Fixed-cluster acceleration algorithm for spin systems.
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Single-unit activity in cortical area MST associated with disparity-vergence eye movements: evidence for population coding.
Single-unit discharges were recorded in the medial superior temporal area (MST) of five behaving monkeys. Brief (230-ms) horizontal disparity steps were applied to large correlated or anticorrelated random-dot patterns (in which the dots had the same or opposite contrast, respectively, at the two eyes), eliciting vergence eye movements at short latencies [65.8 +/- 4.5 (SD) ms]. Disparity tuning curves, describing the dependence of the initial vergence responses (measured over the period 50-110 ms after the step) on the magnitude of the steps, resembled the derivative of a Gaussian, the curves obtained with correlated and anticorrelated patterns having opposite sign. Cells with disparity-related activity were isolated using correlated stimuli, and disparity tuning curves describing the dependence of these initial neuronal responses (measured over the period of 40-100 ms) on the magnitude of the disparity step were constructed (n = 102 cells). Using objective criteria and the fuzzy c-means clustering algorithm, disparity tuning curves were sorted into four groups based on their shapes. A post hoc comparison indicated that these four groups had features in common with four of the classes of disparity-selective neurons in striate cortex, but three of the four groups appeared to be part of a continuum. Most of the data were obtained from two monkeys, and when the disparity tuning curves of all the individual neurons recorded from either monkey were summed together, they fitted the disparity tuning curve for that same animal's vergence responses remarkably well (r(2): 0.93, 0.98). Fifty-six of the neurons recorded from these two monkeys were also tested with anticorrelated patterns, and all showed significant modulation of their activity (P < 0.005, 1-way ANOVA). Further, when all of the disparity tuning curves obtained with these patterns from either monkey were summed together, they too fitted the disparity tuning curve for that same animal's vergence responses very well (r(2): 0.95, 0.96). Indeed, the summed activity even reproduced idiosyncratic differences in the vergence responses of the two monkeys. Based on these and other observations on the temporal coding of events, we hypothesize that the magnitude, direction, and time course of the initial vergence velocity responses associated with disparity steps applied to large patterns are all encoded in the summed activity of the disparity-sensitive cells in MST. Latency data suggest that this activity in MST occurs early enough to play an active role in the generation of vergence eye movements at short latencies.
Algorithms↗
Detection of evolutionarily stable fragments of cellular pathways by hierarchical clustering of phyletic patterns.
BACKGROUND: Phyletic patterns denote the presence and absence of orthologous genes in completely sequenced genomes and are used to infer functional links between genes, on the assumption that genes involved in the same pathway or functional system are co-inherited by the same set of genomes. However, this basic premise has not been quantitatively tested, and the limits of applicability of the phyletic-pattern method remain unknown. RESULTS: We characterized a hierarchy of 3,688 phyletic patterns encompassing more than 5,000 known protein-coding genes from 66 complete microbial genomes, using different distances, clustering algorithms, and measures of cluster quality. The most sensitive set of parameters recovered 223 clusters, each consisting of genes that belong to the same metabolic pathway or functional system. Fifty-six clusters included unexpected genes with plausible functional links to the rest of the cluster. Only a small percentage of known pathways and multiprotein complexes are co-inherited as one cluster; most are split into many clusters, indicating that gene loss and displacement has occurred in the evolution of most pathways. CONCLUSIONS: Phyletic patterns of functionally linked genes are perturbed by differential gains, losses and displacements of orthologous genes in different species, reflecting the high plasticity of microbial genomes. Groups of genes that are co-inherited can, however, be recovered by hierarchical clustering, and may represent elementary functional modules of cellular metabolism. The phyletic patterns approach alone can confidently predict the functional linkages for about 24% of the entire data set.
Cluster Analysis↗
Cluster analysis and promoter modelling as bioinformatics tools for the identification of target genes from expression array data.
Expression arrays yield enormous amounts of data linking genes, via their cDNA sequences, to gene expression patterns. This now allows the characterisation of gene expression in normal and diseased tissues, as well as the response of tissues to the application of therapeutic reagents. Expression array data can be analysed with respect to the underlying protein sequences, which facilitates the precise determination of when and where certain groups of genes are expressed. More recent developments of clustering algorithms take additional parameters of the experimental set-up into account, focusing more directly on co-regulated set of genes. However, the information concerning transcriptional regulatory networks responsible for the observed expression patterns is not contained within the cDNA sequences used to generate the arrays. Regulation of expression is determined to a large extent by the promoter sequences of the individual genes (and/or enhancers). The complete sequence of the human genome now provides the molecular basis for the identification of many regulatory regions. Promoter sequences for specific cDNAs can be obtained reliably from genomic sequences by exon mapping. In the many cases in which cDNAs are 5'-incomplete, high quality promoter prediction tools can be used to locate promoters directly in the genomic sequence. Once sufficient numbers of promoter sequences have been obtained, a comparative promoter analysis of the co-regulated genes and groups of genes can be applied in order to generate models describing the higher order levels of transcription factor binding site organisation within these promoter regions. Such modules represent the molecular mechanisms through which regulatory networks influence gene expression, and candidates can be determined solely by bioinformatics. This approach also provides a powerful alternative for elucidating the functional features of genes with no detectable sequence similarity, by linking them to other genes on the basis of their common promoter structures.
