A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New bounds for convex clustering under graph connectivity.
Clusters on simple manifolds have connected boundaries.
This paper explains spectral clustering and its equivalence to PCA, breaking it into fully connected and multi-connected cases.
A recent proposal of data dependent similarity called Isolation Kernel/Similarity has enabled SVM to produce better classification accuracy. We identify shortcomings of using a tree method to implement Isolation Similarity; and propose a nearest neighbour method instead. We formally prove the characteristic of Isolatio…
Proposes CRG_IMSC for better clustering of multi-view data.
Interpolates mean shift and spectral clustering on graphs.
We study the connections between spectral clustering and the problems of maximum margin clustering, and estimation of the components of level sets of a density function. Specifically, we obtain bounds on the eigenvectors of graph Laplacian matrices in terms of the between cluster separation, and within cluster connecti…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first consider the similarity of elements in the data as the connectivity of nodes in an…
A new clustering algorithm GDT improves on HDBSCAN for uneven data.
Subspace clustering is the problem of clustering data points into a union of low-dimensional linear/affine subspaces. It is the mathematical abstraction of many important problems in computer vision, image processing and machine learning. A line of recent work (4, 19, 24, 20) provided strong theoretical guarantee for s…
We consider the task of estimating a Gaussian graphical model in the high-dimensional setting. The graphical lasso, which involves maximizing the Gaussian log likelihood subject to an l1 penalty, is a well-studied approach for this task. We begin by introducing a surprising connection between the graphical lasso and hi…
Defines hierarchical clustering axioms for various densities.
Proposes variational Wasserstein barycenters for geometric clustering.
Sparse Subspace Clustering (SSC) is one of the most popular methods for clustering data points into their underlying subspaces. However, SSC may suffer from heavy computational burden. Orthogonal Matching Pursuit applied on SSC accelerates the computation but the trade-off is the loss of clustering accuracy. In this pa…
New insights into spectral clustering reveal strong connections within eigenvectors.
Proposes a method to cluster fMRI data and estimate brain connectivity networks.
Efficient algorithms find solutions in a rare well-connected cluster at low constraint densities.
This paper focuses on density-based clustering, particularly the Density Peak (DP) algorithm and the one based on density-connectivity DBSCAN; and proposes a new method which takes advantage of the individual strengths of these two methods to yield a density-based hierarchical clustering algorithm. Our investigation be…
Develops a new framework to measure network connectedness across and within markets.
Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii) a measure of connectivity between clusters, (iii) a technique for choosing the …
Connectedness of small clusters in Riemannian and Finsler manifolds proven.
The paper connects two clustering methods by showing gradient ascent flow can move up the cluster tree.
The paper connects knot theory and cluster algebras via dimer face polynomials.
ClusTR improves clustering-based models' robustness without adversarial training.
In this paper, a frequency coefficient based on the Sen-Shorrocks-Thon (SST) poverty index notion is proposed. The clustering SST index can be used as the method for determination of the connection between similar neighbor sub-clusters. Consequently, connections can reveal existence of natural homogeneous. Through esti…
We present a hybrid method for latent information discovery on the data sets containing both text content and connection structure based on constrained low rank approximation. The new method jointly optimizes the Nonnegative Matrix Factorization (NMF) objective function for text clustering and the Symmetric NMF (SymNMF…
Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its robust and effective performance. Tremendous research efforts have been made to t…
A new method clusters subjects based on brain networks without vectorizing fMRI data.
Study exact partition recovery with same-cluster oracle, bounded error.
Spectral clustering has become one of the most widely used clustering techniques when the structure of the individual clusters is non-convex or highly anisotropic. Yet, despite its immense popularity, there exists fairly little theory about performance guarantees for spectral clustering. This issue is partly due to the…
Paper characterizes optimal graph clustering limits under a new model.
A new clustering algorithm inspired by Wittgenstein's philosophy.
We study clustering algorithms based on neighborhood graphs on a random sample of data points. The question we ask is how such a graph should be constructed in order to obtain optimal clustering results. Which type of neighborhood graph should one choose, mutual k-nearest neighbor or symmetric k-nearest neighbor? What …
In the present paper, we studied a Dynamic Stochastic Block Model (DSBM) under the assumptions that the connection probabilities, as functions of time, are smooth and that at most nodes can switch their class memberships between two consecutive time points. We estimate the edge probability tensor by a kernel-type p…
Variation Autoencoder (VAE) has become a powerful tool in modeling the non-linear generative process of data from a low-dimensional latent space. Recently, several studies have proposed to use VAE for unsupervised clustering by using mixture models to capture the multi-modal structure of latent representations. This st…
We propose two related unsupervised clustering algorithms which, for input, take data assumed to be sampled from a uniform distribution supported on a metric space , and output a clustering of the data based on the selection of a topological model for the connected components of . Both algorithms work by selectin…
New method clusters variables using robust nodewise regression.
Framework clusters noisy MTS with robust fuzzy clustering, improving accuracy over existing methods.
Study connects Morse theory with cluster variables for wall-crossing in Cerf diagrams.
Paper develops a new objective for hierarchical clustering in Euclidean space.
New algorithms recover clusters with minimal queries, connecting margins to recoverability.
We introduce a principled and theoretically sound spectral method for -way clustering in signed graphs, where the affinity measure between nodes takes either positive or negative values. Our approach is motivated by social balance theory, where the task of clustering aims to decompose the network into disjoint group…
Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining \cite{Duda,Mishra}. Recently, Ames and Vavasis have suggested a novel method for finding cliques i…
Unified view of clustering algorithms presented.
We present two related methods for deriving connectivity-based brain atlases from individual connectomes. The proposed methods exploit a previously proposed dense connectivity representation, termed continuous connectivity, by first performing graph-based hierarchical clustering of individual brains, and subsequently a…
We propose a new method to model multi-way similarities into hypergraphs for clustering.
This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. We investigate the…
Localized sum-of-norms clustering separates balls in data.