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Results for “Graph neural network”

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At least 127 records · Page 7Linked to original sources
PubMed2006

Small-world network organization of functional connectivity of EEG slow-wave activity during sleep.

OBJECTIVE: To analyze the functional connectivity patterns of the EEG slow-wave activity during the different sleep stages and Cyclic Alternating Pattern (CAP) conditions, using concepts derived from Graph Theory. METHODS: We evaluated spatial patterns of EEG slow-wave synchronization between all possible pairs of electrodes (19) placed over the scalp of 10 sleeping healthy young normal subjects using two graph theoretical measures: the clustering coefficient (Cp) and the characteristic path length (Lp). The measures were obtained during the different sleep stages and CAP conditions from the real EEG connectivity networks and randomized control (surrogate) networks (Cp-s and Lp-s). RESULTS: Cp and Cp/Cp-s increased significantly from wakefulness to sleep while Lp and Lp/Lp-s did not show changes. Cp/Cp-s was higher for A1 phases, compared to B phases of CAP. CONCLUSIONS: The network organization of the EEG slow-wave synchronization during sleep shows features characteristic of small-world networks (high Cp combined with low Lp); this type of organization is slightly but significantly more evident during the CAP A1 subtypes. SIGNIFICANCE: Our results show feasibility of using graph theoretical measures to characterize the complexity of brain networks during sleep and might indicate sleep, and the A1 phases of CAP in particular, as a period during which slow-wave synchronization shows optimal network organization for information processing.

Adult↗
PubMedDate not supplied

Pattern completion through phase coding in population neurodynamics.

This article presents an alternative phase coding mechanism for Freeman's KIII model of population neurodynamics. Motivated by experimental evidence that supports the existence of a neural code based on synchronous oscillations, we propose an analogy between synchronization in neural populations and phase locking in KIII channels. An efficient method is proposed to extract phase differences across granule channels from their state-space trajectories. First, the scale invariance of the KIII model with respect to phase information is established. The phase code is then compared against the conventional amplitude code in terms of their bit-wise and across-fiber pattern recovery capabilities using decision-theoretic principles and a Hamming-distance classifier. Graph isomorphism in the Hebbian connections is exploited to perform an exhaustive evaluation of patterns on an 8-channel KIII model. Simulation results show that phase information outperforms amplitude information in the recovery of incomplete or corrupted stimuli.

Models, Neurological↗
PubMed2004

Defining and identifying communities in networks.

The investigation of community structures in networks is an important issue in many domains and disciplines. This problem is relevant for social tasks (objective analysis of relationships on the web), biological inquiries (functional studies in metabolic and protein networks), or technological problems (optimization of large infrastructures). Several types of algorithms exist for revealing the community structure in networks, but a general and quantitative definition of community is not implemented in the algorithms, leading to an intrinsic difficulty in the interpretation of the results without any additional nontopological information. In this article we deal with this problem by showing how quantitative definitions of community are implemented in practice in the existing algorithms. In this way the algorithms for the identification of the community structure become fully self-contained. Furthermore, we propose a local algorithm to detect communities which outperforms the existing algorithms with respect to computational cost, keeping the same level of reliability. The algorithm is tested on artificial and real-world graphs. In particular, we show how the algorithm applies to a network of scientific collaborations, which, for its size, cannot be attacked with the usual methods. This type of local algorithm could open the way to applications to large-scale technological and biological systems.

Algorithms↗
PubMed2006

Convergence properties of the degree distribution of some growing network models.

In this article we study a class of randomly grown graphs that includes some preferential attachment and uniform attachment models, as well as some evolving graph models that have been discussed previously in the literature. The degree distribution is assumed to form a Markov chain; this gives a particularly simple form for a stochastic recursion of the degree distribution. We show that for this class of models the empirical degree distribution tends almost surely and in norm to the expected degree distribution as the size of the graph grows to infinity and we provide a simple asymptotic expression for the expected degree distribution. Convergence of the empirical degree distribution has consequences for statistical analysis of network data in that it allows the full data to be summarized by the degree distribution of the nodes without losing the ability to obtain consistent estimates of parameters describing the network.

Markov Chains↗
PubMed2006

Complexity and non-commutativity of learning operations on graphs.