Algorithms↗
Clustering genes using gene expression and text literature data.
Clustering of gene expression data is a standard technique used to identify closely related genes. In this paper, we develop a new clustering algorithm, MSC (Multi-Source Clustering), to perform exploratory analysis using two or more diverse sources of data. In particular, we investigate the problem of improving the clustering by integrating information obtained from gene expression data with knowledge extracted from biomedical text literature. In each iteration of algorithm MSC, an EM-type procedure is employed to bootstrap the model obtained from one data source by starting with the cluster assignments obtained in the previous iteration using the other data sources. Upon convergence, the two individual models are used to construct the final cluster assignment. We compare the results of algorithm MSC for two data sources with the results obtained when the clustering is applied on the two sources of data separately. We also compare it with that obtained using the feature level integration method that performs the clustering after simply concatenating the features obtained from the two data sources. We show that the z-scores of the clustering results from MSC are better than that from the other methods. To evaluate our clusters better, function enrichment results are presented using terms from the Gene Ontology database. Finally, by investigating the success of motif detection programs that use the clusters, we show that our approach integrating gene expression data and text data reveals clusters that are biologically more meaningful than those identified using gene expression data alone.
Artificial Intelligence↗
On the calculation of absolute free energies from molecular-dynamics or Monte Carlo data.
We propose a method for calculating absolute free energies from Monte Carlo or molecular-dynamics data. The method is based on the identity that expresses the partition function Q as a Boltzmann average: 1Q=w(p,x)exp[betaH(p,x)], where w(p,x) is an arbitrary weight function such that its integral over the phase space is equal to 1. In practice, to minimize statistical errors the weight function is chosen such that the regions of the phase space where sampling statistics are poor are excluded from the average. The "ideal" weight function would be the equilibrium phase-space density exp[-betaH(p,x)]Q itself. We consider two methods for constructing the weight function based on different estimates of the equilibrium phase-space density from simulation data. In the first method, it is chosen to be a Gaussian function, whose parameters are obtained from the covariance matrix of the atomic coordinates. In the second, a clustering algorithm is used to attempt partitioning the data into clusters corresponding to different basins of attraction visited by the system. The weight function is then constructed as a superposition of Gaussians calculated for each cluster separately. We show that these strategies can be used to improve upon previous methods of estimating absolute entropies from covariance matrices.
Algorithms↗
Using Greedy algorithm: DBSCAN revisited II.
The density-based clustering algorithm presented is different from the classical Density-Based Spatial Clustering of Applications with Noise (DBSCAN) (Ester et al., 1996), and has the following advantages: first, Greedy algorithm substitutes for R(*)-tree (Bechmann et al., 1990) in DBSCAN to index the clustering space so that the clustering time cost is decreased to great extent and I/O memory load is reduced as well; second, the merging condition to approach to arbitrary-shaped clusters is designed carefully so that a single threshold can distinguish correctly all clusters in a large spatial dataset though some density-skewed clusters live in it. Finally, authors investigate a robotic navigation and test two artificial datasets by the proposed algorithm to verify its effectiveness and efficiency.
Algorithms↗
How to avoid spurious cluster validation? A methodological investigation on simulated and fMRI data.
This paper presents an evaluation of a common approach that has been considered as a promising option for exploratory fMRI data analyses. The approach includes two stages: creating from the data a sequence of partitions with increasing number of subsets (clustering) and selecting the one partition in this sequence that exhibits the clearest indications of an existing structure (cluster validation). In order to achieve that the selected partition is actually the best characterization of the data structure, previous studies were directed to find the most appropriate validity function(s). In our analysis protocol, we first optimize the sequence of partitions according to the given objective function. Our study showed that an insufficient optimization of the partition, for one or more numbers of clusters, can easily yield a spurious validation result which, in turn, may lead the analyst to a misleading interpretation of the fMRI experiment. However, a sufficient optimization, for each included number of clusters, provided the basis for a reliable, adequate characterization of the data Furthermore, it enabled an adequate evaluation of the validity functions. These findings were obtained independently for three clustering algorithms (representing the hard and fuzzy clustering variant) and three up-to-date cluster validity functions. The findings were derived from analyses of Gaussian clusters, simulated data sets that mimic typical fMRI response signals, andreal fMRI data. Based on our results we propose a number of options of how to configure improved clustering tools.
