Expectation-Maximization Binary Clustering for Behavioural Annotation

The growing capacity to process and store animal tracks has spurred the development of new methods to segment animal trajectories into elementary units of movement. Key challenges for movement trajectory segmentation are to (i) minimize the need of supervision, (ii) reduce computational costs, (iii) minimize the need of prior assumptions (e.g. simple parametrizations), and (iv) capture biologically meaningful semantics, useful across a broad range of species. We introduce the Expectation-Maximization binary Clustering (EMbC), a general purpose, unsupervised approach to multivariate data clustering. The EMbC is a variant of the Expectation-Maximization Clustering (EMC), a clustering algorithm based on the maximum likelihood estimation of a Gaussian mixture model. This is an iterative algorithm with a closed form step solution and hence a reasonable computational cost. The method looks for a good compromise between statistical soundness and ease and generality of use (by minimizing prior assumptions and favouring the semantic interpretation of the final clustering). Here we focus on the suitability of the EMbC algorithm for behavioural annotation of movement data. We show and discuss the EMbC outputs in both simulated trajectories and empirical movement trajectories including different species and different tracking methodologies. We use synthetic trajectories to assess the performance of EMbC compared to classic EMC and Hidden Markov Models. Empirical trajectories allow us to explore the robustness of the EMbC to data loss and data inaccuracies, and assess the relationship between EMbC output and expert label assignments. Additionally, we suggest a smoothing procedure to account for temporal correlations among labels, and a proper visualization of the output for movement trajectories. Our algorithm is available as an R-package with a set of complementary functions to ease the analysis.     

Identifying differentially expressed genes in meta-analysis via Bayesian model-based clustering

A Bayesian model-based clustering approach is proposed for identifying differentially expressed genes in meta-analysis. A Bayesian hierarchical model is used as a scientific tool for combining information from different studies, and a mixture prior is used to separate differentially expressed genes from non-differentially expressed genes. Posterior estimation of the parameters and missing observations are done by using a simple Markov chain Monte Carlo method. From the estimated mixture model, useful measure of significance of a test such as the Bayesian false discovery rate (FDR), the local FDR (Efron et al., 2001), and the integration-driven discovery rate (IDR; Choi et al., 2003) can be easily computed. The model-based approach is also compared with commonly used permutation methods, and it is shown that the model-based approach is superior to the permutation methods when there are excessive under-expressed genes compared to over-expressed genes or vice versa. The proposed method is applied to four publicly available prostate cancer gene expression data sets and simulated data sets.     

Calculation of self-diffusion coefficients of the [BMIM][TFSA]/water system by molecular dynamics simulation

We performed a molecular dynamics simulation to calculate the self-diffusion coefficients of 1-Butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide and water in a water–ionic liquid mixture. We then compared the simulated self-diffusion coefficients of cation, anion and water molecules with experimental data and with simulated data from the literature. Although the simulation overestimated the self-diffusion coefficients of ions, the simulated results qualitatively reproduced the enhancement of the self-diffusion coefficients of water as the water molar fraction increased. We also calculated the radial distribution functions to investigate the solution structure, i.e. the clustering of water molecules. The clustering of water in ionic liquid was found to play an important role in the enhancement of the diffusion of water molecules in the ionic liquid.     

Simultaneous estimation of haplotype frequencies and quantitative trait parameters: applications to the test of association between phenotype and diplotype configuration

The analysis of the haplotype-phenotype relationship has become more and more important. We have developed an algorithm, using individual genotypes at linked loci as well as their quantitative phenotypes, to estimate the parameters of the distribution of the phenotypes for subjects with and without a particular haplotype by an expectation-maximization (EM) algorithm. We assumed that the phenotype for a diplotype configuration follows a normal distribution. The algorithm simultaneously calculates the maximum likelihood (L0max) under the null hypothesis (i.e., nonassociation between the haplotype and phenotype), and the maximum likelihood (Lmax) under the alternative hypothesis (i.e., association between the haplotype and phenotype). Then we tested the association between the haplotype and the phenotype using a test statistic, -2 log(L0max/Lmax). The above algorithm along with some extensions for different modes of inheritance was implemented as a computer program, QTLHAPLO. Simulation studies using single-nucleotide polymorphism (SNP) genotypes have clarified that the estimation was very accurate when the linkage disequilibrium between linked loci was rather high. Empirical power using the simulated data was high enough. We applied QTLHAPLO for the analysis of the real data of the genotypes at the calpain 10 gene obtained from diabetic and control subjects in various laboratories.     

