Related papers: Statistical Inference for Cluster Trees
We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…
The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is…
Clustering is widely studied in statistics and machine learning, with applications in a variety of fields. As opposed to classical algorithms which return a single clustering solution, Bayesian nonparametric models provide a posterior over…
A random forest is a popular tool for estimating probabilities in machine learning classification tasks. However, the means by which this is accomplished is unprincipled: one simply counts the fraction of trees in a forest that vote for a…
Consensus methods provide a useful strategy for combining information from a collection of gene trees. An important application of consensus methods is to combine gene trees to estimate a species tree. To investigate the theoretical…
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly…
We herein introduce a new method of interpretable clustering that uses unsupervised binary trees. It is a three-stage procedure, the first stage of which entails a series of recursive binary splits to reduce the heterogeneity of the data…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
There are many cluster analysis methods that can produce quite different clusterings on the same dataset. Cluster validation is about the evaluation of the quality of a clustering; "relative cluster validation" is about using such criteria…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…
We introduce a novel statistical significance-based approach for clustering hierarchical data using semi-parametric linear mixed-effects models designed for responses with laws in the exponential family (e.g., Poisson and Bernoulli). Within…
The literature on concept formation has demonstrated that humans are capable of learning concepts incrementally, with a variety of attribute types, and in both supervised and unsupervised settings. Many models of concept formation focus on…
Phylogenetic trees (i.e. evolutionary trees, additive trees or X-trees) play a key role in the processes of modeling and representing species evolution. Genome evolution of a given group of species is usually modeled by a species…
Many biological studies involve inferring the evolutionary history of a sample of individuals from a large population and interpreting the reconstructed tree. Such an ascertained tree typically represents only a small part of a…
A key issue in cluster analysis is the choice of an appropriate clustering method and the determination of the best number of clusters. Different clusterings are optimal on the same data set according to different criteria, and the choice…
Clustering is a fundamental data mining tool that aims to divide data into groups of similar items. Generally, intuition about clustering reflects the ideal case -- exact data sets endowed with flawless dissimilarity between individual…
We propose some axioms for hierarchical clustering of probability measures and investigate their ramifications. The basic idea is to let the user stipulate the clusters for some elementary measures. This is done without the need of any…
We introduce a general semiparametric clusterwise elliptical distribution to assess how latent cluster structure shapes continuous outcomes. Using a subjectwise representation, we first estimate cluster-specific mean vectors and a…
Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one…