Building alternative consensus trees and supertrees using k-means and Robinson and Foulds distance

Each gene has its own evolutionary history which can substantially differ from the evolutionary histories of other genes. For example, some individual genes or operons can be affected by specific horizontal gene transfer and recombination events. Thus, the evolutionary history of each gene should be represented by its own phylogenetic tree which may display different evolutionary patterns from the species tree that accounts for the main patterns of vertical descent. The output of traditional consensus tree or supertree inference methods is a unique consensus tree or supertree. Here, we describe a new efficient method for inferring multiple alternative consensus trees and supertrees to best represent the most important evolutionary patterns of a given set of phylogenetic trees (i.e. additive trees or X-trees). We show how a specific version of the popular k-means clustering algorithm, based on some interesting properties of the Robinson and Foulds topological distance, can be used to partition a given set of trees into one (when the data are homogeneous) or multiple (when the data are heterogeneous) cluster(s) of trees. We adapt the popular Caliński-Harabasz, Silhouette, Ball and Hall, and Gap cluster validity indices to tree clustering with k-means. A special attention is paid to the relevant but very challenging problem of inferring alternative supertrees, built from phylogenies constructed for different, but mutually overlapping, sets of taxa. The use of the Euclidean approximation in the objective function of the method makes it faster than the existing tree clustering techniques, and thus perfectly suitable for the analysis of large genomic datasets. In this study, we apply it to discover alternative supertrees characterizing the main patterns of evolution of SARS-CoV-2 and the related betacoronaviruses.

A deep learning approach for building multiple trees classification

Each gene has its own evolutionary history which can substantially differ from the evolutionary histories of other genes. For example, some individual genes or operons can be affected by specific horizontal gene transfer or hybridization events. Thus, the evolutionary history of each gene should be represented by its own phylogenetic tree which may display different evolutionary patterns from the species tree, or Tree of Life, that represents the main patterns of vertical descent. Here, we present a new efficient method for inferring single or multiple consensus trees and supertrees for a given set of phylogenetic trees (i.e. additive trees or X-trees). The output of the traditional tree consensus methods is a unique consensus tree or supertree. Here, we show how Machine Learning (ML) models, based on some interesting properties of the Robinson and Foulds topological distance, can be used to partition a given set of trees into one (when the data are homogeneous) or multiple (when the data are heterogeneous) cluster(s) of trees. We adapt the popular Accuracy, Precision, Sensitivity, and F1 scores to the tree clustering. A special attention is paid to the relevant, but very challenging, problem of inferring alternative supertrees that are built from phylogenies defined on different, but mutually overlapping, sets of species. The use of an approximate objective function in clustering makes the new method faster than the existing tree clustering techniques and thus suitable for the analysis of large genomic datasets.

Minimum description length and psychological clustering models

Clustering is one of the most basic and useful methods of data analysis. This chapter describes a number of powerful clustering models, developed in psychology, for representing objects using data that measure the similarities between pairs of objects. These models place few restrictions on how objects are assigned to clusters,and allow for very general measures of the similarities between objects and clusters.Geometric Complexity Criteria (GCC) are derived for these models, and are used to fit the models to similarity data in a way that balances goodness-of-fit with complexity. Complexity analyses, based on the GCC, are presented for the two most widely used psychological clustering models, known as “additive clustering”and “additive trees”

Mapping brand similarities: Comparing consumer online comments versus survey data

Online consumer behavior has become a valuable and viable source of consumer insights. Consumer comments in online forums, or discussion groups, have proven useful as a source to extract brand similarity data from. Apart from the cost and speed advantages, such data can be captured easily over different time periods. Both online consumer-generated data (CGD) and surveys have their pros and cons. To date, little is known as to how these two data sources compare in terms of brand insights. In this study, we discuss the results from analyzing survey and consumer-generated online data pertaining to the U.S. skincare market. Our study included 57 brands, and we used multidimensional scaling (MDS), t-stochastic neighbor embedding (t-SNE; an alternative to MDS), hierarchical clustering, and additive similarity trees (an extension of hierarchical clustering) to analyze the data. We show that the outcomes vary between CGD and surveys. As an additional insight, we show that, rather than the spatial scaling methods, additive trees result in a much better fit of brand similarity data in cases where we have many brands.

Radical right parties and European economic integration: Evidence from the seventh European Parliament

This article explores the differences in radical right parties' voting behaviour on economic matters at the European Parliament. As the literature highlights the heterogeneity of these parties in relation to their economic programmes, we test whether divergences survive the elections and translate into dissimilar voting patterns. Using voting records from the seventh term of the European Parliament, we show that radical right parties do not act as a consolidated party family. We then analyse the differences between radical right parties by the means of different statistical methods (NOMINATE, Ward's clustering criterion, and additive trees) and find that these are described along two dimensions: the degree of opposition to the European Union and the classical left–right economic cleavage. We provide a classification of these parties compromising four groups: pro-welfare conditional, pro-market conditional, and rejecting. Our results indicate that radical right parties do not act as a party family at the European Parliament. This remains true regardless of the salience of the policy issues in their agendas. The article also derives streams for future research on the heterogeneity of radical right parties.