SMART: Unique Splitting-While-Merging Framework for Gene Clustering

Successful clustering algorithms are highly dependent on parameter settings. The clustering performance degrades significantly unless parameters are properly set, and yet, it is difficult to set these parameters a priori. To address this issue, in this paper, we propose a unique splitting-while-merging clustering framework, named “splitting merging awareness tactics” (SMART), which does not require any a priori knowledge of either the number of clusters or even the possible range of this number. Unlike existing self-splitting algorithms, which over-cluster the dataset to a large number of clusters and then merge some similar clusters, our framework has the ability to split and merge clusters automatically during the process and produces the the most reliable clustering results, by intrinsically integrating many clustering techniques and tasks. The SMART framework is implemented with two distinct clustering paradigms in two algorithms: competitive learning and finite mixture model. Nevertheless, within the proposed SMART framework, many other algorithms can be derived for different clustering paradigms. The minimum message length algorithm is integrated into the framework as the clustering selection criterion. The usefulness of the SMART framework and its algorithms is tested in demonstration datasets and simulated gene expression datasets. Moreover, two real microarray gene expression datasets are studied using this approach. Based on the performance of many metrics, all numerical results show that SMART is superior to compared existing self-splitting algorithms and traditional algorithms. Three main properties of the proposed SMART framework are summarized as: (1) needing no parameters dependent on the respective dataset or a priori knowledge about the datasets, (2) extendible to many different applications, (3) offering superior performance compared with counterpart algorithms.     

Reducing the Time Requirement of k-Means Algorithm

Traditional k-means and most k-means variants are still computationally expensive for large datasets, such as microarray data, which have large datasets with large dimension size d. In k-means clustering, we are given a set of n data points in d-dimensional space R^d and an integer k. The problem is to determine a set of k points in R^d, called centers, so as to minimize the mean squared distance from each data point to its nearest center. In this work, we develop a novel k-means algorithm, which is simple but more efficient than the traditional k-means and the recent enhanced k-means. Our new algorithm is based on the recently established relationship between principal component analysis and the k-means clustering. We provided the correctness proof for this algorithm. Results obtained from testing the algorithm on three biological data and six non-biological data (three of these data are real, while the other three are simulated) also indicate that our algorithm is empirically faster than other known k-means algorithms. We assessed the quality of our algorithm clusters against the clusters of a known structure using the Hubert-Arabie Adjusted Rand index (ARI_HA). We found that when k is close to d, the quality is good (ARI_HA>0.8) and when k is not close to d, the quality of our new k-means algorithm is excellent (ARI_HA>0.9). In this paper, emphases are on the reduction of the time requirement of the k-means algorithm and its application to microarray data due to the desire to create a tool for clustering and malaria research. However, the new clustering algorithm can be used for other clustering needs as long as an appropriate measure of distance between the centroids and the members is used. This has been demonstrated in this work on six non-biological data.     

Efficient Record Linkage Algorithms Using Complete Linkage Clustering

Data from different agencies share data of the same individuals. Linking these datasets to identify all the records belonging to the same individuals is a crucial and challenging problem, especially given the large volumes of data. A large number of available algorithms for record linkage are prone to either time inefficiency or low-accuracy in finding matches and non-matches among the records. In this paper we propose efficient as well as reliable sequential and parallel algorithms for the record linkage problem employing hierarchical clustering methods. We employ complete linkage hierarchical clustering algorithms to address this problem. In addition to hierarchical clustering, we also use two other techniques: elimination of duplicate records and blocking. Our algorithms use sorting as a sub-routine to identify identical copies of records. We have tested our algorithms on datasets with millions of synthetic records. Experimental results show that our algorithms achieve nearly 100% accuracy. Parallel implementations achieve almost linear speedups. Time complexities of these algorithms do not exceed those of previous best-known algorithms. Our proposed algorithms outperform previous best-known algorithms in terms of accuracy consuming reasonable run times.     