Evaluation and comparison of gene clustering methods in microarray analysis

MOTIVATION: Microarray technology has been widely applied in biological and clinical studies for simultaneous monitoring of gene expression in thousands of genes. Gene clustering analysis is found useful for discovering groups of correlated genes potentially co-regulated or associated to the disease or conditions under investigation. Many clustering methods including hierarchical clustering, K-means, PAM, SOM, mixture model-based clustering and tight clustering have been widely used in the literature. Yet no comprehensive comparative study has been performed to evaluate the effectiveness of these methods. RESULTS: In this paper, six gene clustering methods are evaluated by simulated data from a hierarchical log-normal model with various degrees of perturbation as well as four real datasets. A weighted Rand index is proposed for measuring similarity of two clustering results with possible scattered genes (i.e. a set of noise genes not being clustered). Performance of the methods in the real data is assessed by a predictive accuracy analysis through verified gene annotations. Our results show that tight clustering and model-based clustering consistently outperform other clustering methods both in simulated and real data while hierarchical clustering and SOM perform among the worst. Our analysis provides deep insight to the complicated gene clustering problem of expression profile and serves as a practical guideline for routine microarray cluster analysis.     

Sampling Issues Affecting Accuracy of Likelihood-based Classification Using Genetical Data

We demonstrate the effectiveness of a genetic algorithm for discovering multi-locus combinations that provide accurate individual assignment decisions and estimates of mixture composition based on likelihood classification. Using simulated data representing different levels of inter-population differentiation (F_st～ 0.01 and 0.10), genetic diversities (four or eight alleles per locus), and population sizes (20, 40, 100 individuals in baseline populations), we show that subsets of loci can be identified that provide comparable levels of accuracy in classification decisions relative to entire multi-locus data sets, where 5, 10, or 20 loci were considered. Microsatellite data sets from hatchery strains of lake trout, Salvelinus namaycush, representing a comparable range of inter-population levels of differentiation in allele frequencies confirmed simulation results. For both simulated and empirical data sets, assignment accuracy was achieved using fewer loci (e.g., three or four loci out of eight for empirical lake trout studies). Simulation results were used to investigate properties of the ‘leave-one-out’ (L1O) method for estimating assignment error rates. Accuracy of population assignments based on L1O methods should be viewed with caution under certain conditions, particularly when baseline population sample sizes are low (<50).     

Measuring effects of linear obstacles on wildlife movements: accounting for the relationship between step length and crossing probability

Animal movements in the landscape are influenced by linear features such as rivers, roads and power lines. Prior studies have investigated how linear features, particularly roads, affect movement rates by comparing animal's movement rate measured as step lengths (i.e., the distance between consecutive observations such as GPS locations) before, during and after crossing of a linear feature. The null hypothesis has been that the length of crossing steps should not differ from other steps, and a deviation from this, mainly that steps are longer during crossing, has been taken as support for a disturbance effect of the linear feature. However, based on the simple relationship between the length of a step and its probability to cross a linear feature, we claim that this assumption is inappropriate to test for behavioural responses to linear features. The probability is related to the proportion of the total length of the trajectory (i.e., the path of movement) a step constitutes. Consequently, care should be taken when formulating hypotheses about how animal moves in relation to linear features in the landscape. Statistical tests should be set up with respect to the expected length based on the distribution of step lengths in the trajectory. We propose two methods that accounts for the bias in crossing frequency that is caused by step lengths, and illustrates their applications by using simulated animal trajectories as well as empirical data on reindeer in an area with a power line.     

Assessing and improving methods used in operational taxonomic unit-based approaches for 16S rRNA gene sequence analysis

