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PubMed1998

Forecasting generalized epileptic seizures from the EEG signal by wavelet analysis and dynamic unsupervised fuzzy clustering.

Dynamic state recognition and event-prediction are fundamental tasks in biomedical signal processing. We present a new, electroencephalogram (EEG)-based, brain-state identification method which could form the basis for forecasting a generalized epileptic seizure. The method relies on the existence in the EEG of a preseizure state, with extractable unique features, a priori undefined. We exposed 25 rats to hyperbaric oxygen until the appearance of a generalized EEG seizure. EEG segments from the preexposure, early exposure, and the period up to and including the seizure were processed by the fast wavelet transform. Features extracted from the wavelet coefficients were imputed to the unsupervised optimal fuzzy clustering (UOFC) algorithm. The UOFC is useful for classifying similar discontinuous temporal patterns in the semistationary EEG to a set of clusters which may represent brain-states. The unsupervised selection of the number of cluster overcomes the a priori unknown and variable number of states. The usually vague brain state transitions are naturally treated by assigning each temporal pattern to one or more fuzzy clusters. The classification succeeded in identifying several, behavior-backed, EEG states such as sleep, resting, alert and active wakefulness, as well as the seizure. In 16 instances a preseizure state, lasting between 0.7 and 4 min was defined. Considerable individual variability in the number and characteristics of the clusters may postpone the realization of an early universal epilepsy warning. University may not be crucial if using a dynamic version of the UOFC which has been taught the individual's normal vocabulary of EEG states and can be expected to detect unspecified new states.

Algorithms↗

PubMed2005

Cluster analysis and association study of structured multilocus genotype data.

We propose an algorithm for testing association using structured multilocus genotype data. The algorithm implements the clustering of the data by a hierarchical clustering technique and a k-means algorithm. After clustering, the program analyzes all the clusters together using the Mantel-Haenszel (MH) test, by which common associations in the clusters are examined. To use the MH test, the number of subpopulations has to be determined. A method of cross-validation (CV) and the k-means algorithm are applied for estimating the number of subpopulations. The algorithm described was implemented in the computer program POPSTRUCT. In the simulation study, we found that when the two groups with different marker allele frequencies were combined, an inflation of the type I errors was observed. The inflation was more marked when the differences in the marker allele frequencies were larger, the difference in the minor allele frequencies at the disease locus was larger, and the genotype relative risk associated with the disease locus was higher. Our simulation study indicated that the MH test was efficient for decreasing type I errors and increasing the power compared with any test performed on each cluster. Then, we compared the results of STRUCTURE, a model-based method, and POPSTRUCT, a distance-based method. When two subgroups with different allele frequencies were mixed together at a high fixed ratio, POPSTRUCT was superior to STRUCTURE in classifying the combined population into the accurate clusters, each of which reflects one of the original groups.

Algorithms↗

PubMed1981

Illness behaviour profiles in chronic pain: the Auckland experience.

Two hundred patients with chronic pain, presenting to the Auckland Hospital Pain Clinic, completed the illness behaviour questionnaire (IBQ) developed by Pilowsky and Spence in Adelaide. These authors have identified 6 taxonomic clusters from a numerical analysis of illness behaviour profiles and have described the characteristics of these groups of patients. This study reports the results of a similar analysis of IBQ scores taken from a larger group of patients and clustered using a variant of the K-means algorithm. Ten clusters were derived. These are described and compared with the groups described by Pilowsky and Spence. Both samples have closely similar illness behaviour profiles. Comparisons of the clusters reveal more similarities than differences and we conclude that this independent replication of the Pilowsky and Spence study enhances the validity of the IBQ and the clusters described.

Adult↗

PubMed1992

Identification of homogeneous geographical areas of mortality for tumours from cluster analysis.

This paper attempts to demonstrate the utility of cluster analysis as a descriptive method of studying mortality in epidemiology. In order to verify which algorithms of clustering best fit the data structure, the method of cophenetic correlation was implemented. Furthermore the probabilistic algorithm proposed by Beale was used to assess the partition. The results show the presence of some striking clusters between Local Sanitary Units of the Emilia Romagna Region for four types of tumour in men.