Algorithms↗
Progress in understanding and using over-the-counter pharmaceuticals for syndromic surveillance.
INTRODUCTION: Public health researchers are increasingly interested in the potential use of monitoring data on over-the-counter (OTC) pharmaceutical sales as a source of timely information about community health. However, fundamental uncertainties persist, including how timely such information is and how best to aggregate information about hundreds of products. OBJECTIVES: This analysis provides new information about OTC timeliness and illustrates a method of OTC product aggregation for surveillance purposes. METHODS: Timeliness measurements were made by correlating pharmaceutical sales counts with counts of physician encounters, after adjustment to remove seasonal effects from both counts. OTC product aggregations were formed by a two-stage process. In the first stage, individual products were placed into small groups based on qualitative observations. In the second stage, a clustering algorithm was used to form supergroups (i.e., product group clusters) sharing similar sales histories. RESULTS: Even after seasonal correction, OTC counts correlated with clinical measures of community illness. However, the lead time of nonseasonal fluctuations was substantially shorter than that for uncorrected data. The clustering approach produced 16 meaningful supergroups containing products that behaved approximately alike. CONCLUSIONS: Measurements of OTC lead time sensitive to the timing of annual cyclic trends in the behavior of persons seeking health care do not reliably indicate the lead time observed for short-term (e. g. weekly or monthly) fluctuations in community health-care utilization.
Algorithms↗
Movement discrimination by single cells in the human pallidum characterised by hidden Markov models.
In patients undergoing pallidotomy for Parkinson's disease, we recorded extracellularly from single neurons in the two internal segments (GPii, GPie) and the external segment (GPe) of the globus pallidus (GP) in response to active (cued) movements of the contralateral wrist, elbow or ankle. The patterns of cell activity occurring both before and after movement onset were analysed using hidden Markov models (HMMs) and clustered by movement type using the generative topographical mapping algorithm. Cluster separation was quantified in order to measure a cell's ability to discriminate between movements. Statistical analysis of variance indicated a significant regional gradient (GPii > GPie > GPe) of movement discrimination, while cells in all regions differentiated better between movements of different joints (wrist, elbow or ankle) than between flexion and extension of the same joint. We found that GP cells generally showed distinguishable firing patterns corresponding to more than one type of movement per cell, in support of the hypothesis that cells in these regions of the basal ganglia are not involved in preparation or execution of a single type of movement but participate in many different movements, analogous to the hidden units of a neural network. Our results also indicate that cell activity both preceding a movement and during its execution may be modelled by HMMs with only a small number of states.
Action Potentials↗
Computing the maximum similarity bi-clusters of gene expression data.
MOTIVATIONS: Bi-clustering is an important approach in microarray data analysis. The underlying bases for using bi-clustering in the analysis of gene expression data are (1) similar genes may exhibit similar behaviors only under a subset of conditions, not all conditions, (2) genes may participate in more than one function, resulting in one regulation pattern in one context and a different pattern in another. Using bi-clustering algorithms, one can obtain sets of genes that are co-regulated under subsets of conditions. RESULTS: We develop a polynomial time algorithm to find an optimal bi-cluster with the maximum similarity score. To our knowledge, this is the first formulation for bi-cluster problems that admits a polynomial time algorithm for optimal solutions. The algorithm works for a special case, where the bi-clusters are approximately squares. We then extend the algorithm to handle various kinds of other cases. Experiments on simulation data and real data show that the new algorithms outperform most of the existing methods in many cases. Our new algorithms have the following advantages: (1) no discretization procedure is required, (2) performs well for overlapping bi-clusters and (3) works well for additive bi-clusters. AVAILABILITY: The software is available at http://www.cs.cityu.edu.hk/~liuxw/msbe/help.html.
Algorithms↗
K-ary clustering with optimal leaf ordering for gene expression data.
