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PubMed1993

Optimization by hierarchical mutant production.

Inspired by the successful description of the first steps of molecular evolution by the quasispecies theory and the successful application of quasispecies-like algorithms to optimization problems, we propose a hierarchically organized algorithm. This new algorithm is able to solve a spin glass and a travelling salesman problem using only point mutations. Furthermore, it performs better under comparable circumstances than the ordinary quasispecies algorithm. Depending on the structure of the fitness landscape of the examined problem under consideration the hierarchically organized algorithm proves to be much more suitable than a simple quasispecies algorithm, especially in clustered landscapes. Tuning the error rates reveals the critical minimum copy fidelity necessary to guarantee optimization. We propose to incorporate hierarchical concepts into optimization algorithms inspired by biological evolution, such a genetic algorithms.

Algorithms↗

PubMed2005

Large scale hierarchical clustering of protein sequences.

BACKGROUND: Searching a biological sequence database with a query sequence looking for homologues has become a routine operation in computational biology. In spite of the high degree of sophistication of currently available search routines it is still virtually impossible to identify quickly and clearly a group of sequences that a given query sequence belongs to. RESULTS: We report on our developments in grouping all known protein sequences hierarchically into superfamily and family clusters. Our graph-based algorithms take into account the topology of the sequence space induced by the data itself to construct a biologically meaningful partitioning. We have applied our clustering procedures to a non-redundant set of about 1,000,000 sequences resulting in a hierarchical clustering which is being made available for querying and browsing at http://systers.molgen.mpg.de/. CONCLUSIONS: Comparisons with other widely used clustering methods on various data sets show the abilities and strengths of our clustering methods in producing a biologically meaningful grouping of protein sequences.

Algorithms↗

PubMed2000

Assessing reliability of gene clusters from gene expression data.

The rapid development of microarray technologies has raised many challenging problems in experiment design and data analysis. Although many numerical algorithms have been successfully applied to analyze gene expression data, the effects of variations and uncertainties in measured gene expression levels across samples and experiments have been largely ignored in the literature. In this article, in the context of hierarchical clustering algorithms, we introduce a statistical resampling method to assess the reliability of gene clusters identified from any hierarchical clustering method. Using the clustering trees constructed from the resampled data, we can evaluate the confidence value for each node in the observed clustering tree. A majority-rule consensus tree can be obtained, showing clusters that only occur in a majority of the resampled trees. We illustrate our proposed methods with applications to two published data sets. Although the methods are discussed in the context of hierarchical clustering methods, they can be applied with other cluster-identification methods for gene expression data to assess the reliability of any gene cluster of interest.

Algorithms↗

PubMed2003

Universality of the crossing probability for the Potts model for q=1, 2, 3, 4.

The universality of the crossing probability pi(hs) of a system to percolate only in the horizontal direction was investigated numerically by a cluster Monte Carlo algorithm for the q-state Potts model for q=2, 3, 4 and for percolation q=1. We check the percolation through Fortuin-Kasteleyn clusters near the critical point on the square lattice by using representation of the Potts model as the correlated site-bond percolation model. It was shown that probability of a system to percolate only in the horizontal direction pi(hs) has the universal form pi(hs)=A(q)Q(z) for q=1,2,3,4 as a function of the scaling variable z=[b(q)L(1/nu(q))[p-p(c)(q,L)]](zeta(q)). Here, p=1-exp(-beta) is the probability of a bond to be closed, A(q) is the nonuniversal crossing amplitude, b(q) is the nonuniversal metric factor, nu(q) is the correlation length index, and zeta(q) is the additional scaling index. The universal function Q(x) approximately equal exp(-/z/). The nonuniversal scaling factors were found numerically.

Journal Article↗

PubMedDate not supplied

Toward an automated analysis system for nuclear magnetic resonance imaging. II. Initial segmentation algorithm.

Image segmentation algorithms based on hierarchical clustering have been developed for analysis of T1 and T2 nuclear magnetic resonance images. Application of these algorithms to simultaneous T1-T2 images of healthy volunteers extracted fundamental tissue types in the brain. These algorithms also were used both to identify the extent of the region of involvement of a subject with a history of a grade 3 astrocytoma of the right frontal lobe of the brain, and to characterize the tissue within the region of involvement. These results suggest that a simple segmentation algorithm can produce reasonable clustering of tissue types within the brain.

Biometry↗

PubMed2002

Rayleigh-Bénard percolation transition of thermal convection in porous media: computational fluid dynamics, NMR velocity mapping, NMR temperature mapping.

