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Analysis of ribosomal RNA sequences by combinatorial clustering.

We present an analysis of multi-aligned eukaryotic and procaryotic small subunit rRNA sequences using a novel segmentation and clustering procedure capable of extracting subsets of sequences that share common sequence features. This procedure consists of: i) segmentation of aligned sequences using a dynamic programming procedure, and subsequent identification of likely conserved segments; ii) for each putative conserved segment, extraction of a locall homogeneous cluster using a novel polynomial procedure; and iii) intersection of clusters associated with each conserved segment. Aside from their utilit in processing large gap-filled multi-alignments, these algorithms can be applied to a broad spectrum of rRNA analysis functions such as subalignment, phylogenetic subtree extraction and construction, and organism tree-placement, and can serve as a framework to organize sequence data in an efficient and easily searchable manner. The sequence classification we obtained using the method presented here shows a remarkable consistency with the independently constructed eukaryotic phylogenetic tree.

Algorithms↗

Larger water clusters with edges and corners on their way to ice: structural trends elucidated with an improved parallel evolutionary algorithm.

For the difficult task of finding global minimum energy structures for molecular clusters of nontrivial size, we present a highly efficient parallel implementation of an evolutionary algorithm. By completely abandoning the traditional concept of generations and by replacing it with a less rigid pool concept, we have managed to eliminate serial bottlenecks completely and can operate the algorithm efficiently on an arbitrary number of parallel processes. Nevertheless, our new algorithm still realizes all of the main features of our old, successful implementation. First tests of the new algorithm are shown for the highly demanding problem of water clusters modeled by a potential with flexible, polarizable monomers (TTM2-F). For this problem, our new algorithm not only reproduces all of the global minima proposed previously in considerably less CPU time but also leads to improved proposals in several cases. These, in turn, qualitatively change our earlier predictions concerning the transitions from all-surface structures to cages with a single interior molecule, and from one to two interior molecules. Furthermore, we compare preliminary results up to n = 105 with locally optimized cuts from several ice modifications. This comparison indicates that relaxed ice structures may start to be competitive already at cluster sizes above n = 90.

Journal Article↗

Analysis of sparse representation and blind source separation.

In this letter, we analyze a two-stage cluster-then-l(1)-optimization approach for sparse representation of a data matrix, which is also a promising approach for blind source separation (BSS) in which fewer sensors than sources are present. First, sparse representation (factorization) of a data matrix is discussed. For a given overcomplete basis matrix, the corresponding sparse solution (coefficient matrix) with minimum l(1) norm is unique with probability one, which can be obtained using a standard linear programming algorithm. The equivalence of the l(1)-norm solution and the l(0)-norm solution is also analyzed according to a probabilistic framework. If the obtained l(1)-norm solution is sufficiently sparse, then it is equal to the l(0)-norm solution with a high probability. Furthermore, the l(1)- norm solution is robust to noise, but the l(0)-norm solution is not, showing that the l(1)-norm is a good sparsity measure. These results can be used as a recoverability analysis of BSS, as discussed. The basis matrix in this article is estimated using a clustering algorithm followed by normalization, in which the matrix columns are the cluster centers of normalized data column vectors. Zibulevsky, Pearlmutter, Boll, and Kisilev (2000) used this kind of two-stage approach in underdetermined BSS. Our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed domain and with the case in which the source number is unknown. It is also robust to additive noise and estimation error in the mixing matrix. Finally, four simulation examples and an EEG data analysis example are presented to illustrate the algorithm's utility and demonstrate its performance.

Algorithms↗

An unbiased population-based search for the geometry optimization of Lennard-Jones clusters: 2 < or = N < or = 372.

This article presents the results obtained using an unbiased Population Based Search (PBS) for optimizing Lennard-Jones clusters. PBS is able to repeatedly obtain all putative global minima, for Lennard-Jones clusters in the range 2 < or = N < or = 372, as reported in the Cambridge Cluster Database. The PBS algorithm incorporates and extends key techniques that have been developed in other Lennard-Jones optimization algorithms over the last decade. Of particular importance are the use of cut-and-paste operators, structure niching (using the cluster strain energy as a metric), two-phase local search, and a new operator, Directed Optimization, which extends the previous concept of directed mutation. In addition, PBS is able to operate in a parallel mode for optimizing larger clusters.

