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An agglomerative hierarchical approach to visualization in Bayesian clustering problems.

ABSTRACT: Clustering problems (including the clustering of individuals into outcrossing populations, hybrid generations, full-sib families and selfing lines) have recently received much attention in population genetics. In these clustering problems, the parameter of interest is a partition of the set of sampled individuals--the sample partition. In a fully Bayesian approach to clustering problems of this type, our knowledge about the sample partition is represented by a probability distribution on the space of possible sample partitions. As the number of possible partitions grows very rapidly with the sample size, we cannot visualize this probability distribution in its entirety, unless the sample is very small. As a solution to this visualization problem, we recommend using an agglomerative hierarchical clustering algorithm, which we call the exact linkage algorithm. This algorithm is a special case of the maximin clustering algorithm that we introduced previously. The exact linkage algorithm is now implemented in our software package PartitionView. The exact linkage algorithm takes the posterior co-assignment probabilities as input and yields as output a rooted binary tree, or more generally, a forest of such trees. Each node of this forest defines a set of individuals, and the node height is the posterior co-assignment probability of this set. This provides a useful visual representation of the uncertainty associated with the assignment of individuals to categories. It is also a useful starting point for a more detailed exploration of the posterior distribution in terms of the co-assignment probabilities.

SUBMITTER: Dawson KJ

PROVIDER: S-EPMC2705916 | biostudies-literature | 2009 Jul

REPOSITORIES: biostudies-literature

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An agglomerative hierarchical approach to visualization in Bayesian clustering problems.

Dawson K J KJ Belkhir K K

Heredity 20090401 1

Clustering problems (including the clustering of individuals into outcrossing populations, hybrid generations, full-sib families and selfing lines) have recently received much attention in population genetics. In these clustering problems, the parameter of interest is a partition of the set of sampled individuals--the sample partition. In a fully Bayesian approach to clustering problems of this type, our knowledge about the sample partition is represented by a probability distribution on the spa ...[more]

PMID: 19337306

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Project description:The major interest domains of single-cell RNA sequential analysis are identification of existing and novel types of cells, depiction of cells, cell fate prediction, classification of several types of tumor, and investigation of heterogeneity in different cells. Single-cell clustering plays an important role to solve the aforementioned questions of interest. Cluster identification in high dimensional single-cell sequencing data faces some challenges due to its nature. Dimensionality reduction models can solve the problem. Here, we introduce a potential cluster specified frequent biomarkers discovery framework using dimensionality reduction and hierarchical agglomerative clustering Louvain for single-cell RNA sequencing data analysis. First, we pre-filtered the features with fewer number of cells and the cells with fewer number of features. Then we created a Seurat object to store data and analysis together and used quality control metrics to discard low quality or dying cells. Afterwards we applied global-scaling normalization method "LogNormalize" for data normalization. Next, we computed cell-to-cell highly variable features from our dataset. Then, we applied a linear transformation and linear dimensionality reduction technique, Principal Component Analysis (PCA) to project high dimensional data to an optimal low-dimensional space. After identifying fifty "significant"principal components (PCs) based on strong enrichment of low p-value features, we implemented a graph-based clustering algorithm Louvain for the cell clustering of 10 top significant PCs. We applied our model to a single-cell RNA sequential dataset for a rare intestinal cell type in mice (NCBI accession ID:GSE62270, 23,630 features and 1872 samples (cells)). We obtained 10 cell clusters with a maximum modularity of 0.885 1. After detecting the cell clusters, we found 3871 cluster-specific biomarkers using an expression feature extraction statistical tool for single-cell sequencing data, Model-based Analysis of Single-cell Transcriptomics (MAST) with a log 2 FC threshold of 0.25 and a minimum feature detection of 25%. From these cluster-specific biomarkers, we found 1892 most frequent markers, i.e., overlapping biomarkers. We performed degree hub gene network analysis using Cytoscape and reported the five highest degree genes (Rps4x, Rps18, Rpl13a, Rps12 and Rpl18a). Subsequently, we performed KEGG pathway and Gene Ontology enrichment analysis of cluster markers using David 6.8 software tool. In summary, our proposed framework that integrated dimensionality reduction and agglomerative hierarchical clustering provides a robust approach to efficiently discover cluster-specific frequent biomarkers, i.e., overlapping biomarkers from single-cell RNA sequencing data.

Project description:BackgroundPost-genomic molecular biology has resulted in an explosion of data, providing measurements for large numbers of genes, proteins and metabolites. Time series experiments have become increasingly common, necessitating the development of novel analysis tools that capture the resulting data structure. Outlier measurements at one or more time points present a significant challenge, while potentially valuable replicate information is often ignored by existing techniques.ResultsWe present a generative model-based Bayesian hierarchical clustering algorithm for microarray time series that employs Gaussian process regression to capture the structure of the data. By using a mixture model likelihood, our method permits a small proportion of the data to be modelled as outlier measurements, and adopts an empirical Bayes approach which uses replicate observations to inform a prior distribution of the noise variance. The method automatically learns the optimum number of clusters and can incorporate non-uniformly sampled time points. Using a wide variety of experimental data sets, we show that our algorithm consistently yields higher quality and more biologically meaningful clusters than current state-of-the-art methodologies. We highlight the importance of modelling outlier values by demonstrating that noisy genes can be grouped with other genes of similar biological function. We demonstrate the importance of including replicate information, which we find enables the discrimination of additional distinct expression profiles.ConclusionsBy incorporating outlier measurements and replicate values, this clustering algorithm for time series microarray data provides a step towards a better treatment of the noise inherent in measurements from high-throughput genomic technologies. Timeseries BHC is available as part of the R package 'BHC' (version 1.5), which is available for download from Bioconductor (version 2.9 and above) via http://www.bioconductor.org/packages/release/bioc/html/BHC.html?pagewanted=all.

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An agglomerative hierarchical approach to visualization in Bayesian clustering problems.

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An agglomerative hierarchical approach to visualization in Bayesian clustering problems.

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