Misty Mountain clustering: application to fast unsupervised flow cytometry gating

Background  

There are many important clustering questions in computational biology for which no satisfactory method exists. Automated clustering algorithms, when applied to large, multidimensional datasets, such as flow cytometry data, prove unsatisfactory in terms of speed, problems with local minima or cluster shape bias. Model-based approaches are restricted by the assumptions of the fitting functions. Furthermore, model based clustering requires serial clustering for all cluster numbers within a user defined interval. The final cluster number is then selected by various criteria. These supervised serial clustering methods are time consuming and frequently different criteria result in different optimal cluster numbers. Various unsupervised heuristic approaches that have been developed such as affinity propagation are too expensive to be applied to datasets on the order of 10⁶ points that are often generated by high throughput experiments.     

SHIPS: Spectral Hierarchical Clustering for the Inference of Population Structure in Genetic Studies

Inferring the structure of populations has many applications for genetic research. In addition to providing information for evolutionary studies, it can be used to account for the bias induced by population stratification in association studies. To this end, many algorithms have been proposed to cluster individuals into genetically homogeneous sub-populations. The parametric algorithms, such as Structure, are very popular but their underlying complexity and their high computational cost led to the development of faster parametric alternatives such as Admixture. Alternatives to these methods are the non-parametric approaches. Among this category, AWclust has proven efficient but fails to properly identify population structure for complex datasets. We present in this article a new clustering algorithm called Spectral Hierarchical clustering for the Inference of Population Structure (SHIPS), based on a divisive hierarchical clustering strategy, allowing a progressive investigation of population structure. This method takes genetic data as input to cluster individuals into homogeneous sub-populations and with the use of the gap statistic estimates the optimal number of such sub-populations. SHIPS was applied to a set of simulated discrete and admixed datasets and to real SNP datasets, that are data from the HapMap and Pan-Asian SNP consortium. The programs Structure, Admixture, AWclust and PCAclust were also investigated in a comparison study. SHIPS and the parametric approach Structure were the most accurate when applied to simulated datasets both in terms of individual assignments and estimation of the correct number of clusters. The analysis of the results on the real datasets highlighted that the clusterings of SHIPS were the more consistent with the population labels or those produced by the Admixture program. The performances of SHIPS when applied to SNP data, along with its relatively low computational cost and its ease of use make this method a promising solution to infer fine-scale genetic patterns.     

Cross-Clustering: A Partial Clustering Algorithm with Automatic Estimation of the Number of Clusters

Four of the most common limitations of the many available clustering methods are: i) the lack of a proper strategy to deal with outliers; ii) the need for a good a priori estimate of the number of clusters to obtain reasonable results; iii) the lack of a method able to detect when partitioning of a specific data set is not appropriate; and iv) the dependence of the result on the initialization. Here we propose Cross-clustering (CC), a partial clustering algorithm that overcomes these four limitations by combining the principles of two well established hierarchical clustering algorithms: Ward’s minimum variance and Complete-linkage. We validated CC by comparing it with a number of existing clustering methods, including Ward’s and Complete-linkage. We show on both simulated and real datasets, that CC performs better than the other methods in terms of: the identification of the correct number of clusters, the identification of outliers, and the determination of real cluster memberships. We used CC to cluster samples in order to identify disease subtypes, and on gene profiles, in order to determine groups of genes with the same behavior. Results obtained on a non-biological dataset show that the method is general enough to be successfully used in such diverse applications. The algorithm has been implemented in the statistical language R and is freely available from the CRAN contributed packages repository.     