In spite of technical advances that have provided increases in orders of magnitude in sequencing coverage, microbial ecologists still grapple with how to interpret the genetic diversity represented by the 16S rRNA gene. Two widely used approaches put sequences into bins based on either their similarity to reference sequences (i.e., phylotyping) or their similarity to other sequences in the community (i.e., operational taxonomic units [OTUs]). In the present study, we investigate three issues related to the interpretation and implementation of OTU-based methods. First, we confirm the conventional wisdom that it is impossible to create an accurate distance-based threshold for defining taxonomic levels and instead advocate for a consensus-based method of classifying OTUs. Second, using a taxonomic-independent approach, we show that the average neighbor clustering algorithm produces more robust OTUs than other hierarchical and heuristic clustering algorithms. Third, we demonstrate several steps to reduce the computational burden of forming OTUs without sacrificing the robustness of the OTU assignment. Finally, by blending these solutions, we propose a new heuristic that has a minimal effect on the robustness of OTUs and significantly reduces the necessary time and memory requirements. The ability to quickly and accurately assign sequences to OTUs and then obtain taxonomic information for those OTUs will greatly improve OTU-based analyses and overcome many of the challenges encountered with phylotype-based methods.     

A Mathematical Framework for Combining Decisions of Multiple Experts toward Accurate and Remote Diagnosis of Malaria Using Tele-Microscopy

We propose a methodology for digitally fusing diagnostic decisions made by multiple medical experts in order to improve accuracy of diagnosis. Toward this goal, we report an experimental study involving nine experts, where each one was given more than 8,000 digital microscopic images of individual human red blood cells and asked to identify malaria infected cells. The results of this experiment reveal that even highly trained medical experts are not always self-consistent in their diagnostic decisions and that there exists a fair level of disagreement among experts, even for binary decisions (i.e., infected vs. uninfected). To tackle this general medical diagnosis problem, we propose a probabilistic algorithm to fuse the decisions made by trained medical experts to robustly achieve higher levels of accuracy when compared to individual experts making such decisions. By modelling the decisions of experts as a three component mixture model and solving for the underlying parameters using the Expectation Maximisation algorithm, we demonstrate the efficacy of our approach which significantly improves the overall diagnostic accuracy of malaria infected cells. Additionally, we present a mathematical framework for performing ‘slide-level’ diagnosis by using individual ‘cell-level’ diagnosis data, shedding more light on the statistical rules that should govern the routine practice in examination of e.g., thin blood smear samples. This framework could be generalized for various other tele-pathology needs, and can be used by trained experts within an efficient tele-medicine platform.     

A hierarchical unsupervised growing neural network for clustering gene expression patterns

MOTIVATION: We describe a new approach to the analysis of gene expression data coming from DNA array experiments, using an unsupervised neural network. DNA array technologies allow monitoring thousands of genes rapidly and efficiently. One of the interests of these studies is the search for correlated gene expression patterns, and this is usually achieved by clustering them. The Self-Organising Tree Algorithm, (SOTA) (Dopazo,J. and Carazo,J.M. (1997) J. Mol. Evol., 44, 226-233), is a neural network that grows adopting the topology of a binary tree. The result of the algorithm is a hierarchical cluster obtained with the accuracy and robustness of a neural network. RESULTS: SOTA clustering confers several advantages over classical hierarchical clustering methods. SOTA is a divisive method: the clustering process is performed from top to bottom, i.e. the highest hierarchical levels are resolved before going to the details of the lowest levels. The growing can be stopped at the desired hierarchical level. Moreover, a criterion to stop the growing of the tree, based on the approximate distribution of probability obtained by randomisation of the original data set, is provided. By means of this criterion, a statistical support for the definition of clusters is proposed. In addition, obtaining average gene expression patterns is a built-in feature of the algorithm. Different neurons defining the different hierarchical levels represent the averages of the gene expression patterns contained in the clusters. Since SOTA runtimes are approximately linear with the number of items to be classified, it is especially suitable for dealing with huge amounts of data. The method proposed is very general and applies to any data providing that they can be coded as a series of numbers and that a computable measure of similarity between data items can be used. AVAILABILITY: A server running the program can be found at: http://bioinfo.cnio.es/sotarray.     

Performance assessment of kernel density clustering for gene expression profile data

Kernel density smoothing techniques have been used in classification or supervised learning of gene expression profile (GEP) data, but their applications to clustering or unsupervised learning of those data have not been explored and assessed. Here we report a kernel density clustering method for analysing GEP data and compare its performance with the three most widely-used clustering methods: hierarchical clustering, K-means clustering, and multivariate mixture model-based clustering. Using several methods to measure agreement, between-cluster isolation, and withincluster coherence, such as the Adjusted Rand Index, the Pseudo F test, the r(2) test, and the profile plot, we have assessed the effectiveness of kernel density clustering for recovering clusters, and its robustness against noise on clustering both simulated and real GEP data. Our results show that the kernel density clustering method has excellent performance in recovering clusters from simulated data and in grouping large real expression profile data sets into compact and well-isolated clusters, and that it is the most robust clustering method for analysing noisy expression profile data compared to the other three methods assessed.     