Algorithms↗

PubMed2004

An integrated tool for microarray data clustering and cluster validity assessment.

UNLABELLED: In this paper we present a data mining system, which allows the application of different clustering and cluster validity algorithms for DNA microarray data. This tool may improve the quality of the data analysis results, and may support the prediction of the number of relevant clusters in the microarray datasets. This systematic evaluation approach may significantly aid genome expression analyses for knowledge discovery applications. The developed software system may be effectively used for clustering and validating not only DNA microarray expression analysis applications but also other biomedical and physical data with no limitations. AVAILABILITY: The program is freely available for non-profit use on request at http://www.cs.tcd.ie/Nadia.Bolshakova/Machaon.html CONTACT: Nadia.Bolshakova@cs.tcd.ie.

Algorithms↗

PubMed2006

Privacy protection versus cluster detection in spatial epidemiology.

OBJECTIVES: Patient data that includes precise locations can reveal patients' identities, whereas data aggregated into administrative regions may preserve privacy and confidentiality. We investigated the effect of varying degrees of address precision (exact latitude and longitude vs the center points of zip code or census tracts) on detection of spatial clusters of cases. METHODS: We simulated disease outbreaks by adding supplementary spatially clustered emergency department visits to authentic hospital emergency department syndromic surveillance data. We identified clusters with a spatial scan statistic and evaluated detection rate and accuracy. RESULTS: More clusters were identified, and clusters were more accurately detected, when exact locations were used. That is, these clusters contained at least half of the simulated points and involved few additional emergency department visits. These results were especially apparent when the synthetic clustered points crossed administrative boundaries and fell into multiple zip code or census tracts. CONCLUSIONS: The spatial cluster detection algorithm performed better when addresses were analyzed as exact locations than when they were analyzed as center points of zip code or census tracts, particularly when the clustered points crossed administrative boundaries. Use of precise addresses offers improved performance, but this practice must be weighed against privacy concerns in the establishment of public health data exchange policies.

Algorithms↗

PubMed1997

Geographical clustering of mortality from systemic sclerosis in the Southeastern United States, 1981-90.

OBJECTIVE: To determine whether elevated rates of mortality from systemic sclerosis (SSc) in the Southeastern United States result from local, multicounty clusters of the disease. METHODS: Detection of spatial clusters of SSc mortality by applying the method of Kulldorff and Nagarwalla to death certificate data from 955 counties in 12 southeastern states. RESULTS: From 1981 to 1990, significant excess mortality from SSc in the Southeastern US occurred among white males [standardized mortality ratio (SMR) = 1.2; p = 0.0004] and black males (SMR = 1.2; p = 0.04), but not among white females (SMR = 0.98; p = 0.55) or black females (SMR = 1.1; p = 0.06). When the cluster detection algorithm was applied to data for white males, 3 significant clusters were identified. The primary cluster (p = 0.001) was centered around Coffee, Tennessee. Two smaller clusters overlapped the primary cluster -- one centered at Calhoun, Alabama, (p = 0.008) and another centered at Chattooga, Georgia, (p = 0.04). Analysis of data for black males resulted in a single significant cluster (p = 0.02) centered at Northampton, North Carolina. When data for white or black females were analyzed, no clusters reached statistical significance. In combination, excess SSc mortality in the detected clusters accounted for 79.0 and 66.2%, respectively, of the excess deaths among white and black males across the whole Southeast. CONCLUSION: Elevation of SSc mortality rates in the Southeastern US results from local clusters of concentrated mortality. These clusters may be artifacts of regional variation in death certificate quality. If not, distinctive environmental factors in these areas may provide new insights into the etiology of SSc.

Adolescent↗

PubMed2005

A novel kernel method for clustering.