A New-Fangled FES-k-Means Clustering Algorithm for Disease Discovery and Visual Analytics

The central purpose of this study is to further evaluate the quality of the performance of a new algorithm. The study provides additional evidence on this algorithm that was designed to increase the overall efficiency of the original k-means clustering technique—the Fast, Efficient, and Scalable k-means algorithm (FES-k-means). The FES-k-means algorithm uses a hybrid approach that comprises the k-d tree data structure that enhances the nearest neighbor query, the original k-means algorithm, and an adaptation rate proposed by Mashor. This algorithm was tested using two real datasets and one synthetic dataset. It was employed twice on all three datasets: once on data trained by the innovative MIL-SOM method and then on the actual untrained data in order to evaluate its competence. This two-step approach of data training prior to clustering provides a solid foundation for knowledge discovery and data mining, otherwise unclaimed by clustering methods alone. The benefits of this method are that it produces clusters similar to the original k-means method at a much faster rate as shown by runtime comparison data; and it provides efficient analysis of large geospatial data with implications for disease mechanism discovery. From a disease mechanism discovery perspective, it is hypothesized that the linear-like pattern of elevated blood lead levels discovered in the city of Chicago may be spatially linked to the city''s water service lines.     

Benchmarking the Clustering Performances of Evolutionary Algorithms: A Case Study on Varying Data Size

Background and objectiveClustering is a widely used popular method for data analysis within many clustering algorithms for years. Today it is used in many predictions, collaborative filtering and automatic segmentation systems on different domains. Also, to be broadly used in practice, such clustering algorithms need to give both better performance and robustness when compared to the ones currently used. In recent years, evolutionary algorithms are used in many domains since they are robust and easy to implement. And many clustering problems can be easily solved with such algorithms if the problem is modeled as an optimization problem. In this paper, we present an optimization approach for clustering by using four well-known evolutionary algorithms which are Biogeography-Based Optimization (BBO), Grey Wolf Optimization (GWO), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO).Methodthe objective function has been specified to minimize the total distance from cluster centers to the data points. Euclidean distance is used for distance calculation. We have applied this objective function to the given algorithms both to find the most efficient clustering algorithm and to compare the clustering performances of algorithms against different data sizes. In order to benchmark the clustering performances of algorithms in the experiments, we have used a number of datasets with different data sizes such as some small scale, medium and big data. The clustering performances have been compared to K-means as it is a widely used clustering algorithm for years in literature. Rand Index, Adjusted Rand Index, Mirkin's Index and Hubert's Index have been considered as parameters for evaluating the clustering performances.ResultAs a result of the clustering experiments of algorithms over different datasets with varying data sizes according to the specified performance criteria, GA and GWO algorithms show better clustering performances among the others.ConclusionsThe results of the study showed that although the algorithms have shown satisfactory clustering results on small and medium scale datasets, the clustering performances on Big data need to be improved.     

Low scaling of a life history variable: Analysing eutherian gestation periods with and without phylogeny-informed statistics

Traditionally, biological times (gestation period, longevity) are proposed to scale to body mass M as M^0.25. Although phylogeny-informed statistics have become widespread, it is still sometimes assumed that in datasets comprising a very large number of species, analyses that do not and that do account for phylogeny will yield similar results. Here we show, in a large dataset on gestation period length in eutherian mammals (1214 species from 20 orders), that the allometric scaling exponent is about twice as high using conventional statistics (ordinary least squares OLS, M^0.18–0.20) as when using phylogenetic generalised least squares (PGLS, M^0.07–0.10), indicating that among closely related taxa, the scaling of gestation is much lower than generally assumed. This matches the well-known absence of scaling among different-sized breeds of domestic animal species, and indicates that changes in M must be more related to changes in development speed rather than development time among closely related species, which has implications for interpreting life history-consequences of insular dwarfism and gigantism. Only when allowing just one species per order (simulated in 100 randomised datasets of n = 20 species across 20 orders) is 0.25 included in the scaling exponent confidence interval in both OLS and PGLS. Differences in scaling at different taxonomic levels in comparative datasets may indicate evolutionary trends where successive taxonomic groups compete by fundamental variation in organismal design not directly linked to changes in M. Allometries then do not necessarily represent universal scaling rules, but snapshots of evolutionary time that depend on diversification and extinction events before the picture was taken. It is either by analysing subsets separately, or by using PGLS in large datasets, that the underlying relationships with M can then be unveiled.     