UVA-induced cyclobutane pyrimidine dimers form predominantly at thymine-thymine dipyrimidines and correlate with the mutation spectrum in rodent cells

Ligation-mediated PCR was employed to quantify cyclobutane pyrimidine dimer (CPD) formation at nucleotide resolution along exon 2 of the adenine phosphoribosyltransferase (aprt) locus in Chinese hamster ovary (CHO) cells following irradiation with either UVA (340–400 nm), UVB (295–320 nm), UVC (254 nm) or simulated sunlight (SSL; λ > 295 nm). The resulting DNA damage spectrum for each wavelength region was then aligned with the corresponding mutational spectrum generated previously in the same genetic target. The DNA sequence specificities of CPD formation induced by UVC, UVB or SSL were very similar, i.e., in each case the overall relative proportion of this photoproduct forming at TT, TC, CT and CC sites was ~28, ~26, ~16 and ~30%, respectively. Furthermore, a clear correspondence was noted between the precise locations of CPD damage hotspots, and of ‘UV signature’ mutational hotspots consisting primarily of C→T and CC→TT transitions within pyrimidine runs. However, following UVA exposure, in strong contrast to the above situation for UVC, UVB or SSL, CPDs were generated much more frequently at TT sites than at TC, CT or CC sites (57% versus 18, 11 and 14%, respectively). This CPD deposition pattern correlates well with the strikingly high proportion of mutations recovered opposite TT dipyrimidines in UVA- irradiated CHO cells. Our results directly implicate the CPD as a major promutagenic DNA photoproduct induced specifically by UVA in rodent cells.     

A Powerful Pathway-Based Adaptive Test for Genetic Association with Common or Rare Variants

In spite of the success of genome-wide association studies (GWASs), only a small proportion of heritability for each complex trait has been explained by identified genetic variants, mainly SNPs. Likely reasons include genetic heterogeneity (i.e., multiple causal genetic variants) and small effect sizes of causal variants, for which pathway analysis has been proposed as a promising alternative to the standard single-SNP-based analysis. A pathway contains a set of functionally related genes, each of which includes multiple SNPs. Here we propose a pathway-based test that is adaptive at both the gene and SNP levels, thus maintaining high power across a wide range of situations with varying numbers of the genes and SNPs associated with a trait. The proposed method is applicable to both common variants and rare variants and can incorporate biological knowledge on SNPs and genes to boost statistical power. We use extensively simulated data and a WTCCC GWAS dataset to compare our proposal with several existing pathway-based and SNP-set-based tests, demonstrating its promising performance and its potential use in practice.     

Role of calcium-phosphate deposition in vascular smooth muscle cell calcification

In this work we are studying whether calcium phosphate deposition (CPD) during vascular calcification is a passive or a cell-mediated mechanism. Passive CPD was studied in fixed vascular smooth muscle cells (VSMC), which calcify faster than live cells in the presence of 1.8 mM Ca2(+) and 2 mM P(i). CPD seems to be a cell-independent process that depends on the concentration of calcium, phosphate, and hydroxyl ions, but not on Ca × P(i) concentration products, given that deposition is obtained with 2 × 2 and 4 × 1 Ca × P(i) mM2 but not with 2 × 1 or 1 × 4 Ca × P(i) mM2. Incubation with 4 mM P(i) without CPD (i.e., plus 1 mM Ca) does not induce osteogene expression. Increased expression of bone markers such as Bmp2 and Cbfa1 is only observed concomitantly with CPD. Hydroxyapatite is the only crystalline phase in both lysed and live cells. Lysed cell deposits are highly crystalline, whereas live cell deposits still contain large amounts of amorphous calcium. High-resolution transmission electron microscopy revealed a nanostructure of rounded crystallites of 5-10 nm oriented at random in lysed cells, which is compatible with spontaneous precipitation. The nanostructure in live cells consisted of long fiber crystals, 10-nm thick, embedded in an amorphous matrix. This structure indicates an active role of cells in the process of hydroxyapatite crystallization. In conclusion, our data suggest that CPD is a passive phenomenon, which triggers the osteogenic changes that are involved in the formation of a well organized, calcified crystalline structure.     