We present results from numerical studies of supervised learning operations in small recurrent networks considered as graphs, leading from a given set of input conditions to predetermined outputs. Graphs that have optimized their output for particular inputs with respect to predetermined outputs are asymptotically stable and can be characterized by attractors, which form a representation space for an associative multiplicative structure of input operations. As the mapping from a series of inputs onto a series of such attractors generally depends on the sequence of inputs, this structure is generally non-commutative. Moreover, the size of the set of attractors, indicating the complexity of learning, is found to behave non-monotonically as learning proceeds. A tentative relation between this complexity and the notion of pragmatic information is indicated.

Artificial Intelligence↗
PubMed2004

Annealing by two sets of interactive dynamics.

This work derives the mean field approximation to the mean configuration of a stochastic Hopfield neural network under the Boltzmann assumption. The new approximation is realized by two sets of interactive mean field equations, respectively estimating mean activations subject to mean correlations and mean correlations subject to mean activations. The two sets of interactive dynamics are derived based on two dual mathematical frameworks. Each aims to optimize the objective quantified by a combiation of the Kullback-Leibler (KL) divergence and the correlation strength between any two distinct fluctuated variables subject to fixed mean correlations or activations. The new method is applied to the graph bisection problem. By numerical simulations, we show that the new method effectively improves in both performance and relaxation efficiency against the naive mean field equation

Algorithms↗
PubMed2004

A dynamically growing self-organizing tree (DGSOT) for hierarchical clustering gene expression profiles.

MOTIVATION: The increasing use of microarray technologies is generating large amounts of data that must be processed in order to extract useful and rational fundamental patterns of gene expression. Hierarchical clustering technology is one method used to analyze gene expression data, but traditional hierarchical clustering algorithms suffer from several drawbacks (e.g. fixed topology structure; mis-clustered data which cannot be reevaluated). In this paper, we introduce a new hierarchical clustering algorithm that overcomes some of these drawbacks. RESULT: We propose a new tree-structure self-organizing neural network, called dynamically growing self-organizing tree (DGSOT) algorithm for hierarchical clustering. The DGSOT constructs a hierarchy from top to bottom by division. At each hierarchical level, the DGSOT optimizes the number of clusters, from which the proper hierarchical structure of the underlying dataset can be found. In addition, we propose a new cluster validation criterion based on the geometric property of the Voronoi partition of the dataset in order to find the proper number of clusters at each hierarchical level. This criterion uses the Minimum Spanning Tree (MST) concept of graph theory and is computationally inexpensive for large datasets. A K-level up distribution (KLD) mechanism, which increases the scope of data distribution in the hierarchy construction, was used to improve the clustering accuracy. The KLD mechanism allows the data misclustered in the early stages to be reevaluated at a later stage and increases the accuracy of the final clustering result. The clustering result of the DGSOT is easily displayed as a dendrogram for visualization. Based on a yeast cell cycle microarray expression dataset, we found that our algorithm extracts gene expression patterns at different levels. Furthermore, the biological functionality enrichment in the clusters is considerably high and the hierarchical structure of the clusters is more reasonable. AVAILABILITY: DGSOT is available upon request from the authors.

Algorithms↗
PubMed1993

A tutorial introduction to stochastic simulation algorithms for belief networks.

Belief networks combine probabilistic knowledge with explicit information about conditional independence assumptions. A belief network consists of a directed acyclic graph in which the nodes represent variables and the edges express relationships of conditional dependence. When information about one variable's state is given to the network in the form of evidence, an update algorithm computes the posterior marginal probability distributions for the remaining variables in the network. Many algorithms for performing this inference task have been proposed. Exact algorithms report precise results for some classes of networks, but take exponential time (in the number of nodes) both in the worst case and for many interesting networks. Stochastic simulation algorithms estimate the posterior marginal probability distribution for many graph topologies that would require exponential time when using an exact algorithm. Nonetheless, for some belief networks, stochastic simulation algorithms are also known to have exponential worst case performance. This article describes at a tutorial level several stochastic simulation algorithms for belief networks, and illustrates them on some simple examples. In addition, the theoretical and empirical performance of the algorithms is briefly surveyed.

Algorithms↗
PubMedDate not supplied

Comparison of a neural net-based QSAR algorithm (PCANN) with Hologram- and multiple linear regression-based QSAR approaches: application to 1,4-dihydropyridine-based calcium channel antagonists.

