Related papers: Clustering in Hilbert simplex geometry

The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…

We present a new method for clustering based on compression. The method doesn't use subject-specific features or background knowledge, and works as follows: First, we determine a universal similarity distance, the normalized compression…

A fundamental question in data analysis, machine learning and signal processing is how to compare between data points. The choice of the distance metric is specifically challenging for high-dimensional data sets, where the problem of…

This paper considers a canonical clustering problem where one receives unlabeled samples drawn from a balanced mixture of two elliptical distributions and aims for a classifier to estimate the labels. Many popular methods including PCA and…

In a landmark result, Chen et al. (2018) showed that multivariate medians induced by halfspace depth attain the minimax optimal convergence rate under Huber contamination and elliptical symmetry, for both location and scatter estimation. We…

We prove the following result on the timelike spherical Hilbert geometry of simplices: Let $\Delta_2$ be a simplex on the 2-sphere and $\tilde{\Delta}_2$ the antipodal simplex. We show that the timelike spherical Hilbert geometry associated…

Finding a set of nested partitions of a dataset is useful to uncover relevant structure at different scales, and is often dealt with a data-dependent methodology. In this paper, we introduce a general two-step methodology for model-based…

In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural…

Graph clustering is a basic technique in machine learning, and has widespread applications in different domains. While spectral techniques have been successfully applied for clustering undirected graphs, the performance of spectral…

Model--based clustering for directional data data has attracted a lot of interest, but most methods utilize rotationally symmetric distributions. This paper suggests the use of elliptically symmetric distributions, namely the elliptically…

There are many distance-based methods for classification and clustering, and for data with a high number of dimensions and a lower number of observations, processing distances is computationally advantageous compared to the raw data matrix.…

We seek to develop a Bures (minimal monotone/statistical distinguishability) metric-based series of formulas for the moments of probability distributions over the determinants $|\rho|$ and $|\rho^{PT}|$ of $4 \times 4$ density matrices,…

Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learning as they can, for…

We face a need of discovering a pattern in locations of a great number of points in a high-dimensional space. Goal is to group the close points together. We are interested in a hierarchical structure, like a B-tree. B-Trees are…

K-Means clustering algorithm is one of the most commonly used clustering algorithms because of its simplicity and efficiency. K-Means clustering algorithm based on Euclidean distance only pays attention to the linear distance between…

This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…

Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering…

We present a novel probabilistic clustering model for objects that are represented via pairwise distances and observed at different time points. The proposed method utilizes the information given by adjacent time points to find the…

In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the…

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…