Clustering trees: a visualization for evaluating clusterings at multiple resolutions

Abstract Clustering techniques are widely used in the analysis of large datasets to group together samples with similar properties. For example, clustering is often used in the field of single-cell RNA-sequencing in order to identify different cell types present in a tissue sample. There are many algorithms for performing clustering, and the results can vary substantially. In particular, the number of groups present in a dataset is often unknown, and the number of clusters identified by an algorithm can change based on the parameters used. To explore and examine the impact of varying clustering resolution, we present clustering trees. This visualization shows the relationships between clusters at multiple resolutions, allowing researchers to see how samples move as the number of clusters increases. In addition, meta-information can be overlaid on the tree to inform the choice of resolution and guide in identification of clusters. We illustrate the features of clustering trees using a series of simulations as well as two real examples, the classical iris dataset and a complex single-cell RNA-sequencing dataset. Clustering trees can be produced using the clustree R package, available from CRAN and developed on GitHub.

[1]  Adrian E. Raftery,et al.  Model-Based Clustering, Discriminant Analysis, and Density Estimation , 2002 .

[2]  Gábor Csárdi,et al.  The igraph software package for complex network research , 2006 .

[3]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[4]  P. Rousseeuw Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

[5]  Hans-Peter Kriegel,et al.  A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise , 1996, KDD.

[6]  C. Wilke Streamlined Plot Theme and Plot Annotations for 'ggplot2' , 2015 .

[7]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[8]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[9]  A. Regev,et al.  Spatial reconstruction of single-cell gene expression , 2015, Nature Biotechnology.

[10]  Luke Zappia,et al.  Clustering trees: a visualisation for evaluating clusterings at multiple resolutions , 2018 .

[11]  Edward M. Reingold,et al.  Tidier Drawings of Trees , 1981, IEEE Transactions on Software Engineering.

[12]  R. L. Thorndike Who belongs in the family? , 1953 .

[13]  Catalin C. Barbacioru,et al.  mRNA-Seq whole-transcriptome analysis of a single cell , 2009, Nature Methods.

[14]  Mitsuhiko Toda,et al.  Methods for Visual Understanding of Hierarchical System Structures , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  Ulrike von Luxburg,et al.  Clustering Stability: An Overview , 2010, Found. Trends Mach. Learn..

[16]  R. Fisher THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

[17]  Grace X. Y. Zheng,et al.  Massively parallel digital transcriptional profiling of single cells , 2016, Nature Communications.

[18]  S. Teichmann,et al.  Computational and analytical challenges in single-cell transcriptomics , 2015, Nature Reviews Genetics.

[19]  E. Forgy,et al.  Cluster analysis of multivariate data : efficiency versus interpretability of classifications , 1965 .

[20]  P. Rousseeuw,et al.  Partitioning Around Medoids (Program PAM) , 2008 .

[21]  Thomas Lin Pedersen,et al.  A Tidy API for Graph Manipulation [R package tidygraph version 1.2.0] , 2020 .

[22]  M. Schaub,et al.  SC3 - consensus clustering of single-cell RNA-Seq data , 2016, Nature Methods.

[23]  Isabelle Guyon,et al.  A Stability Based Method for Discovering Structure in Clustered Data , 2001, Pacific Symposium on Biocomputing.

[24]  Judea Pearl,et al.  The recovery of causal poly-trees from statistical data , 1987, Int. J. Approx. Reason..

[25]  Hadley Wickham,et al.  ggplot2 - Elegant Graphics for Data Analysis (2nd Edition) , 2017 .