Analysis of Whole-Brain Resting-State fMRI Data Using Hierarchical Clustering Approach

Background

Previous studies using hierarchical clustering approach to analyze resting-state fMRI data were limited to a few slices or regions-of-interest (ROIs) after substantial data reduction.

Purpose

To develop a framework that can perform voxel-wise hierarchical clustering of whole-brain resting-state fMRI data from a group of subjects.

Materials and Methods

Resting-state fMRI measurements were conducted for 86 adult subjects using a single-shot echo-planar imaging (EPI) technique. After pre-processing and co-registration to a standard template, pair-wise cross-correlation coefficients (CC) were calculated for all voxels inside the brain and translated into absolute Pearson''s distances after imposing a threshold CC≥0.3. The group averages of the Pearson''s distances were then used to perform hierarchical clustering with the developed framework, which entails gray matter masking and an iterative scheme to analyze the dendrogram.

Results

With the hierarchical clustering framework, we identified most of the functional connectivity networks reported previously in the literature, such as the motor, sensory, visual, memory, and the default-mode functional networks (DMN). Furthermore, the DMN and visual system were split into their corresponding hierarchical sub-networks.

Conclusion

It is feasible to use the proposed hierarchical clustering scheme for voxel-wise analysis of whole-brain resting-state fMRI data. The hierarchical clustering result not only confirmed generally the finding in functional connectivity networks identified previously using other data processing techniques, such as ICA, but also revealed directly the hierarchical structure within the functional connectivity networks.     

cola: an R/Bioconductor package for consensus partitioning through a general framework

Classification of high-throughput genomic data is a powerful method to assign samples to subgroups with specific molecular profiles. Consensus partitioning is the most widely applied approach to reveal subgroups by summarizing a consensus classification from a list of individual classifications generated by repeatedly executing clustering on random subsets of the data. It is able to evaluate the stability of the classification. We implemented a new R/Bioconductor package, cola, that provides a general framework for consensus partitioning. With cola, various parameters and methods can be user-defined and easily integrated into different steps of an analysis, e.g., feature selection, sample classification or defining signatures. cola provides a new method named ATC (ability to correlate to other rows) to extract features and recommends spherical k-means clustering (skmeans) for subgroup classification. We show that ATC and skmeans have better performance than other commonly used methods by a comprehensive benchmark on public datasets. We also benchmark key parameters in the consensus partitioning procedure, which helps users to select optimal parameter values. Moreover, cola provides rich functionalities to apply multiple partitioning methods in parallel and directly compare their results, as well as rich visualizations. cola can automate the complete analysis and generates a comprehensive HTML report.     

Link Clustering with Extended Link Similarity and EQ Evaluation Division

Link Clustering (LC) is a relatively new method for detecting overlapping communities in networks. The basic principle of LC is to derive a transform matrix whose elements are composed of the link similarity of neighbor links based on the Jaccard distance calculation; then it applies hierarchical clustering to the transform matrix and uses a measure of partition density on the resulting dendrogram to determine the cut level for best community detection. However, the original link clustering method does not consider the link similarity of non-neighbor links, and the partition density tends to divide the communities into many small communities. In this paper, an Extended Link Clustering method (ELC) for overlapping community detection is proposed. The improved method employs a new link similarity, Extended Link Similarity (ELS), to produce a denser transform matrix, and uses the maximum value of EQ (an extended measure of quality of modularity) as a means to optimally cut the dendrogram for better partitioning of the original network space. Since ELS uses more link information, the resulting transform matrix provides a superior basis for clustering and analysis. Further, using the EQ value to find the best level for the hierarchical clustering dendrogram division, we obtain communities that are more sensible and reasonable than the ones obtained by the partition density evaluation. Experimentation on five real-world networks and artificially-generated networks shows that the ELC method achieves higher EQ and In-group Proportion (IGP) values. Additionally, communities are more realistic than those generated by either of the original LC method or the classical CPM method.     