Stationary thermal convection and heat conduction were studied in random-site percolation clusters in a Rayleigh-Bénard configuration experimentally by NMR microscopy techniques and numerically with the aid of a finite volume method. The porosity of the percolation clusters, and the temperature difference applied to the convection cell were varied. Two-dimensional percolation networks were generated with the aid of a random-number algorithm. The resulting clusters were used as templates for the fabrication of model objects. The convective velocity distribution of silicon oil or ethylene glycol filled into the pore space was mapped and evaluated in the form of histograms. The flow patterns visualized in the simulated and the measured velocity maps show good coincidence. In the histograms, two velocity regimes can be distinguished and attributed to local convection rolls responsible for the low-velocity part, and cluster-spanning flow loops characterized by a high-velocity cut-off, respectively. The maximum velocity as a function of the porosity and the overall temperature difference is shown to be indicative for the hydro-thermodynamic Rayleigh-Bénard instability and the geometrical percolation threshold. The coincidence of the Rayleigh-Bénard instability (modified for porous media) and the percolation transition (modified for closed loops) gives rise to a new critical phenomenon termed the Rayleigh-Bénard percolation transition. It occurs at a certain combination of the porosity and the overall temperature difference in the cell. Temperature maps were recorded with the aid of a relaxation-based NMR technique. The consequence of different thermal conductivities in the matrix and in the fluid is that horizontal-temperature gradients arise even in the absence of flow. This leads to a superposition of uncritical convective flow driven by the horizontal-temperature gradients whenever closed-loop pathways are possible and the critical Rayleigh-Bénard convection based on vertical-temperature gradients.

Journal Article↗

PubMed2006

Defining molecular profiles of poor outcome in patients with invasive bladder cancer using oligonucleotide microarrays.

PURPOSE: Bladder cancer is a common malignancy characterized by a poor clinical outcome when tumors progress into invasive disease. We sought to define genetic signatures characteristic of aggressive clinical behavior in advanced bladder tumors. METHODS: Oligonucleotide arrays were utilized to analyze the transcript profiles of 105 bladder tumors: 33 superficial, 72 invasive lesions, and 52 normal urothelium. Hierarchical clustering and supervised algorithms were used to classify and stratify bladder tumors on the basis of stage, node metastases, and overall survival. Immunohistochemical analyses on bladder cancer tissue arrays (n = 294 cases) served to validate associations between marker expression, staging and outcome. RESULTS: Hierarchical clustering classified normal urothelium, superficial, and invasive tumors with 82.2% accuracy, and stratified bladder tumors on the basis of clinical outcome. Predictive algorithms rendered an 89%-correct rate for tumor staging using genes differentially expressed between superficial and invasive tumors. Accuracies of 82% and 90% were obtained for predicting overall survival when considering all patients with bladder cancer or only patients with invasive disease, respectively. A genetic profile consisting of 174 probes was identified in those patients with positive lymph nodes and poor survival. Two independent Global Test runs confirmed the robust association of this profile with lymph node metastases (P = 7.3(-13)) and overall survival (P = 1.9(-14)) simultaneously. Immunohistochemical analyses on tissue arrays sustained the significant association of synuclein with tumor staging and clinical outcome (P = .002). CONCLUSION: Gene profiling provides a genomic-based classification scheme of diagnostic and prognostic utility for stratifying advanced bladder cancer. Identification of this poor outcome profile could assist in selecting patients who may benefit from more aggressive therapeutic intervention.

Gene Expression Profiling↗

PubMed2005

An algorithm to classify amino acid sequences into protein groups of Bothrops jararacussu venomous gland.

An algorithm for automatic clustering of database protein sequences from Bothrops jararacussu venomous gland, according to sequence similarities of their domains, is described. The program was written in C and Perl languages. This algorithm compares a domain with each ORF protein sequence in the database. Each nucleotide FASTA sequence generates six ORFs. As a result, the user has a list containing all sequences found in a specific domain and a display of the sequence, domain and number of hits. The algorithm lists only the sequences that present a minimum similarity of 30 hits and the best alignment. This limit was considered appropriate. The algorithm is available in the Internet (www.compbionet.org.br/cgi-domains/homesnake) and it can quickly and accurately organizes large database into classes.

Algorithms↗

PubMed2004

CLUSTAG: hierarchical clustering and graph methods for selecting tag SNPs.

UNLABELLED: Cluster and set-cover algorithms are developed to obtain a set of tag single nucleotide polymorphisms (SNPs) that can represent all the known SNPs in a chromosomal region, subject to the constraint that all SNPs must have a squared correlation R2>C with at least one tag SNP, where C is specified by the user. AVAILABILITY: http://hkumath.hku.hk/web/link/CLUSTAG/CLUSTAG.html CONTACT: mng@maths.hku.hk.