Kernel Methods are algorithms that, by replacing the inner product with an appropriate positive definite function, implicitly perform a nonlinear mapping of the input data into a high-dimensional feature space. In this paper, we present a kernel method for clustering inspired by the classical K-Means algorithm in which each cluster is iteratively refined using a one-class Support Vector Machine. Our method, which can be easily implemented, compares favorably with respect to popular clustering algorithms, like K-Means, Neural Gas, and Self-Organizing Maps, on a synthetic data set and three UCI real data benchmarks (IRIS data, Wisconsin breast cancer database, Spam database).

Algorithms↗

PubMed2006

Spectral analysis of two-signed microarray expression data.

We give a simple and informative derivation of a spectral algorithm for clustering and reordering complementary DNA microarray expression data. Here, expression levels of a set of genes are recorded simultaneously across a number of samples, with a positive weight reflecting up-regulation and a negative weight reflecting down-regulation. We give theoretical support for the algorithm based on a biologically justified hypothesis about the structure of the data, and illustrate its use on public domain data in the context of unsupervised tumour classification. The algorithm is derived by considering a discrete optimization problem and then relaxing to the continuous realm. We prove that in the case where the data have an inherent 'checkerboard' sign pattern, the algorithm will automatically reveal that pattern. Further, our derivation shows that the algorithm may be regarded as imposing a random graph model on the expression levels and then clustering from a maximum likelihood perspective. This indicates that the output will be tolerant to perturbations and will reveal 'near-checkerboard' patterns when these are present in the data. It is interesting to note that the checkerboard structure is revealed by the first (dominant) singular vectors--previous work on spectral methods has focussed on the case of nonnegative edge weights, where only the second and higher singular vectors are relevant. We illustrate the algorithm on real and synthetic data, and then use it in a tumour classification context on three different cancer data sets. Our results show that respecting the two-signed nature of the data (thereby distinguishing between up-regulation and down-regulation) reveals structures that cannot be gleaned from the absolute value data (where up- and down-regulation are both regarded as 'changes').

Algorithms↗

PubMed1996

Feature extraction and clustering of EEG epileptic spikes.

This paper treats algorithms for feature extraction and clustering of multichannel EEG transients occurring in epilepsy, so called spikes. Hermite functions with a variable width parameter is used as features. We study nonlinear optimization of a series expansion for multichannel spikes. For the clustering problem, the nearest mean (NM) algorithm, generalized to matrix features, is used. The number of classes is assumed to be known a priori. The series expansion gives good signal description while reducing information. A simulation to estimate the space resolution capability of the algorithms indicates that perfect clustering requires approximately one head radius distance between the dipoles, which each generate one cluster. The NM algorithm was used to cluster two sets of clinically recorded spikes, and the clustering was compared to the manual clustering obtained by a neurophysiologist. For both spike sets evaluated, the clusters obtained by the algorithms had high accordance with the result of the neurophysiologist.

Algorithms↗

PubMed2002

High similarity sequence comparison in clustering large sequence databases.

We present a fast algorithm for sequence clustering and searching which works with large sequence databases. It uses a strictly defined similarity measure. The algorithm is faster than conventional EST clustering approaches because its complexity is directly related to the number of subwords shared by the sequences. Furthermore, the algorithm also works with proteic sequences and large sequences like entire chromosomes. We present a theoretical study of our approach and provide experimental results.

Algorithms↗

PubMed2005

Finding instabilities in the community structure of complex networks.

The problem of finding clusters in complex networks has been studied by mathematicians, computer scientists, and, more recently, by physicists. Many of the existing algorithms partition a network into clear clusters without overlap. Here we introduce a method to identify the nodes lying "between clusters," allowing for a general measure of the stability of the clusters. This is done by adding noise over the edge weights. Our method can in principle be used with almost any clustering algorithm able to deal with weighted networks. We present several applications on real-world networks using two different clustering algorithms.

Journal Article↗

PubMed2005

An algebraic geometry approach to protein structure determination from NMR data.

