Stergios Papadimitriou

Radial basis function neural networks for the characterization of heart rate variability dynamics.

This study introduces new neural network based methods for the assessment of the dynamics of the heart rate variability (HRV) signal. The heart rate regulation is assessed as a dynamical system operating in chaotic regimes. Radial-basis function (RBF) networks are applied as a tool for learning and predicting the HRV dynamics. HRV signals are analyzed from normal subjects before and after pharmacological autonomic nervous system (ANS) blockade and from diabetic patients with dysfunctional ANS. The heart rate of normal subjects presents notable predictability. The prediction error is minimized, in fewer degrees of freedom, in the case of diabetic patients. However, for the case of pharmacological ANS blockade, although correlation dimension approaches indicate significant reduction in complexity, the RBF networks fail to reconstruct adequately the underlying dynamics. The transient attributes of the HRV dynamics under the pharmacological disturbance is elucidated as the explanation for the prediction inability.

Secure communication with chaotic systems of difference equations

The paper presents chaotic systems of difference equations that can effectively encrypt information. Two classes of systems are presented: The first one (Class 1) is optimized for secure communications over reliable channels, while the second (Class 2) tolerates transmission noise at the expense of reduced parameter space size. The nonlinearity of these systems is achieved by designing proper piecewise linear functions and by using module operations. The utilization of additional nonlinear terms can improve the enciphering efficiency. The encrypting performance of the algorithms is evaluated analytically and by simulation experiments. Also, the case of an imperfect transmission channel that inserts noise in the transmitted signal is addressed and the design is modified in order to offer reliable secure transmission over channels with very small signal to noise ratios.

Gene expression data analysis with a dynamically extended self-organized map that exploits class information

MOTIVATION Currently the most popular approach to analyze genome-wide expression data is clustering. One of the major drawbacks of most of the existing clustering methods is that the number of clusters has to be specified a priori. Furthermore, by using pure unsupervised algorithms prior biological knowledge is totally ignored Moreover, most current tools lack an effective framework for tight integration of unsupervised and supervised learning for the analysis of high-dimensional expression data and only very few multi-class supervised approaches are designed with the provision for effectively utilizing multiple functional class labeling. RESULTS The paper adapts a novel Self-Organizing map called supervised Network Self-Organized Map (sNet-SOM) to the peculiarities of multi-labeled gene expression data. The sNet-SOM determines adaptively the number of clusters with a dynamic extension process. This process is driven by an inhomogeneous measure that tries to balance unsupervised, supervised and model complexity criteria. Nodes within a rectangular grid are grown at the boundary nodes, weights rippled from the internal nodes towards the outer nodes of the grid, and whole columns inserted within the map The appropriate level of expansion is determined automatically. Multiple sNet-SOM models are constructed dynamically each for a different unsupervised/supervised balance and model selection criteria are used to select the one optimum one. The results indicate that sNet-SOM yields competitive performance to other recently proposed approaches for supervised classification at a significantly reduced computational cost and it provides extensive exploratory analysis potentiality within the analysis framework. Furthermore, it explores simple design decisions that are easier to comprehend and computationally efficient.

Adaptive Denoising and Multiscale Detection of the V Wave in Brainstem Auditory Evoked Potentials

This paper describes a wavelet-transform-based system for the V wave identification in brainstem auditory evoked potentials (BAEP). The system combines signal denoising and rule-based localization modules. The signal denoising module has the potential of effective noise reduction after signal averaging. It analyses adaptively the evolution of the wavelet transform maxima across scales. The singularities of the signal create wavelet maxima with different properties from those of the induced noise. A non-linear filtering process implemented with a neural network extracts out the noise-induced maxima. The filtered wavelet details are subsequently analysed by the rule-based localization module for the automatic identification of the V wave. In the first phase, it implements a set of statistical observations as well as heuristic criteria used by human experts in order to classify the IV–V complex. At the second phase, using a multiscale focusing algorithm, the IV and V waves are positioned on the BAEP signal. Our experiments revealed that the system provides accurate results even for signals exhibiting unclear IV–V complexes.

Fetal heart rate signal denoising by processing the wavelet transform modulus maxima

The Wavelet Transform Analysis offers the possibility to decompose time series into both time and scale components. The paper applies the Wavelet Transform to analyse the Fetal Heart Rate (FHR) signal. A noise reduction technique that detects noise components by analysing the evolution of the Wavelet Transform modulus maxima across scales is adapted to improve the quality of FHR recording. The denoising scheme relies on the elimination of those multiscale maxima that correspond to noise components. The denoised FHR signal is reconstructed from the processed maxima by the inverse Wavelet Transform. The algorithm effectively removes transient spikes and reduces noise (both Gaussian and coloured) without destroying the frequency information content of the signal (as traditional low pass filtering does).