A Bayesian Alternative to Mutual Information for the Hierarchical Clustering of Dependent Random Variables

The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC) raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bayesian model comparison. We found that the Bayesian formulation naturally shrinks the empirical covariance matrix towards a matrix set a priori (e.g., the identity), provides an automated stopping rule, and corrects for dimensionality using a term that scales up the measure as a function of the dimensionality of the variables. Also, the resulting log Bayes factor is asymptotically proportional to the plug-in estimate of mutual information, with an additive correction for dimensionality in agreement with the Bayesian information criterion. We investigated the behavior of these Bayesian alternatives (in exact and asymptotic forms) to mutual information on simulated and real data. An encouraging result was first derived on simulations: the hierarchical clustering based on the log Bayes factor outperformed off-the-shelf clustering techniques as well as raw and normalized mutual information in terms of classification accuracy. On a toy example, we found that the Bayesian approaches led to results that were similar to those of mutual information clustering techniques, with the advantage of an automated thresholding. On real functional magnetic resonance imaging (fMRI) datasets measuring brain activity, it identified clusters consistent with the established outcome of standard procedures. On this application, normalized mutual information had a highly atypical behavior, in the sense that it systematically favored very large clusters. These initial experiments suggest that the proposed Bayesian alternatives to mutual information are a useful new tool for hierarchical clustering.     

Bayesian Hierarchical Clustering for Studying Cancer Gene Expression Data with Unknown Statistics

Clustering analysis is an important tool in studying gene expression data. The Bayesian hierarchical clustering (BHC) algorithm can automatically infer the number of clusters and uses Bayesian model selection to improve clustering quality. In this paper, we present an extension of the BHC algorithm. Our Gaussian BHC (GBHC) algorithm represents data as a mixture of Gaussian distributions. It uses normal-gamma distribution as a conjugate prior on the mean and precision of each of the Gaussian components. We tested GBHC over 11 cancer and 3 synthetic datasets. The results on cancer datasets show that in sample clustering, GBHC on average produces a clustering partition that is more concordant with the ground truth than those obtained from other commonly used algorithms. Furthermore, GBHC frequently infers the number of clusters that is often close to the ground truth. In gene clustering, GBHC also produces a clustering partition that is more biologically plausible than several other state-of-the-art methods. This suggests GBHC as an alternative tool for studying gene expression data.The implementation of GBHC is available at https://sites.google.com/site/gaussianbhc/     

Improved Gravitation Field Algorithm and Its Application in Hierarchical Clustering

Background

Gravitation field algorithm (GFA) is a new optimization algorithm which is based on an imitation of natural phenomena. GFA can do well both for searching global minimum and multi-minima in computational biology. But GFA needs to be improved for increasing efficiency, and modified for applying to some discrete data problems in system biology.

Method

An improved GFA called IGFA was proposed in this paper. Two parts were improved in IGFA. The first one is the rule of random division, which is a reasonable strategy and makes running time shorter. The other one is rotation factor, which can improve the accuracy of IGFA. And to apply IGFA to the hierarchical clustering, the initial part and the movement operator were modified.

Results

Two kinds of experiments were used to test IGFA. And IGFA was applied to hierarchical clustering. The global minimum experiment was used with IGFA, GFA, GA (genetic algorithm) and SA (simulated annealing). Multi-minima experiment was used with IGFA and GFA. The two experiments results were compared with each other and proved the efficiency of IGFA. IGFA is better than GFA both in accuracy and running time. For the hierarchical clustering, IGFA is used to optimize the smallest distance of genes pairs, and the results were compared with GA and SA, singular-linkage clustering, UPGMA. The efficiency of IGFA is proved.