Our paper describes the first provably-efficient algorithm for determining protein structures de novo, solely from experimental data. We show how the global nature of a certain kind of NMR data provides quantifiable complexity-theoretic benefits, allowing us to classify our algorithm as running in polynomial time. While our algorithm uses NMR data as input, it is the first polynomial-time algorithm to compute high-resolution structures de novo using any experimentally-recorded data, from either NMR spectroscopy or X-Ray crystallography. Improved algorithms for protein structure determination are needed, because currently, the process is expensive and time-consuming. For example, an area of intense research in NMR methodology is automated assignment of nuclear Overhauser effect (NOE) restraints, in which structure determination sits in a tight inner-loop (cycle) of assignment/refinement. These algorithms are very time-consuming, and typically require a large cluster. Thus, algorithms for protein structure determination that are known to run in polynomial time and provide guarantees on solution accuracy are likely to have great impact in the long-term. Methods stemming from a technique called "distance geometry embedding" do come with provable guarantees, but the NP-hardness of these problem formulations implies that in the worst case these techniques cannot run in polynomial time. We are able to avoid the NP-hardness by (a) some mild assumptions about the protein being studied, (b) the use of residual dipolar couplings (RDCs) instead of a dense network of NOEs, and (c) novel algorithms and proofs that exploit the biophysical geometry of (a) and (b), drawing on a variety of computer science, computational geometry, and computational algebra techniques. In our algorithm, RDC data, which gives global restraints on the orientation of internuclear bond vectors, is used in conjunction with very sparse NOE data to obtain a polynomial-time algorithm for protein structure determination. An implementation of our algorithm has been applied to 6 different real biological NMR data sets recorded for 3 proteins. Our algorithm is combinatorially precise, polynomial-time, and uses much less NMR data to produce results that are as good or better than previous approaches in terms of accuracy of the computed structure as well as running time. In practice approaches such as restrained molecular dynamics and simulated annealing, which lack both combinatorial precision and guarantees on running time and solution quality, are commonly used. Our results show that by using a different "slice" of the data, an algorithm that is polynomial time and that has guarantees about solution quality can be obtained. We believe that our techniques can be extended and generalized for other structure-determination problems such as computing side-chain conformations and the structure of nucleic acids from experimental data.

Algorithms↗

PubMed2006

A traveling salesman approach for predicting protein functions.

BACKGROUND: Protein-protein interaction information can be used to predict unknown protein functions and to help study biological pathways. RESULTS: Here we present a new approach utilizing the classic Traveling Salesman Problem to study the protein-protein interactions and to predict protein functions in budding yeast Saccharomyces cerevisiae. We apply the global optimization tool from combinatorial optimization algorithms to cluster the yeast proteins based on the global protein interaction information. We then use this clustering information to help us predict protein functions. We use our algorithm together with the direct neighbor algorithm 1 on characterized proteins and compare the prediction accuracy of the two methods. We show our algorithm can produce better predictions than the direct neighbor algorithm, which only considers the immediate neighbors of the query protein. CONCLUSION: Our method is a promising one to be used as a general tool to predict functions of uncharacterized proteins and a successful sample of using computer science knowledge and algorithms to study biological problems.

Journal Article↗

PubMed2003

Structural optimization of model colloidal clusters at the air-water interface using genetic algorithms.

The structure of colloidal clusters observed at the air-water interface is studied theoretically in this paper using a recently developed global optimization routine based on a genetic algorithm. A model potential with a secondary minimum produced from the attractive van der Waals interaction and repulsive dipolar interaction is used for the colloid-colloid interaction. The structures predicted from the genetic algorithm are not always consistent with the experimental observations; the theoretical results predict the growth of cluster as a spreading of triangular networks, however, the experimental observations seem to suggest the formation of a circular shell structure. More thorough theoretical as well as experimental studies are called for in order to obtain more conclusive evidence regarding these matters.

Air↗

PubMed2006

Inspiratory flow shape clustering: an automated method to monitor upper airway performance during sleep.