Journal Article↗

Coupled two-way clustering analysis of gene microarray data.

We present a coupled two-way clustering approach to gene microarray data analysis. The main idea is to identify subsets of the genes and samples, such that when one of these is used to cluster the other, stable and significant partitions emerge. The search for such subsets is a computationally complex task. We present an algorithm, based on iterative clustering, that performs such a search. This analysis is especially suitable for gene microarray data, where the contributions of a variety of biological mechanisms to the gene expression levels are entangled in a large body of experimental data. The method was applied to two gene microarray data sets, on colon cancer and leukemia. By identifying relevant subsets of the data and focusing on them we were able to discover partitions and correlations that were masked and hidden when the full dataset was used in the analysis. Some of these partitions have clear biological interpretation; others can serve to identify possible directions for future research.

Cluster Analysis↗

Novel direct and self-regulating approaches to determine optimum growing multi-experts network structure.

This paper presents two novel approaches to determine optimum growing multi-experts network (GMN) structure. The first method called direct method deals with expertise domain and levels in connection with local experts. The growing neural gas (GNG) algorithm is used to cluster the local experts. The concept of error distribution is used to apportion error among the local experts. After reaching the specified size of the network, redundant experts removal algorithm is invoked to prune the size of the network based on the ranking of the experts. However, GMN is not ergonomic due to too many network control parameters. Therefore, a self-regulating GMN (SGMN) algorithm is proposed. SGMN adopts self-adaptive learning rates for gradient-descent learning rules. In addition, SGMN adopts a more rigorous clustering method called fully self-organized simplified adaptive resonance theory in a modified form. Experimental results show SGMN obtains comparative or even better performance than GMN in four benchmark examples, with reduced sensitivity to learning parameters setting. Moreover, both GMN and SGMN outperform the other neural networks and statistical models. The efficacy of SGMN is further justified in three industrial applications and a control problem. It provides consistent results besides holding out a profound potential and promise for building a novel type of nonlinear model consisting of several local linear models.

Algorithms↗

A comparison of methods for alignment of NMR peaks in the context of cluster analysis.

This paper compares the performance of two recently developed algorithms and methods for peak alignment of first-order NMR data of complex biological samples. The NMR spectra of such samples exhibit variations in peak position and peak shape due to variations in the sample matrix and to instrumental instabilities. The first method comprises an alignment of spectral segments with linear interpolation and shift correction to accommodate correspondence between a target and a test spectrum by a beam search or genetic algorithm. The second method is based on peak picking and needle vector representation of the NMR data with subsequent breadth-first search to establish shift corrections between the target and the test spectrum. The two proposed peak alignment methods and their respective merits are discussed for a real metabonomics application. Both alignment methods have been shown to enhance the interpretability of the resulting multivariate models, thereby increasing the prospect of detecting and following the onset of subtle biological changes reflected in the NMR data.

Algorithms↗

Parallel tandem: a program for parallel processing of tandem mass spectra using PVM or MPI and X!Tandem.

A method for the rapid correlation of tandem mass spectra to a list of protein sequences in a database has been developed. The combination of the fast and accurate computational search algorithm, X!Tandem, and a Linux cluster parallel computing environment with PVM or MPI, significantly reduces the time required to perform the correlation of tandem mass spectra to protein sequences in a database. A file of tandem mass spectra is divided into a specified number of files, each containing an equal number of the spectra from the larger file. These files are then searched in parallel against a protein sequence database. The results of each parallel output file are collated into one file for viewing through a web interface. Thousands of spectra can be searched in an accurate, practical, and time effective manner. The source code for running Parallel Tandem utilizing either PVM or MPI on Linux operating system is available from http://www.thegpm.org. This source code is made available under Artistic License from the authors.

Algorithms↗

Measuring clusters of spontaneous spike-wave discharges in absence epileptic rats.