Using clustering techniques to improve hit selection in high-throughput screening

A typical modern high-throughput screening (HTS) operation consists of testing thousands of chemical compounds to select active ones for future detailed examination. The authors describe 3 clustering techniques that can be used to improve the selection of active compounds (i.e., hits). They are designed to identify quality hits in the observed HTS measurements. The considered clustering techniques were first tested on simulated data and then applied to analyze the assay inhibiting Escherichia coli dihydrofo-late reductase produced at the HTS laboratory of McMaster University.     

Cross-validation of protein structural class prediction using statistical clustering and neural networks.

We present an approach to predicting protein structural class that uses amino acid composition and hydrophobic pattern frequency information as input to two types of neural networks: (1) a three-layer back-propagation network and (2) a learning vector quantization network. The results of these methods are compared to those obtained from a modified Euclidean statistical clustering algorithm. The protein sequence data used to drive these algorithms consist of the normalized frequency of up to 20 amino acid types and six hydrophobic amino acid patterns. From these frequency values the structural class predictions for each protein (all-alpha, all-beta, or alpha-beta classes) are derived. Examples consisting of 64 previously classified proteins were randomly divided into multiple training (56 proteins) and test (8 proteins) sets. The best performing algorithm on the test sets was the learning vector quantization network using 17 inputs, obtaining a prediction accuracy of 80.2%. The Matthews correlation coefficients are statistically significant for all algorithms and all structural classes. The differences between algorithms are in general not statistically significant. These results show that information exists in protein primary sequences that is easily obtainable and useful for the prediction of protein structural class by neural networks as well as by standard statistical clustering algorithms.     

A new algorithm for comparing and visualizing relationships between hierarchical and flat gene expression data clusterings

MOTIVATION: Clustering is one of the most widely used methods in unsupervised gene expression data analysis. The use of different clustering algorithms or different parameters often produces rather different results on the same data. Biological interpretation of multiple clustering results requires understanding how different clusters relate to each other. It is particularly non-trivial to compare the results of a hierarchical and a flat, e.g. k-means, clustering. RESULTS: We present a new method for comparing and visualizing relationships between different clustering results, either flat versus flat, or flat versus hierarchical. When comparing a flat clustering to a hierarchical clustering, the algorithm cuts different branches in the hierarchical tree at different levels to optimize the correspondence between the clusters. The optimization function is based on graph layout aesthetics or on mutual information. The clusters are displayed using a bipartite graph where the edges are weighted proportionally to the number of common elements in the respective clusters and the weighted number of crossings is minimized. The performance of the algorithm is tested using simulated and real gene expression data. The algorithm is implemented in the online gene expression data analysis tool Expression Profiler. AVAILABILITY: http://www.ebi.ac.uk/expressionprofiler     

Evolutionary HMMs: a Bayesian approach to multiple alignment

MOTIVATION: We review proposed syntheses of probabilistic sequence alignment, profiling and phylogeny. We develop a multiple alignment algorithm for Bayesian inference in the links model proposed by Thorne et al. (1991, J. Mol. Evol., 33, 114-124). The algorithm, described in detail in Section 3, samples from and/or maximizes the posterior distribution over multiple alignments for any number of DNA or protein sequences, conditioned on a phylogenetic tree. The individual sampling and maximization steps of the algorithm require no more computational resources than pairwise alignment. METHODS: We present a software implementation (Handel) of our algorithm and report test results on (i) simulated data sets and (ii) the structurally informed protein alignments of BAliBASE (Thompson et al., 1999, Nucleic Acids Res., 27, 2682-2690). RESULTS: We find that the mean sum-of-pairs score (a measure of residue-pair correspondence) for the BAliBASE alignments is only 13% lower for Handelthan for CLUSTALW(Thompson et al., 1994, Nucleic Acids Res., 22, 4673-4680), despite the relative simplicity of the links model (CLUSTALW uses affine gap scores and increased penalties for indels in hydrophobic regions). With reference to these benchmarks, we discuss potential improvements to the links model and implications for Bayesian multiple alignment and phylogenetic profiling. AVAILABILITY: The source code to Handelis freely distributed on the Internet at http://www.biowiki.org/Handel under the terms of the GNU Public License (GPL, 2000, http://www.fsf.org./copyleft/gpl.html).