A QSAR algorithm (PCANN) has been developed and applied to a set of calcium channel blockers which are of special interest because of their role in cardiac disease and also because many of them interact with P-glycoprotein, a membrane protein associated with multidrug resistance to anticancer agents. A database of 46 1,4-dihydropyridines with known Ca2+ channel binding affinities was employed for the present analysis. The QSAR algorithm can be summarized as follows: (1) a set of 90 graph theoretic and information theoretic descriptors representing various structural and topological characteristics was calculated for each of the 1,4-dihydropyridines and (2) principal component analysis (PCA) was used to compress these 90 into the eight best orthogonal composite descriptors for the database. These eight sufficed to explain 96% of the variance in the original descriptor set. (3) Two important empirical descriptors, the Leo-Hansch lipophilic constant and the Hammet electronic parameter, were added to the list of eight. (4) The 10 resulting descriptors were used as inputs to a back-propagation neural network whose output was the predicted binding affinity. (5) The predictive ability of the network was assessed by cross-validation. A comparison of the present approach with two other QSAR approaches (multiple linear regression using the same variables and a Hologram QSAR model) is made and shows that the PCANN approach can yield better predictions, once the right network configuration is identified. The present approach (PCANN) may prove useful for rapid assessment of the potential for biological activity when dealing with large chemical libraries.

Algorithms↗
PubMed2002

Community structure in social and biological networks.

A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known--a collaboration network and a food web--and find that it detects significant and informative community divisions in both cases.

Algorithms↗
PubMed2006

Using graph theoretical analysis of multi channel EEG to evaluate the neural efficiency hypothesis.

Previous studies demonstrated that intelligence is significantly related to an impressive array of psychological, social, biological and genetic factors and that working memory (WM) can be considered as a general cognitive resource strongly related with a wide variety of higher order cognitive competencies and intelligence. Also, evaluating the WM of subjects might allow one to test the neural efficiency hypothesis (NEH). WM typically involves functional interactions between frontal and parietal cortices. We recorded EEG signals to study neuronal interactions during one WM test in individuals who had few years of formal education (LE) as compared to individuals with university degrees (UE). The two groups of individuals differed in the scores they obtained in psychological tests. To quantify the synchronization between EEG channels in several frequency bands, we evaluated the "synchronization likelihood" (SL), which takes into consideration nonlinear processes as well as linear ones. SL was then converted into graphs to estimate the distance from "small-world network" (SWN) organization, i.e., an optimally organized network that would give rise to the data. In comparison to LE subjects, those with university degrees exhibited less prominent SWN properties in most frequency bands during the WM task. This finding supports the NEH and suggests that the connections between brain areas of well-educated subjects engaged in WM tasks are not as well-organized in the sense of SWN.

Adult↗
PubMed2004

Functional connectivity patterns of human magnetoencephalographic recordings: a 'small-world' network?

EEG and MEG (magnetoencephalography) are widely used to study functional connectivity between different brain regions. We address the question whether such connectivity patterns display an optimal organization for information processing. MEG recordings of five healthy human subjects were converted to sparsely connected graphs (N=126; k=15) by applying a suitable threshold to the N * N matrix of synchronization strengths. For intermediate frequencies (8-30 Hz) the synchronization patterns were similar to those of an ordered graph with a consistent drop of synchronization strength as a function of distance. For low (<8 Hz) and high (>30 Hz) frequency bands the synchronization patterns displayed the features of a so-called 'small-world' network. This might reflect an optimal organization pattern for information processing, connecting any two brain area by only a small number of intermediate steps.

Action Potentials↗
PubMed2006

On analytical approaches to epidemics on networks.

One way to describe the spread of an infection on a network is by approximating the network by a random graph. However, the usual way of constructing a random graph does not give any control over the number of triangles in the graph, while these triangles will naturally arise in many networks (e.g. in social networks). In this paper, random graphs with a given degree distribution and a given expected number of triangles are constructed. By using these random graphs we analyze the spread of two types of infection on a network: infections with a fixed infectious period and infections for which an infective individual will infect all of its susceptible neighbors or none. These two types of infection can be used to give upper and lower bounds for R(0), the probability of extinction and other measures of dynamics of infections with more general infectious periods.

Communicable Diseases↗
PubMed1998

Neural Network Computer Analysis of Fetal Heart Rate.