Spike-wave discharges (SWDs) characterizing absence epilepsy appear in closely packed aggregated sequences, which gave rise to the name "pyknolepsy" for this disease. In WAG/Rij rats, genetically prone to absence epilepsy, spontaneous SWDs seem to occur in clusters as well. Here, we aimed to quantify the seizures' clusters. SWDs sequences were extracted from long-term (complete estrous cycle) EEG recordings of adult female WAG/Rij rats. Spectral characteristics and half-decay time of autocorrelation functions (AC-tau) were calculated for time series of i(SWD) (proportion of time occupied by spike-wave activity), measured for subsequent periods. The clusters were characterized by means of AC-tau calculated for time series of i(SWD). The absence seizures were indeed clustered in a minute range. The clustering had a non-periodical character, since no significant and consistent periodicity was found in the minute range. AC-tau correlated positively with propensity of SWDs: i.e. the aggravation of absence epilepsy led to longer sequences of paroxysms and thus to a less random distribution. AC-tau was not sensitive to various phases of the estrous cycle, but was larger in the dark than in the light periods. We suggest that AC-tau can be used to quantify aggregation of epileptic events in the search for physiological basis of its temporal clustering.

Algorithms↗

Role of dendritic spines in action potential backpropagation: a numerical simulation study.

Two remarkable aspects of pyramidal neurons are their complex dendritic morphologies and the abundant presence of spines, small structures that are the sites of excitatory input. Although the channel properties of the dendritic shaft membrane have been experimentally probed, the influence of spine properties in dendritic signaling and action potential propagation remains unclear. To explore this we have performed multi-compartmental numerical simulations investigating the degree of consistency between experimental data on dendritic channel densities and backpropagation behavior, as well as the necessity and degree of influence of excitable spines. Our results indicate that measured densities of Na(+) channels in dendritic shafts cannot support effective backpropagation observed in apical dendrites due to suprathreshold inactivation. We demonstrate as a potential solution that Na(+) channels in spines at higher densities than those measured in the dendritic shaft can support extensive backpropagation. In addition, clustering of Na(+) channels in spines appears to enhance their effect due to their unique morphology. Finally, we show that changes in spine morphology significantly influence backpropagation efficacy. These results suggest that, by clustering sodium channels, spines may serve to control backpropagation.

Action Potentials↗

A divide-and-conquer approach to fragment assembly.

MOTIVATION: One of the major problems in DNA sequencing is assembling the fragments obtained by shotgun sequencing. Most existing fragment assembly techniques follow the overlap-layout-consensus approach. This framework requires extensive computation in each phase and becomes inefficient with increasing number of fragments. RESULTS: We propose a new algorithm which solves the overlap, layout, and consensus phases simultaneously. The fragments are clustered with respect to their Average Mutual Information (AMI) profiles using the k-means algorithm. This removes the unnecessary burden of considering the collection of fragments as a whole. Instead, the orientation and overlap detection are solved efficiently, within the clusters. The algorithm has successfully reconstructed both artificial and real data. AVAILABILITY: Available on request from the authors.

Algorithms↗

An effective cluster-based model for robust speech detection and speech recognition in noisy environments.

This paper shows an accurate speech detection algorithm for improving the performance of speech recognition systems working in noisy environments. The proposed method is based on a hard decision clustering approach where a set of prototypes is used to characterize the noisy channel. Detecting the presence of speech is enabled by a decision rule formulated in terms of an averaged distance between the observation vector and a cluster-based noise model. The algorithm benefits from using contextual information, a strategy that considers not only a single speech frame but also a neighborhood of data in order to smooth the decision function and improve speech detection robustness. The proposed scheme exhibits reduced computational cost making it adequate for real time applications, i.e., automated speech recognition systems. An exhaustive analysis is conducted on the AURORA 2 and AURORA 3 databases in order to assess the performance of the algorithm and to compare it to existing standard voice activity detection (VAD) methods. The results show significant improvements in detection accuracy and speech recognition rate over standard VADs such as ITU-T G.729, ETSI GSM AMR, and ETSI AFE for distributed speech recognition and a representative set of recently reported VAD algorithms.

Algorithms↗

Clustering microarray gene expression data using weighted Chinese restaurant process.

