Related papers: Clustering Tree-structured Data on Manifold

Topological Data Analysis (TDA) has recently gained significant attention in the field of financial prediction. However, the choice of point cloud construction methods, topological feature representations, and classification models has a…

Unsupervised machine learning, and in particular data clustering, is a powerful approach for the analysis of datasets and identification of characteristic features occurring throughout a dataset. It is gaining popularity across scientific…

Clustering is one of the most common unsupervised learning tasks in machine learning and data mining. Clustering algorithms have been used in a plethora of applications across several scientific fields. However, there has been limited…

Multidimensional data distributions can have complex topologies and variable local dimensions. To approximate complex data, we propose a new type of low-dimensional ``principal object'': a principal cubic complex. This complex is a…

The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most…

We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC synthesizes desirable features from spectral clustering and…

In machine learning, observation features are measured in a metric space to obtain their distance function for optimization. Given similar features that are statistically sufficient as a population, a statistical distance between two…

State-of-the-art clustering algorithms use heuristics to partition the feature space and provide little insight into the rationale for cluster membership, limiting their interpretability. In healthcare applications, the latter poses a…

Face clustering is an essential tool for exploiting the unlabeled face data, and has a wide range of applications including face annotation and retrieval. Recent works show that supervised clustering can result in noticeable performance…

Clustering aims to form groups of similar data points in an unsupervised regime. Yet, clustering complex datasets containing critically intertwined shapes poses significant challenges. The prevailing clustering algorithms widely depend on…

With the recent popularity of graphical clustering methods, there has been an increased focus on the information between samples. We show how learning cluster structure using edge features naturally and simultaneously determines the most…

Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…

Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological -- and indeed, linear -- algebra. However, matrices in this domain are typically large, with rows and columns…

A wide range of (multivariate) temporal (1D) and spatial (2D) data analysis tasks, such as grouping vehicle sensor trajectories, can be formulated as clustering with given metric constraints. Existing metric-constrained clustering…

Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…

A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a…

A major limitation of clustering approaches is their lack of explainability: methods rarely provide insight into which features drive the grouping of similar observations. To address this limitation, we propose an ensemble-based clustering…

In this work, we propose trait-based merge trees a generalization of merge trees to feature level sets, targeting the analysis of tensor field or general multi-variate data. For this, we employ the notion of traits defined in attribute…

Model-based clustering integrated with variable selection is a powerful tool for uncovering latent structures within complex data. However, its effectiveness is often hindered by challenges such as identifying relevant variables that define…

Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…