We describe an automated method for monitoring airflow dynamics in the upper airway of a sleeping subject. Its main task is to determine a set of inspiratory flow shape representatives and their relative incidence in a given respiratory airflow material. The flow shape clustering aims at reducing redundant information in the data, and thereby decreases the time needed to score overnight sleep recordings. Compared with previous computer-assisted systems, built on a pre-defined classification of prototype shapes, we require no a priori assumptions of the flow shape clusters to be discovered. The intrinsic flow shape clustering is performed with a modification of the Isodata algorithm, and the K-means clustering is used as a reference in comparison studies. The operation of the method is demonstrated on clinical sleep recordings both from patients with nocturnal breathing disorders and from non-symptomatic individuals. The feasible results obtained in the practical research design suggest that application of clustering algorithms to respiratory airflow measurements could give important insights into the subtle flow shape abnormalities underlying obstructive sleep-disordered breathing.

Algorithms↗

PubMed2005

Reproducible clusters from microarray research: whither?

MOTIVATION: In cluster analysis, the validity of specific solutions, algorithms, and procedures present significant challenges because there is no null hypothesis to test and no 'right answer'. It has been noted that a replicable classification is not necessarily a useful one, but a useful one that characterizes some aspect of the population must be replicable. By replicable we mean reproducible across multiple samplings from the same population. Methodologists have suggested that the validity of clustering methods should be based on classifications that yield reproducible findings beyond chance levels. We used this approach to determine the performance of commonly used clustering algorithms and the degree of replicability achieved using several microarray datasets. METHODS: We considered four commonly used iterative partitioning algorithms (Self Organizing Maps (SOM), K-means, Clutsering LARge Applications (CLARA), and Fuzzy C-means) and evaluated their performances on 37 microarray datasets, with sample sizes ranging from 12 to 172. We assessed reproducibility of the clustering algorithm by measuring the strength of relationship between clustering outputs of subsamples of 37 datasets. Cluster stability was quantified using Cramer's v2 from a kXk table. Cramer's v2 is equivalent to the squared canonical correlation coefficient between two sets of nominal variables. Potential scores range from 0 to 1, with 1 denoting perfect reproducibility. RESULTS: All four clustering routines show increased stability with larger sample sizes. K-means and SOM showed a gradual increase in stability with increasing sample size. CLARA and Fuzzy C-means, however, yielded low stability scores until sample sizes approached 30 and then gradually increased thereafter. Average stability never exceeded 0.55 for the four clustering routines, even at a sample size of 50. These findings suggest several plausible scenarios: (1) microarray datasets lack natural clustering structure thereby producing low stability scores on all four methods; (2) the algorithms studied do not produce reliable results and/or (3) sample sizes typically used in microarray research may be too small to support derivation of reliable clustering results. Further research should be directed towards evaluating stability performances of more clustering algorithms on more datasets specially having larger sample sizes with larger numbers of clusters considered.

Cluster Analysis↗

PubMed2003

Bulk and surface critical behavior of the three-dimensional Ising model and conformal invariance.

Using a continuous cluster Monte Carlo algorithm, we investigate the critical three-dimensional Ising model in its anisotropic limit. From the ratio of the magnetic correlations in the strong- and the weak-coupling directions, we determine the length ratio relating the isotropic Ising model and the anisotropic limit. On this basis, we simulate the critical Ising model on a spherocylinder S2 x R1, i.e., a curved geometry obtained from a conformal mapping of the infinite space R3. From correlation lengths along the spherocylinder, combined with the prediction of conformal invariance, we estimate the magnetic and thermal scaling dimensions as X(h)=0.5182(6) and X(t)=1.419(7), respectively. The behavior of the Binder cumulant is also determined in the limit of an infinitely long spherocylinder. Next, free boundary conditions are imposed on the equators of the spherocylinder, and thus the geometry S1 x S+ x R1 is obtained. The surface magnetic scaling dimension is estimated as X(s)(h)=1.263(5). The consistency of the aforementioned estimations and existing results confirms that the three-dimensional Ising model is conformally invariant. Further, the precision of these results reveals that, as in two dimensions, conformal mappings provide a powerful tool to investigate critical phenomena. With the continuous cluster algorithm, we also perform simulations of systems inside a conventional solid cylinder. The surface magnetic correlation length differs, within the estimated error margin, by a factor pi/2 from that along a half spherocylinder S1 x S+ x R1 with the same radius.

Journal Article↗