> Objective: A nonsubjective evaluation of intrapartum fetal heart rate (FHR) with a neural network (NNW) computer system and its clinical application. Methods: Eight simple FHR data were input into the NNW computer after 16-step normalizations. The computer was composed of 40 units in the input layer, 30 in intermediate layer, and 3 in the output layer, and the probabilities to be normal, suspicious, and pathological were obtained at the output. Before use, the computer was trained 10,000 times by 50-min teacher FHR data of 20 cases with known outcomes. The trained NNW computer was tested by FHRs of another 29 cases. The outcome probabilities in 15 min were calculated every 5 min in another 10 cases, and the bar graphs of the probabilities were displayed in sequence in the trendgrams. Results: The trained NNW computer was 100% accurate in the internal check; in the external check 86% of the results were evaluated correctly with the cardiotocogram, Apgar score, and umbilical arterial pH of the 29 test cases. The FHR scores of our conventional computer FHR analysis were higher in the suspicious and pathological groups than the normal group, and the fetal distress index was high in the pathological group. The trendgrams were simply accurate in typically normal or abnormal cases, transitory abnormal probabilities were shown in intermediate cases, and mixed suspicious and pathological probabilities suggested pathological outcome. Conclusions: The outcome probabilities and their trendgrams in the NNW FHR analysis are promising in objective decision making in the intrapartum stage.

Journal Article↗
PubMed2005

Complex networks emerging from fluctuating random graphs: analytic formula for the hidden variable distribution.

In analogy to superstatistics, which connects Boltzmann-Gibbs statistical mechanics to its generalizations through temperature fluctuations, complex networks are constructed from fluctuating Erdös-Rényi random graphs. Using a quantum-mechanical method, the exact analytic formula for the hidden variable distribution is presented which describes the nature of the fluctuations and generates a generic degree distribution through the Poisson transformation. As an example, a static scale-free network is discussed and the corresponding hidden variable distribution is found to decay as a power law and to diverge at the origin.

Algorithms↗
PubMed2004

Physical network models.

We develop a new framework for inferring models of transcriptional regulation. The models, which we call physical network models, are annotated molecular interaction graphs. The attributes in the model correspond to verifiable properties of the underlying biological system such as the existence of protein-protein and protein-DNA interactions, the directionality of signal transduction in protein-protein interactions, as well as signs of the immediate effects of these interactions. Possible configurations of these variables are constrained by the available data sources. Some of the data sources, such as factor-binding data, involve measurements that are directly tied to the variables in the model. Other sources, such as gene knock-outs, are functional in nature and provide only indirect evidence about the variables. We associate each observed knock-out effect in the deletion mutant data with a set of causal paths (molecular cascades) that could in principle explain the effect, resulting in aggregate constraints about the physical variables in the model. The most likely settings of all the variables, specifying the most likely graph annotations, are found by a recursive application of the max-product algorithm. By testing our approach on datasets related to the pheromone response pathway in S. cerevisiae, we demonstrate that the resulting model is consistent with previous studies about the pathway. Moreover, we successfully predict gene knock-out effects with a high degree of accuracy in a cross-validation setting. When applying this approach genome-wide, we extract submodels consistent with previous studies. The approach can be readily extended to other data sources or to facilitate automated experimental design.

Computational Biology↗
PubMed2005

An incremental regression method for graph structured data.

In this paper, we consider learning problems defined on graph-structured data. We propose an incremental supervised learning algorithm for network-based estimators using diffusion kernels. Diffusion kernel nodes are iteratively added in the training process. For each new node added, the kernel function center and the output connection weight are decided according to an empirical risk driven rule based on an extended chained version of the Nadaraja-Watson estimator. Then the diffusion parameters are determined by a genetic-like optimization technique.

Algorithms↗
PubMed2005

Estimation of distribution algorithms with Kikuchi approximations.

The question of finding feasible ways for estimating probability distributions is one of the main challenges for Estimation of Distribution Algorithms (EDAs). To estimate the distribution of the selected solutions, EDAs use factorizations constructed according to graphical models. The class of factorizations that can be obtained from these probability models is highly constrained. Expanding the class of factorizations that could be employed for probability approximation is a necessary step for the conception of more robust EDAs. In this paper we introduce a method for learning a more general class of probability factorizations. The method combines a reformulation of a probability approximation procedure known in statistical physics as the Kikuchi approximation of energy, with a novel approach for finding graph decompositions. We present the Markov Network Estimation of Distribution Algorithm (MN-EDA), an EDA that uses Kikuchi approximations to estimate the distribution, and Gibbs Sampling (GS) to generate new points. A systematic empirical evaluation of MN-EDA is done in comparison with different Bayesian network based EDAs. From our experiments we conclude that the algorithm can outperform other EDAs that use traditional methods of probability approximation in the optimization of functions with strong interactions among their variables.

Algorithms↗