Related papers: Beta diffusion trees and hierarchical feature allo…
Predicting urban growth is important for practical reasons, and also for the challenge it presents to theoretical frameworks for cluster dynamics. Recently, the model of diffusion limited aggregation (DLA) has been applied to describe urban…
Datasets in the real world are often complex and to some degree hierarchical, with groups and sub-groups of data sharing common characteristics at different levels of abstraction. Understanding and uncovering the hidden structure of these…
A wavelet-like model for distributions of objects in natural and man-made terrestrial environments is developed. The model is constructed in a self-similar fashion, with the sizes, amplitudes, and numbers of objects occurring at a constant…
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of…
Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary…
Many high dimensional vector distances tend to a constant. This is typically considered a negative "contrast-loss" phenomenon that hinders clustering and other machine learning techniques. We reinterpret "contrast-loss" as a blessing.…
The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
Diffusion limited aggregation is studied from the perspective of computational complexity. A parallel algorithm is exhibited that requires a number of steps that scales as the depth of the tree defined by the cluster. The existence of this…
A hierarchical structure describing the inter-relationships of species has long been a fundamental concept in systematic biology, from Linnean classification through to the more recent quest for a 'Tree of Life.' In this paper we use an…
A new method for hierarchical clustering is presented. It combines treelets, a particular multiscale decomposition of data, with a projection on a reproducing kernel Hilbert space. The proposed approach, called kernel treelets (KT),…
The reconstruction of transmission trees for epidemics from genetic data has been the subject of some recent interest. It has been demonstrated that the transmission tree structure can be investigated by augmenting internal nodes of a…
This paper presents a clustering algorithm that is an extension of the Category Trees algorithm. Category Trees is a clustering method that creates tree structures that branch on category type and not feature. The development in this paper…
Latent tree analysis seeks to model the correlations among a set of random variables using a tree of latent variables. It was proposed as an improvement to latent class analysis --- a method widely used in social sciences and medicine to…
The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…
Given a set of species whose evolution is represented by a species tree, a gene family is a group of genes having evolved from a single ancestral gene. A gene family evolves along the branches of a species tree through various mechanisms,…
Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…
A new ``Percolation with Clustering'' (PWC) model is introduced, where (the probabilities of) site percolation configurations on the leaf set of a binary tree are rewarded exponentially according to a generic function, which measures the…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
The metric space of phylogenetic trees defined by Billera, Holmes, and Vogtmann, which we refer to as BHV space, provides a natural geometric setting for describing collections of trees on the same set of taxa. However, it is sometimes…