Temujin Gautama

Rotation Invariant Complex Empirical Mode Decomposition

A new method to extend the empirical mode decomposition (EMD) into the complex domain is proposed. Unlike the existing method for EMD in the complex domain, this is achieved in a generic way so that the mathematical development of this method mirrors the algorithm defined for EMD in the real domain. The so derived intrinsic mode functions (IMFs) are complex by design and are shown to provide a consistent framework for handling both real and complex data. The simulations on real world complex-valued signals illustrate the applications of the technique.

A novel method for determining the nature of time series

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.

Collaborative Adaptive Learning using Hybrid Filters

A novel stable and robust algorithm for training of finite impulse response adaptive filters is proposed. This is achieved based on a convex combination of the least mean square (LMS) and a recently proposed generalised normalised gradient descent (GNGD) algorithm. In this way, the desirable fast convergence and stability of GNGD is combined with the robustness and small steady state misadjustment of LMS. Simulations on linear and nonlinear signals in the prediction setting support the analysis.

Estimating the global order of the fMRI noise model.

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.

An Assessment of Qualitative Performance of Machine Learning Architectures: Modular Feedback Networks

A framework for the assessment of qualitative performance of machine learning architectures is proposed. For generality, the analysis is provided for the modular nonlinear pipelined recurrent neural network (PRNN) architecture. This is supported by a sensitivity analysis, which is achieved based upon the prediction performance with respect to changes in the nature of the processed signal and by utilizing the recently introduced delay vector variance (DVV) method for phase space signal characterization. Comprehensive simulations combining the quantitative and qualitative analysis on both linear and nonlinear signals suggest that better quantitative prediction performance may need to be traded in order to preserve the nature of the processed signal, especially where the signal nature is of primary importance (biomedical applications).

An online method for detecting nonlinearity within a signal

A novel method for online analysis of the changes in signal modality is proposed. This is achieved by tracking the dynamics of the mixing parameter within a hybrid filter rather than the actual filter performance. An implementation of the proposed hybrid filter using a combination of the Least Mean Square (LMS) and the Generalised Normalised Gradient Descent (GNGD) algorithms is analysed and the potential of such a scheme for tracking signal nonlinearity is highlighted. Simulations on linear and nonlinear signals in a prediction configuration support the analysis. Biological applications of the approach have been illustrated on EEG data of epileptic patients.

Optimal Smoothing of Kernel-Based Topographic Maps with Application to Density-Based Clustering of Shapes

A crucial issue when applying topographic maps for clustering purposes is how to select the maps overall degree of smoothness. In this paper, we develop a new strategy for optimally smoothing, by a common scale factor, the density estimates generated by Gaussian kernel-based topographic maps. We also introduce a new representation structure for images of shapes, and a new metric for clustering them. These elements are incorporated into a hierarchical, density-based clustering procedure. As an application, we consider the clustering of shapes of marine animals taken from the SQUID image database. The results are compared to those obtained with the CSS retrieval system developed by Mokhtarian and co-workers, and with the more familiar Euclidean distance-based clustering metric.

A hierarchical density-based clustering analysis of auditory fMRI activation data

A novel tool for analysing functional magnetic resonance imaging (fMRI) data is introduced. The tool is based on the hierarchical clustering of the Fourier-transformed regression coefficients obtained by regressing the known task sequence with the individual fMRI signals. The clustering analysis is density-based and performed with topographic maps. The tool is tested on a standard data set and the results are compared with those obtained by statistical parametric mapping (SPM), the most widely used tool in the field.

Hierarchical density-based clustering in high-dimensional spaces using topographic maps

A novel way to perform hierarchical, divisive clustering is outlined in this paper. Rather than exhaustively subdividing the complete data set, a density estimate, obtained using topographic maps, is analyzed at every level in the hierarchy in order to determine the number of clusters and to divide the data into new subsets to be analyzed at the next level. Our algorithm is illustrated using a real-world example comprising high-dimensional music data (spectrograms). The different levels of similarity one intuitively perceives in the music signal, correspond to the clustering results found by the algorithm.

Batch map extensions of the kernel-based maximum entropy learning rule

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.This correspondence points out an incorrect statement in Adetona et al., 2000, and Adetona et al., 2004, about the application of the proposed control law to nonminimum phase systems. A counterexample shows the limitations of the control law and, furthermore, its control capability to nonminimum phase systems is explained.