Carlos García Puntonet

A Geometric Algorithm for Overcomplete Linear ICA

Abstract Geometric algorithms for linear square independent component analysis (ICA) have recently received some attention due to their pictorial description and their relative ease of implementation. The geometric approach to ICA was proposed first by Puntonet and Prieto (Neural Process. Lett. 2 (1995), Signal Processing 46 (1995) 267) in order to separate linear mixtures. We generalize these algorithms to overcomplete cases with more sources than sensors. With geometric ICA we get an efficient method for the matrix-recovery step in the framework of a two-step approach to the source separation problem. The second step—source-recovery—uses a maximum-likelihood approach. There we prove that the shortest-path algorithm as proposed by Bofill and Zibulevsky (in: P. Pajunen, J. Karhunen (Eds.), Independent Component Analysis and Blind Signal Separation (Proceedings of ICA’2000), 2000, pp. 87–92) indeed solves the maximum-likelihood conditions.

18F-FDG PET imaging analysis for computer aided Alzheimer's diagnosis

Finding sensitive and appropriate technologies for non-invasive observation and early detection of Alzheimers disease (AD) is of fundamental importance to develop early treatments. In this work we develop a fully automatic computer aided diagnosis (CAD) system for high-dimensional pattern classification of baseline ^1^8F-FDG PET scans from Alzheimers disease neuroimaging initiative (ADNI) participants. Image projection as feature space dimension reduction technique is combined with an eigenimage based decomposition for feature extraction, and support vector machine (SVM) is used to manage the classification task. A two folded objective is achieved by reaching relevant classification performance complemented with an image analysis support for final decision making. A 88.24% accuracy in identifying mild AD, with 88.64% specificity, and 87.70% sensitivity is obtained. This method also allows the identification of characteristic AD patterns in mild cognitive impairment (MCI) subjects.

Linear geometric ICA: fundamentals and algorithms

Geometric algorithms for linear independent component analysis (ICA) have recently received some attention due to their pictorial description and their relative ease of implementation. The geometric approach to ICA was proposed first by Puntonet and Prieto (1995). We will reconsider geometric ICA in a theoretic framework showing that fixed points of geometric ICA fulfill a geometric convergence condition (GCC), which the mixed images of the unit vectors satisfy too. This leads to a conjecture claiming that in the nongaussian unimodal symmetric case, there is only one stable fixed point, implying the uniqueness of geometric ICA after convergence. Guided by the principles of ordinary geometric ICA, we then present a new approach to linear geometric ICA based on histograms observing a considerable improvement in separation quality of different distributions and a sizable reduction in computational cost, by a factor of 100, compared to the ordinary geometric approach. Furthermore, we explore the accuracy of the algorithm depending on the number of samples and the choice of the mixing matrix, and compare geometric algorithms with classical ICA algorithms, namely, Extended Infomax and FastICA. Finally, we discuss the problem of high-dimensional data sets within the realm of geometrical ICA algorithms.

A Novel LMS Algorithm Applied to Adaptive Noise Cancellation

In this letter, we propose a novel least-mean-square (LMS) algorithm for filtering speech sounds in the adaptive noise cancellation (ANC) problem. It is based on the minimization of the squared Euclidean norm of the difference weight vector under a stability constraint defined over the a posteriori estimation error. To this purpose, the Lagrangian methodology has been used in order to propose a nonlinear adaptation rule defined in terms of the product of differential inputs and errors which means a generalization of the normalized (N)LMS algorithm. The proposed method yields better tracking ability in this context as shown in the experiments which are carried out on the AURORA 2 and 3 speech databases. They provide an extensive performance evaluation along with an exhaustive comparison to standard LMS algorithms with almost the same computational load, including the NLMS and other recently reported LMS algorithms such as the modified (M)-NLMS, the error nonlinearity (EN)-LMS, or the normalized data nonlinearity (NDN)-LMS adaptation.