Algorithms↗

PubMed2001

Stabilizing interactions in the dimer interface of alpha-subunit in Escherichia coli RNA polymerase: a graph spectral and point mutation study.

The formation of alpha(2) dimer in Escherichia coli core RNA polymerase (RNAP) is thought to be the first step toward the assembly of the functional enzyme. A large number of evidences indicate that the alpha-subunit dimerizes through its N-terminal domain (NTD). The crystal structures of the alpha-subunit NTD and that of a homologous Thermus aquaticus core RNAP are known. To identify the stabilizing interactions in the dimer interface of the alpha-NTD of E. coli RNAP, we identified side-chain clusters by using the crystal structure coordinates of E. coli alpha-NTD. A graph spectral algorithm was used to identify side-chain clusters. This algorithm considers the global nonbonded side-chain interactions of the residues for the clustering procedure and is unique in identifying residues that make the largest number of interactions among the residues that form clusters in a very quantitative way. By using this algorithm, a nine-residue cluster consisting of polar and hydrophobic residues was identified in the subunit interface adjacent to the hydrophobic core. The residues forming the cluster are relatively rigid regions of the interface, as measured by the thermal factors of the residues. Most of the cluster residues in the E. coli enzyme were topologically and sequentially conserved in the T. aquaticus RNAP crystal structure. Residues 35F and 46I were predicted to be important in the stability of the alpha-dimer interface, with 35F forming the center of the cluster. The predictions were tested by isolating single-point mutants alpha-F35A and alpha-I46S on the dimer interface, which were found to disrupt dimerization. Thus, the identified cluster at the edge of the dimer interface seems to be a vital component in stabilizing the alpha-NTD.

Algorithms↗

PubMed1999

Combinatorial evolution of regression nodes in feedforward neural networks.

A number of techniques exist with which neural network architectures such as multilayer perceptrons and radial basis function networks can be trained. These include backpropagation, k-means clustering and evolutionary algorithms. The latter method is particularly useful as it is able to avoid local optima in the search space and can optimise parameters for which no gradient information exists. Unfortunately, only moderately sized networks can be trained by this method, owing to the fact that evolutionary optimisation is very computationally intensive. In this paper a novel algorithm (CERN) is therefore proposed which uses a special form of combinatorial search to optimise groups of neural nodes. Oriented, ellipsoidal basis nodes optimised with CERN achieved significantly better accuracy with fewer nodes than spherical basis nodes optimised by k-means clustering. Multilayer perceptrons optimised by CERN were found to be as accurate as those trained by advanced gradient descent techniques. CERN was also found to be significantly more efficient than a conventional evolutionary algorithm that does not use a combinatorial search.

Journal Article↗

PubMed2001

Automatic determination of radial basis functions: an immunity-based approach.

The appropriate operation of a radial basis function (RBF) neural network depends mainly upon an adequate choice of the parameters of its basis functions. The simplest approach to train an RBF network is to assume fixed radial basis functions defining the activation of the hidden units. Once the RBF parameters are fixed, the optimal set of output weights can be determined straightforwardly by using a linear least squares algorithm, which generally means reduction in the learning time as compared to the determination of all RBF network parameters using supervised learning. The main drawback of this strategy is the requirement of an efficient algorithm to determine the number, position, and dispersion of the RBFs. The approach proposed here is inspired by models derived from the vertebrate immune system, that will be shown to perform unsupervised cluster analysis. The algorithm is introduced and its performance is compared to that of the random, k-means center selection procedures and other results from the literature. By automatically defining the number of RBF centers, their positions and dispersions, the proposed method leads to parsimonious solutions. Simulation results are reported concerning regression and classification problems.

Algorithms↗

PubMed2005

Hybrid hierarchical clustering with applications to microarray data.

In this paper, we propose a hybrid clustering method that combines the strengths of bottom-up hierarchical clustering with that of top-down clustering. The first method is good at identifying small clusters but not large ones; the strengths are reversed for the second method. The hybrid method is built on the new idea of a mutual cluster: a group of points closer to each other than to any other points. Theoretical connections between mutual clusters and bottom-up clustering methods are established, aiding in their interpretation and providing an algorithm for identification of mutual clusters. We illustrate the technique on simulated and real microarray datasets.

Algorithms↗

PubMed1999

Stability of the interface between neural tissue and chronically implanted intracortical microelectrodes.

