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.
Enhanced spectral clustering for geometric graphs improves clustering accuracy.
GCML preserves geometric structure in manifold clustering for diverse data types.
A new model for graph clustering using curvature spaces.
Geometric framework links clustering accuracy to structural recovery.
Integrable dynamics explained via geometric maps and cluster algebras.
The information bottleneck (IB) approach to clustering takes a joint distribution and maps the data to cluster labels which retain maximal information about (Tishby et al., 1999). This objective results in an algorithm that clusters data points based upon the similarity of their condit…
A new geometric method for clustering SPD data improves upon Euclidean and Riemannian approaches.
Proposes variational Wasserstein barycenters for geometric clustering.
New method clusters large datasets using geometric properties.
New theory for clustering in geometric and adaptive settings.
This manuscript develops the theory of agglomerative clustering with Bregman divergences. Geometric smoothing techniques are developed to deal with degenerate clusters. To allow for cluster models based on exponential families with overcomplete representations, Bregman divergences are developed for nondifferentiable co…
Spectral clustering for geometric graphs achieves strong consistency in community recovery.
Geometrically, Legendrian surfaces related by surgery have related skein-valued cluster spaces.
We explore the geometrical interpretation of the PCA based clustering algorithm Principal Direction Divisive Partitioning (PDDP). We give several examples where this algorithm breaks down, and suggest a new method, gap partitioning, which takes into account natural gaps in the data between clusters. Geometric features …
Active learning (AL) repeatedly trains the classifier with the minimum labeling budget to improve the current classification model. The training process is usually supervised by an uncertainty evaluation strategy. However, the uncertainty evaluation always suffers from performance degeneration when the initial labeled …
A Python tool generates synthetic data for cluster analysis from high-level descriptions.
We construct geometric realization for non-exceptional mutation-finite cluster algebras by extending the theory of Fomin and Thurston to skew-symmetrizable case. Cluster variables for these algebras are renormalized lambda lengths on certain hyperbolic orbifolds. We also compute growth rate of these cluster algebras, p…
Signed networks allow to model positive and negative relationships. We analyze existing extensions of spectral clustering to signed networks. It turns out that existing approaches do not recover the ground truth clustering in several situations where either the positive or the negative network structures contain no noi…
We propose an algorithm, HPREF (Hierarchical Partitioning by Repeated Features), that produces a hierarchical partition of a set of clusterings of a fixed dataset, such as sets of clusterings produced by running a clustering algorithm with a range of parameters. This gives geometric structure to such sets of clustering…
We prove the existence of Lagrangian fillings for -type Legendrian links.
Paper proposes a robust method for federated ICA with geometric median aggregation.
A graph clustering method that moves nodes to highest-degree neighbors.
A new method clusters complex networks using topological and geometric structure.
Geometric model of unbounded sl3 laminations with tropical coordinates.
Skeleton clustering detects clusters in high-dimensional data without needing prototypes.
Although consistency is a minimum requirement of any estimator, little is known about consistency of the mean partition approach in consensus clustering. This contribution studies the asymptotic behavior of mean partitions. We show that under normal assumptions, the mean partition approach is consistent and asymptotic …
Unified framework for various geometric constructions.
Root Laplacian Eigenmaps help in spectral embedding of graphs.
We introduce the {\it diffusion -means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion -means constructs a random walk on the similarity graph with vertices as data points randomly sampled on the manifolds and edges as …
This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance how many subspaces there are nor do we have any information about their dimension…
With inspiration from Random Forests (RF) in the context of classification, a new clustering ensemble method---Cluster Forests (CF) is proposed. Geometrically, CF randomly probes a high-dimensional data cloud to obtain "good local clusterings" and then aggregates via spectral clustering to obtain cluster assignments fo…
Quantum cluster algebras for surfaces with coefficients defined using skein theory.
In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given group. Algebraically, such group-invariant subspaces are also referred to as su…
Agglomerative hierarchical clustering can be implemented with several strategies that differ in the way elements of a collection are grouped together to build a hierarchy of clusters. Here we introduce versatile linkage, a new infinite system of agglomerative hierarchical clustering strategies based on generalized mean…
Training generative models like Generative Adversarial Network (GAN) is challenging for noisy data. A novel curriculum learning algorithm pertaining to clustering is proposed to address this issue in this paper. The curriculum construction is based on the centrality of underlying clusters in data points. The data point…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it receives level set estimates from a kernel density estimator. In particular, we derive…
For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, we construct a geometric realization in terms of suitable decorated Teichmueller space of the surface. On the geometric side, this requires opening the surface at each interior marked point into an addit…
Develops TCD maps to relate discrete differential geometry and cluster algebras.
Geometric approach clusters intersecting manifolds with high probability.
MCBP detects boundaries in high-dimensional data using curvature.
The paper introduces curvature-based clustering algorithms for graph analysis.
A new hybrid fuzzy-crisp clustering algorithm addresses imbalanced cluster sizes.
A new clustering method estimates non-linear boundaries and automatically selects the number of clusters.
A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a nonlinear NMF with explicit orthogonality and derive general kernel-based orthogonal m…
Multiple clustering aims at discovering diverse ways of organizing data into clusters. Despite the progress made, it's still a challenge for users to analyze and understand the distinctive structure of each output clustering. To ease this process, we consider diverse clusterings embedded in different subspaces, and ana…
The paper presents a method for analyzing shape graphs using specific features.
We propose clustering algorithms based on a recently developed geometric digraph family called cluster catch digraphs (CCDs). These digraphs are used to devise clustering methods that are hybrids of density-based and graph-based clustering methods. CCDs are appealing digraphs for clustering, since they estimate the num…
We construct invariants of four-dimensional piecewise-linear manifolds, represented as simplicial complexes, with respect to rebuildings that transform a cluster of three 4-simplices having a common two-dimensional face in a different cluster of the same type and having the same boundary. Our construction is based on t…