Biomedical subjects
Publications and source records attributed to Temujin Gautama.
In this letter, two batch-map extensions are described for the kernel-based maximum entropy learning rule (kMER). In the first, the weights are iteratively set to weighted component-wise medians, while in the second the generalized median is used, enabling kMER to process symbolic data. Simulations are performed to illustrate the extensions.
One of the major issues in GLM-based fMRI analysis techniques is the presence of temporal autocorrelations in the residual signal after regression. A possible correction method is that of prewhitening, which fits an autoregressive (or other) model to the residual and uses the expected temporal autocorrelations of the model to transform the data and design matrix such that the residual becomes white noise. In this article, a method is introduced to estimate the global autoregressive model order of a data set, based on the residuals after regression. The proposed global standardized partial autocorrelation (SPAC) method tests whether the spatial profile of partial autocorrelations at a certain lag is random, and uses random field theory to account for the spatial correlations typical for fMRI data. It is tested both on synthetic and fMRI data, and is compared to two traditional techniques for model order estimation.
In the General Linear Model (GLM) framework for the statistical analysis of fMRI data, the problem of temporal autocorrelations in the residual signal (after regression) has been frequently addressed in the open literature. There exist various methods for correcting the ensuing bias in the statistical testing, among which the prewhitening strategy, which uses a prewhitening matrix for rendering the residual signal white (i.e., without temporal autocorrelations). This correction is only exact when the autocorrelation structure of the noise-generating process is accurately known, and the estimates derived from the fMRI data are too noisy to be used for correction. Recently, Worsley and co-workers proposed to spatially smooth the noisy autocorrelation estimates, effectively reducing their variance and allowing for a better correction. In this article, a systematic study into the effect of the smoothing kernel width is performed and a method is introduced for choosing this bandwidth in an "optimal" manner. Several aspects of the prewhitening strategy are investigated, namely the choice of the autocorrelation estimate (biased or unbiased), the accuracy of the estimates, the degree of spatial regularisation and the order of the autoregressive model used for characterising the noise. The proposed method is extensively evaluated on both synthetic and real fMRI data.
The delay vector variance (DVV) method, which analyzes the nature of a time series with respect to the prevalence of deterministic or stochastic components, is introduced. Due to the standardization within the DVV method, it is possible both to statistically test for the presence of nonlinearities in a time series, and to visually inspect the results in a DVV scatter diagram. This approach is convenient for interpretation as it conveys information about the linear or nonlinear nature, as well as about the prevalence of deterministic or stochastic components in the time series, thus unifying the existing approaches which deal either with only deterministic versus stochastic, or the linear versus nonlinear aspect. The results on biomedical time series, namely heart rate variability (HRV) and functional Magnetic Resonance Imaging (fMRI) time series, illustrate the applicability of the proposed DVV-method.
The dynamical properties of electroencephalogram (EEG) segments have recently been analyzed by Andrzejak and co-workers for different recording regions and for different brain states, using the nonlinear prediction error and an estimate of the correlation dimension. In this paper, we further investigate the nonlinear properties of the EEG signals using two established nonlinear analysis methods, and introduce a "delay vector variance" (DVV) method for better characterizing a time series. The proposed DVV method is shown to enable a comprehensive characterization of the time series, allowing for a much improved classification of signal modes. This way, the analysis of Andrzejak and co-workers can be extended toward classification of different brain states. The obtained results comply with those described by Andrzejak et al., and provide complementary indications of nonlinearity in the signals.
In this paper, we introduce a methodology for comparing the nonlinearities present in sets of time series using four different nonlinearity measures, one of which, the "delay vector variance" method, is a novel approach to the characterization of a time series. It is then applied to examine the difference in nonlinearity between functional magnetic resonance imaging (fMRI) signals that have been recorded using different contrast agents. Recently, an exogenous contrast agent, monocrystalline iron oxide particle (MION), has been introduced for fMRI, which has been shown to increase the functional sensitivity compared with the traditional blood oxygen level dependent (BOLD) technique. The resulting fMRI signals are influenced by cerebral blood volume, whereas the more traditionally recorded BOLD signals are influenced not only by cerebral blood volume, but also by the cerebral blood flow and the metabolic rate of oxygen. The proposed methodology is applied to address the question whether this difference in the number of physiological variables is reflected in a difference in the degree of nonlinearity. We therefore analyze two sets of fMRI signals, one from a BOLD and the other from a MION monkey study with similar experimental designs. In the neuroimaging context, the proposed nonlinearity analyses are different from those described in the literature, since no a priori model is assumed: rather than pinpointing the source(s) of nonlinearity, nonparametric analyses are performed on BOLD and MION fMRI signals. Furthermore, we introduce a strategy for analyzing a population of fMRI signals, rather than focusing the analysis on one signal, as is traditionally done in the domain of nonlinear signal processing. Our results show that, overall, the BOLD signals are more nonlinear in nature than the MION ones, which is in agreement with current hypotheses.