MOTIVATION: Clustering microarray gene expression data is a powerful tool for elucidating co-regulatory relationships among genes. Many different clustering techniques have been successfully applied and the results are promising. However, substantial fluctuation contained in microarray data, lack of knowledge on the number of clusters and complex regulatory mechanisms underlying biological systems make the clustering problems tremendously challenging. RESULTS: We devised an improved model-based Bayesian approach to cluster microarray gene expression data. Cluster assignment is carried out by an iterative weighted Chinese restaurant seating scheme such that the optimal number of clusters can be determined simultaneously with cluster assignment. The predictive updating technique was applied to improve the efficiency of the Gibbs sampler. An additional step is added during reassignment to allow genes that display complex correlation relationships such as time-shifted and/or inverted to be clustered together. Analysis done on a real dataset showed that as much as 30% of significant genes clustered in the same group display complex relationships with the consensus pattern of the cluster. Other notable features including automatic handling of missing data, quantitative measures of cluster strength and assignment confidence. Synthetic and real microarray gene expression datasets were analyzed to demonstrate its performance. AVAILABILITY: A computer program named Chinese restaurant cluster (CRC) has been developed based on this algorithm. The program can be downloaded at http://www.sph.umich.edu/csg/qin/CRC/.

Algorithms↗

A fast Monte Carlo algorithm to simulate the spectrum of DNA damages formed by ionizing radiation.

Ionizing radiation produces both singly and multiply damaged DNA sites. Multiply damaged sites (MDS) have been implicated in radiation-induced cell killing and mutagenesis. The spatial distribution of elementary damages (strand breaks and base damages) that constitute MDS is of special interest, since the complexity of MDS has an impact on damage repair. A fast and easy-to-implement algorithm to simulate the local clustering of elementary damages produced by ionizing radiation is proposed. This algorithm captures the major trends in the DNA damage spectrum predicted using detailed track- structure simulations. An attractive feature of the proposed algorithm is that only four adjustable parameters need to be identified to simulate the formation of DNA damage. A convenient recipe to determine the parameters used in the fast Monte Carlo damage simulation algorithm is provided for selected low- and high-LET radiations. The good agreement among the damage yields predicted by the fast and detailed damage formation algorithms suggests that the small-scale spatial distribution of damage sites is determined primarily by independent and purely stochastic events and processes.

Algorithms↗

Condition-specific coregulation with cis-regulatory motifs and modules in the mouse genome.

Deciphering genetic regulatory codes remains a challenge. Here, we present an effective approach to identifying in vivo condition-specific coregulation with cis-regulatory motifs and modules in the mouse genome. A resampling-based algorithm was adopted to cluster our microarray data of a stress response, which generated 35 tight clusters with unique expression patterns containing 811 genes of 5652 genes significantly altered. Database searches identified many known motifs within the 3-kb regulatory regions of 40 genes from 3 clusters and modules with six to nine motifs that were commonly shared by 60-100% of these genes. The upstream regulatory region contained the highest frequency of these common motifs. CisModule program predictions were comparable with the results from database searches and found four potentially novel motifs. This result indicates that these motifs and modules could be responsible for gene coregulation of the stress response in the lacrimal gland.

Algorithms↗

Active clusters in disordered systems.

We introduce an exact algorithm to calculate the distribution of large low energy clusters (droplets) in disordered manifolds and disordered magnets, and we analyze the extent to which these clusters can be treated as independent two-level systems. We show that interfaces in randomly diluted networks always have broad droplet distributions, while diluted antiferromagnets in a field can have either power law or exponential droplet distributions.

Journal Article↗

GeneCluster 2.0: an advanced toolset for bioarray analysis.

SUMMARY: GeneCluster 2.0 is a software package for analyzing gene expression and other bioarray data, giving users a variety of methods to build and evaluate class predictors, visualize marker lists, cluster data and validate results. GeneCluster 2.0 greatly expands the data analysis capabilities of GeneCluster 1.0 by adding classification, class discovery and permutation test methods. It includes algorithms for building and testing supervised models using weighted voting and k-nearest neighbor algorithms, a module for systematically finding and evaluating clustering via self-organizing maps, and modules for marker gene selection and heat map visualization that allow users to view and sort samples and genes by many criteria. GeneCluster 2.0 is a stand-alone Java application and runs on any platform that supports the Java Runtime Environment version 1.3.1 or greater. AVAILABILITY: http://www.broad.mit.edu/cancer/software

Algorithms↗