The stability of the interface between neural tissue and chronically implanted microelectrodes is very important for obtaining reliable control signals for neuroprosthetic devices. Stability is also crucial for chronic microstimulation of the cerebral cortex. However, changes of the electrode-tissue interface can be caused by a variety of mechanisms. In the present study, intracortical microelectrode arrays were implanted into the pericruciate gyrus of cats and neural activities were recorded on a regular basis for several months. An algorithm based on cluster analysis and interspike interval analysis was developed to sort the extracellular action potentials into single units. We tracked these units based on their waveform and their response to somatic stimulation or stereotypical movements by the cats. Our results indicate that, after implantation, the electrode-tissue interface may change from day-to-day over the first 1-2 weeks, week-to-week for 1-2 months, and become quite stable thereafter. A stability index is proposed to quantify the stability of the electrode-tissue interface. The reasons for the pattern of changes are discussed.

Action Potentials↗

PubMed2005

Clustering ensembles: models of consensus and weak partitions.

Clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph-based, combinatorial, or statistical perspectives. This study extends previous research on clustering ensembles in several respects. First, we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem. Second, we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings. A combined partition is found as a solution to the corresponding maximum-likelihood problem using the EM algorithm. Third, we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition. Finally, we demonstrate the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits. A simple explanatory model is offered for the behavior of combinations of such weak clustering components. Combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions. We also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus. Experimental results demonstrate the effectiveness of the proposed methods on several real-world data sets.

Algorithms↗

PubMed1994

A neural network-based spike discriminator.

A software routine to reconstruct individual spike trains from multi-neuron, single-channel extracellular recordings was designed. Using a neural network algorithm that automatically clusters and sorts the spikes, the only user input needed is the threshold level for spike detection and the number of unit types present in the recording. Adaptive features are included in the algorithm to allow for tracking of spike trains during periods of amplitude variation and also to identify noise spikes. The routine will operate on-line during extracellular studies of the cochlear nucleus in cats.

Action Potentials↗

PubMed2006

Speech utterance clustering based on the maximization of within-cluster homogeneity of speaker voice characteristics.

This paper investigates the problem of how to partition unknown speech utterances into a set of clusters, such that each cluster consists of utterances from only one speaker, and the number of clusters reflects the unknown speaker population size. The proposed method begins by specifying a certain number of clusters, corresponding to one of the possible speaker population sizes, and then maximizes the level of overall within-cluster homogeneity of the speakers' voice characteristics. The within-cluster homogeneity is characterized by the likelihood probability that a cluster model, trained using all the utterances within a cluster, matches each of the within-cluster utterances. To attain the maximal sum of likelihood probabilities for all utterances, the proposed method applies a genetic algorithm to determine the cluster in which each utterance should be located. For greater computational efficiency, also proposed is a clustering criterion that approximates the likelihood probability with a divergence-based model similarity between a cluster and each of the within-cluster utterances. The clustering method then examines various legitimate numbers of clusters by adapting the Bayesian information criterion to determine the most likely speaker population size. The experimental results show the superiority of the proposed method over conventional methods based on hierarchical clustering.

Algorithms↗

PubMed1986

Discrete representation of perceptual structure underlying consonant confusions.

The perceptual representation of speech is generally assumed to be discrete rather than continuous, pointing to the need for general discrete analytic models to represent observed perceptual similarities among speech sounds. The INDCLUS (INdividual Differences CLUStering) model and algorithm [J.D. Carroll and P. Arabie, Psychometrika 48, 157-169 (1983)] can provide this generality, representing symmetric three-way similarity data (stimuli X stimuli X conditions) as an additive combination of overlapping, and generally not hierarchial, clusters whose weights (which are numerical values gauging the importance of the clusters) vary both as a function of the cluster and condition being considered. INDCLUS was used to obtain a discrete representation of underlying perceptual structure in the Miller and Nicely consonant confusion data [G.A. Miller and P.E. Nicely, J. Acoust. Soc. Am. 27, 338-352 (1955)]. A 14-cluster solution accounted for 82.9% of total variance across the 17 listening conditions. The cluster composition and the variations in cluster weights as a function of stimulus degradation were interpreted in terms of the common and unique perceptual attributes of the consonants within each cluster. Low-pass filtering and noise masking selectively degraded unique attributes, especially the cues for place of articulation, while high-pass filtering degraded both unique and common attributes. The clustering results revealed that perceptual similarities among consonants are accurately modeled by additive combinations of their specific and discrete acoustic attributes whose weights are determined by the nature of the stimulus degradation.

Attention↗