MOTIVATION: A major challenge in gene expression analysis is effective data organization and visualization. One of the most popular tools for this task is hierarchical clustering. Hierarchical clustering allows a user to view relationships in scales ranging from single genes to large sets of genes, while at the same time providing a global view of the expression data. However, hierarchical clustering is very sensitive to noise, it usually lacks of a method to actually identify distinct clusters, and produces a large number of possible leaf orderings of the hierarchical clustering tree. In this paper we propose a new hierarchical clustering algorithm which reduces susceptibility to noise, permits up to k siblings to be directly related, and provides a single optimal order for the resulting tree. RESULTS: We present an algorithm that efficiently constructs a k-ary tree, where each node can have up to k children, and then optimally orders the leaves of that tree. By combining k clusters at each step our algorithm becomes more robust against noise and missing values. By optimally ordering the leaves of the resulting tree we maintain the pairwise relationships that appear in the original method, without sacrificing the robustness. Our k-ary construction algorithm runs in O(n(3)) regardless of k and our ordering algorithm runs in O(4(k)n(3)). We present several examples that show that our k-ary clustering algorithm achieves results that are superior to the binary tree results in both global presentation and cluster identification. AVAILABILITY: We have implemented the above algorithms in C++ on the Linux operating system.
Algorithms↗
Exploring expression data: identification and analysis of coexpressed genes.
Analysis procedures are needed to extract useful information from the large amount of gene expression data that is becoming available. This work describes a set of analytical tools and their application to yeast cell cycle data. The components of our approach are (1) a similarity measure that reduces the number of false positives, (2) a new clustering algorithm designed specifically for grouping gene expression patterns, and (3) an interactive graphical cluster analysis tool that allows user feedback and validation. We use the clusters generated by our algorithm to summarize genome-wide expression and to initiate supervised clustering of genes into biologically meaningful groups.
Algorithms↗
Judging the quality of gene expression-based clustering methods using gene annotation.
We compare several commonly used expression-based gene clustering algorithms using a figure of merit based on the mutual information between cluster membership and known gene attributes. By studying various publicly available expression data sets we conclude that enrichment of clusters for biological function is, in general, highest at rather low cluster numbers. As a measure of dissimilarity between the expression patterns of two genes, no method outperforms Euclidean distance for ratio-based measurements, or Pearson distance for non-ratio-based measurements at the optimal choice of cluster number. We show the self-organized-map approach to be best for both measurement types at higher numbers of clusters. Clusters of genes derived from single- and average-linkage hierarchical clustering tend to produce worse-than-random results.
Algorithms↗
Comparing multiple RNA secondary structures using tree comparisons.
In a previous paper, an algorithm was presented for analyzing multiple RNA secondary structures utilizing a multiple string alignment algorithm. In this paper we present another approach to the problem of comparing many secondary structures by utilizing a very efficient tree-matching algorithm that will compare two trees in O([T1] X [T2] X L1 X L2) in the worst case and very close to O([T1] X [T2]) for average trees representing secondary structures. The result of the pairwise comparison algorithm is then used with a cluster algorithm to produce a multiple structure clustering which can be displayed in a taxonomy tree to show related structures.
Algorithms↗
Systematic tuning of parameters in support vector clustering.
Clustering algorithms divide a set of observations into groups so that members of the same group share common features. In most of the algorithms, tunable parameters are set arbitrarily or by trial and error, resulting in less than optimal clustering. This paper presents a global optimization strategy for the systematic and optimal selection of parameter values associated with a clustering method. In the process, a performance criterion for the optimization model is proposed and benchmarked against popular performance criteria from the literature (namely, the Silhouette coefficient, Dunn's index, and Davies-Bouldin index). The tuning strategy is illustrated using the support vector clustering (SVC) algorithm and simulated annealing. In order to reduce the computational burden, the paper also proposes an alternative to the adjacency matrix method (used for the assignment of cluster labels), namely the contour plotting approach. Datasets tested include the iris and the thyroid datasets from the UCI repository, as well as lymphoma and breast cancer data. The optimal tuning parameters are determined efficiently, while the contour plotting approach leads to significant reductions in computational effort (CPU time) especially for large datasets. The performance criteria comparisons indicate mixed results. Specifically, the Silhouette coefficient and the Davies-Bouldin index perform better, while the Dunn's index is worse on average than the proposed performance index.
Algorithms↗
Cluster analysis by testing the statistical hypothesis of uniformity.
This paper presents a cluster algorithm that defines the number of clusters and allows classification of data points. The basic task of the algorithm is to identify accumulations of vectors in the analysis sample of vectors. The accumulations of vectors are determined by testing the statistical hypothesis of uniformity. On the basis of accumulations, clusters are formed.
Algorithms↗
HCPM--program for hierarchical clustering of protein models.
HCPM is a tool for clustering protein structures from comparative modeling, ab initio structure prediction, etc. A hierarchical clustering algorithm is designed and tested, and a heuristic is provided for an optimal cluster selection. The method has been successfully tested during the CASP6 experiment.
Algorithms↗