analysis for the finite mixture model. We start with a Parzen window estimator which has the Gaussian kernels with a common covariance matrix, the local component analysis is initially applied to find the covariance matrix using expectation maximization algorithm. Since the constraint on the mixing coefficients of a finite mixture model is on the multinomial manifold, we then use the well-known Riemannian trust-region algorithm to find the set of sparse mixing coefficients. The first and second order Riemannian geometry of the multinomial manifold are utilized in the Riemannian trust-region algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Ecological niche modeling and principal component analysis of Krameria Loefl. (Krameriaceae)

Krameria plants are found in arid regions of the Americas and present a floral system that attracts oil-collecting bees. Niche modeling and multivariate tools were applied to examine ecological and geographical aspects of the 18 species of this genus, using occurrence data obtained from herbaria and literature. Niche modeling showed the potential areas of occurrence for each species and the analysis of climatic variables suggested that North American species occur mostly in deserted or xeric ecoregions with monthly precipitation below 140 mm and large temperature ranges. South American species are mainly found in deserted ecoregions and subtropical savannas where monthly precipitation often exceeds 150 mm and temperature ranges are smaller. Principal Component Analysis (PCA) performed with values of temperature and precipitation showed that the distribution limits of Krameria species are primarily associated with maximum and minimum temperatures. Modeling of Krameria species proved to be a useful tool for analyzing the influence of the ecological niche variables in the geographical distribution of species, providing new information to guide future investigations. (C) 2011 Elsevier Ltd. All rights reserved.

Chemotaxonomic relationships in Celastraceae inferred from principal component analysis (PCA) and partial least squares (PLS)

This paper describes a chemotaxonomic analysis of a database of triterpenoid compounds from the Celastraceae family using principal component analysis (PCA). The numbers of occurrences of thirty types of triterpene skeleton in different tribes of the family were used as variables. The study shows that PCA applied to chemical data can contribute to an intrafamilial classification of Celastraceae, once some questionable taxa affinity was observed, from chemotaxonomic inferences about genera and they are in agreement with the phylogeny previously proposed. The inclusion of Hippocrateaceae within Celastraceae is supported by the triterpene chemistry.

A neural networks learning algorithm for minor component analysis and its convergence analysis

The eigenvector associated with the smallest eigenvalue of the autocorrelation matrix of input signals is called minor component. Minor component analysis (MCA) is a statistical approach for extracting minor component from input signals and has been applied in many fields of signal processing and data analysis. In this letter, we propose a neural networks learning algorithm for estimating adaptively minor component from input signals. Dynamics of the proposed algorithm are analyzed via a deterministic discrete time (DDT) method. Some sufficient conditions are obtained to guarantee convergence of the proposed algorithm.

Bivariate variance-component analysis, with application to systolic blood pressure and total cholesterol levels in the Framingham Heart Study

Background :
The correlations between systolic blood pressure (SBP) and total cholesterol levels (CHOL) might result from genetic or environmental factors that determine variation in the phenotypes and are shared by family members. Based on 330 nuclear families in the Framingham Heart Study, we used a multivariate normal model, implemented in the software FISHER, to estimate genetic and shared environmental components of variation and genetic and shared environmental correlation between the phenotypes. The natural logarithm of the phenotypes measured at the last visit in both Cohort 1 and 2 was used in the analyses. The antihypertensive treatment effect was corrected before adjustment of the systolic blood pressure for age, sex, and cohort.
Results :
The univariate correlation coefficient was statistically significant for sibling pairs and parent-offspring pairs, but not significant for spouse pairs. In the bivariate analysis, the cross-trait correlation coefficients were not statistically significant for all relative pairs. The shared environmental correlation was statistically significant, but the genetic correlation was not significant.
Conclusion :
There is no significant evidence for a close genetic correlation between systolic blood pressure and total cholesterol levels. However, some shared environmental factors may determine the variation of both phenotypes.

Nonnegative blind source separation by sparse component analysis based on determinant measure

The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many real-world signals are sparse, we deal with NBSS by sparse component analysis. First, a determinant-based sparseness measure, named D-measure, is introduced to gauge the temporal and spatial sparseness of signals. Based on this measure, a new NBSS model is derived, and an iterative sparseness maximization (ISM) approach is proposed to solve this model. In the ISM approach, the NBSS problem can be cast into row-to-row optimizations with respect to the unmixing matrix, and then the quadratic programming (QP) technique is used to optimize each row. Furthermore, we analyze the source identifiability and the computational complexity of the proposed ISM-QP method. The new method requires relatively weak conditions on the sources and the mixing matrix, has high computational efficiency, and is easy to implement. Simulation results demonstrate the effectiveness of our method.

Snapshots of complexity: using motion capture and principal component analysis to reconceptualise dance

This article brings together the disparate worlds of dance practice, motion capture and statistical analysis. Digital technologies such as motion capture offer dance artists new processes for recording and studying dance movement. Statistical analysis of these data can reveal hidden patterns in movement in ways that are semantically ‘blind’, and are hence able to challenge accepted culturo-physical ‘grammars’ of dance creation. The potential benefit to dance artists is to open up new ways of understanding choreographic movement. However, quantitative analysis does not allow for the uncertainty inherent in emergent, artistic practices such as dance. This article uses motion capture and principal component analysis (PCA), a common statistical technique in human movement recognition studies, to examine contemporary dance movement, and explores how this analysis might be interpreted in an artistic context to generate a new way of looking at the nature and role of movement patterning in dance creation.

Nonnegative Blind Source Separation by Sparse Component Analysis Based on Determinant Measure

The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many real-world signals are sparse, we deal with NBSS by sparse component analysis. First, a determinant-based sparseness measure, named D-measure, is introduced to gauge the temporal and spatial sparseness of signals. Based on this measure, a new NBSS model is derived, and an iterative sparseness maximization (ISM) approach is proposed to solve this model. In the ISM approach, the NBSS problem can be cast into row-to-row optimizations with respect to the unmixing matrix, and then the quadratic programming (QP) technique is used to optimize each row. Furthermore, we analyze the source identifiability and the computational complexity of the proposed ISM-QP method. The new method requires relatively weak conditions on the sources and the mixing matrix, has high computational efficiency, and is easy to implement. Simulation results demonstrate the effectiveness of our method.