RADIAL BASIS FUNCTION NETWORKS AS CHAOTIC GENERATORS FOR SECURE COMMUNICATION SYSTEMS

This paper improves upon a new class of discrete chaotic systems (i.e. chaotic maps) recently introduced for effective information encryption. The nonlinearity and adaptability of these systems are achieved by designing proper radial basis function networks. The potential for automatic synchronization, the lack of periodicity and the extremely large parameter spaces of these chaotic maps offer robust transmission security. The Radial Basis Function (RBF) networks offer a large number of parameters (i.e. the centers and spreads of the RBF kernels and the weights of the linear layer) while at the same time as universal approximators they have the flexibility to implement any function. The RBF networks can learn the dynamics of chaotic systems (maps or flows) and mimic them accurately by using many more parameters than the original dynamical recurrence. Since the parameter space size increases exponentially with respect to the number of parameters, the RBF based systems greatly outperform previous designs in...

Chaotic real-time encryption using systems of difference equations with large parameter spaces

We present a new class of discrete chaotic systems (i.e. chaotic maps) that can effectively encrypt information. The nonlinearity of these systems is achieved by designing proper piecewise linear functions and by using modulo operations. The chaotic maps are used as pseudo-noise generators and as the synchronization mechanism of a secure spread-spectrum communication system design. The potential for automatic synchronization, the lack of periodicity and the extremely large parameter spaces that our chaotic maps exhibit offer great advantages over the traditional linear feedback shift registers pseudo-noise generators for spread spectrum system design.

Secure communication protocols with discrete nonlinear chaotic maps

Abstract The discrete nonlinear chaotic maps (DNCMs) exploit a novel approach to encryption: the information is injected to a properly designed DNCM system and affects its dynamics. The evolution of a proper variable of this system composes the transmitted ciphertext. Consequently, this variable controls the dynamics of another DNCM system that acts as the decipher. The paper proposes two new secure communications protocols that utilise the peculiarities of the DNCM systems. At the first one, the DNCM systems are used to construct a unique authentication scheme. With the second protocol the participants instead of exchanging the symmetric key (encrypted with the public key) exchange the encryption components themselves. This protocol is well suited to the possibility for dynamic “randomized” construction of DNCM systems. Therefore, a new dimension to security is added: not only the symmetric encryption key of a communication session is randomized but also the encryption algorithm itself is generated randomly (subject to some design rules).

Hierarchical state space partitioning with a network self-organising map for the recognition of ST-T segment changes.

The problem of maximising the performance of ST-T segment automatic recognition for ischaemia detection is a difficult pattern classification problem. The paper proposes the network self-organising map (NetSOM) model as an enhancement to the Kohonen self-organised map (SOM) model. This model is capable of effectively decomposing complex large-scale pattern classification problems into a number of partitions, each of which is more manageable with a local classification device. The NetSOM attempts to generalise the regularisation and ordering potential of the basic SOM from the space of vectors to the space of approximating functions. It becomes a device for the ordering of local experts (i.e. independent neural networks) over its lattice of neurons and for their selection and co-ordination. Each local expert is an independent neural network that is trained and activated under the control of the NetSOM. This method is evaluated with examples from the European ST-T database. The first results obtained after the application of NetSOM to ST-T segment change recognition show a significant improvement in the performance compared with that obtained with monolithic approaches, i.e. with single network types. The basic SOM model has attained an average ischaemic beat sensitivity of 73.6% and an average ischaemic beat predictivity of 68.3%. The work reports and discusses the improvements that have been obtained from the implementation of a NetSOM classification system with both multilayer perceptrons and radial basis function (RBF) networks as local experts for the ST-T segment change problem. Specifically, the NetSOM with multilayer perceptrons (radial basis functions) as local experts has improved the results over the basic SOM to an average ischaemic beat sensitivity of 75.9% (77.7%) and an average ischaemic beat predictivity of 72.5% (74.1%).

Denoising of the fetal heart rate signal with non-linear filtering of the wavelet transform maxima

The fetal heart rate (FHR) signal provides valuable information for fetal development and well-being. However, the FHR traces derived from present-day ultrasound cardiotocographs are not of the desired quality. The paper applies the wavelet transform (WT) in order to denoise effectively the FHR signal. The denoising procedure analyses the evolution of the WT maxima across scales. The singularities of the signal create wavelet maxima with different properties from those of the induced noise. Since it is difficult to formulate precise rules that distinguish between the wavelet maxima of the FHR signal from those of the noise we have trained a neural network for this classification task. The neural network draws out successfully the noise induced wavelet maxima. An improved FHR signal can be obtained from the coarser wavelet approximation signal component and the filtered wavelet maxima by means of the inverse dyadic wavelet transform. Also, feature extraction and processing algorithms can be defined on the denoised wavelet coefficients (instead of on the original signal).