Improved RAN sequential prediction using orthogonal techniques

Abstract A new learning strategy for time-series prediction using radial basis function (RBF) networks is introduced. Its potential is examined in the particular case of the resource allocating network model, although the same ideas could apply to extend any other procedure. In the early stages of learning, addition of successive new groups of RBFs provides an increased rate of convergence. At the same time, the optimum lag structure is determined using orthogonal techniques such as QR factorization and singular value decomposition (SVD). We claim that the same techniques can be applied to the pruning problem, and thus they are a useful tool for compaction of information. Our comparison with the original RAN algorithm shows a comparable error measure but much smaller-sized networks. The extra effort required by QR and SVD is balanced by the simplicity of only using least mean squares for the iterative parameter adaptation.

Separation of sources: a geometry-based procedure for reconstruction of n-valued signals

Abstract In many Signal Processing applications, data sampled by sensors comprise a mixture of signals from different sources. The problem of separation lies in the reconstruction of sources from the mixtures. In this paper a new method is proposed for the separation of mixed digital sources, based on geometrical considerations, which is applied to the separation of binary and n-valued sources. After a brief introduction, we present the principles of the new method and provide a description of the algorithms together with examples to illustrate their efficiency and utility.

Brain connectivity analysis: a short survey

This short survey the reviews recent literature on brain connectivity studies. It encompasses all forms of static and dynamic connectivity whether anatomical, functional, or effective. The last decade has seen an ever increasing number of studies devoted to deduce functional or effective connectivity, mostly from functional neuroimaging experiments. Resting state conditions have become a dominant experimental paradigm, and a number of resting state networks, among them the prominent default mode network, have been identified. Graphical models represent a convenient vehicle to formalize experimental findings and to closely and quantitatively characterize the various networks identified. Underlying these abstract concepts are anatomical networks, the so-called connectome, which can be investigated by functional imaging techniques as well. Future studies have to bridge the gap between anatomical neuronal connections and related functional or effective connectivities.

Computer aided diagnosis of Alzheimer's disease using component based SVM

Abstract: Alzheimers disease (AD) is a progressive neurodegenerative disorder first affecting memory functions and then gradually affecting all cognitive functions with behavioural impairments and eventually causing death. Functional brain imaging as single-photon emission computed tomography (SPECT) is commonly used to guide the clinicians diagnosis. However, conventional evaluation of these scans often relies on manual reorientation, visual reading and semi-quantitative analysis of certain regions of the brain. These steps are time consuming, subjective and prone to error. This paper shows a fully automatic computer-aided diagnosis (CAD) system for improving the accuracy in the early diagnosis of the AD. The proposed approach is based on a first automatic feature selection, and secondly a combination of component-based support vector machine (SVM) classification and a pasting votes technique of assembling SVM classifiers.

Feature selection using factor analysis for Alzheimer's diagnosis using 18F-FDG PET images.

PURPOSE This article presents a computer-aided diagnosis technique for improving the accuracy of the early diagnosis of Alzheimers disease (AD). Two hundred and tenF18-FDG PET images from the ADNI initiative [52 normal controls (NC), 114 mild cognitive impairment (MCI), and 53 AD subjects] are studied. METHODS The proposed methodology is based on the selection of voxels of interest using the t-test and a posterior reduction of the feature dimension using factor analysis. Factor loadings are used as features for three different classifiers: Two multivariate Gaussian mixture model, with linear and quadratic discriminant function, and a support vector machine with linear kernel. RESULTS An accuracy rate up to 95% when NC and AD are considered and an accuracy rate up to 88% and 86% for NC-MCI and NC-MCI, AD, respectively, are obtained using SVM with linear kernel. CONCLUSIONS Results are compared to the voxel-as-features and a PCA- based approach and the proposed methodology achieves better classification performance.

Neural net approach for blind separation of sources based on geometric properties

Abstract This paper presents a new approach to recover original signals (“sources”) from their linear mixtures, observed by the same number of sensors. The algorithms proposed only assume that the input distributions are bounded. The method is simpler than other proposals and is based on geometric algebra properties. We present a geometric algorithm and a neural network approach to show that with two networks, one for the separation of sources and one for weight learning, running in parallel, it is possible to efficiently recover the original signals. The learning rule is unsupervised and each computational element uses only local information. To achieve the required separation, it is necessary to detect an input vector at each of the edges of the hyperparallelepiped cone that contains the observational space; if this condition is verified the network is able to separate even statistically dependent components of the inputs.