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.
Quantum theory improves counting overlapping clusters.
Study connects Morse theory with cluster variables for wall-crossing in Cerf diagrams.
Jones polynomials derived from K-theory of a cluster algebra.
iCVI-ARTMAP accelerates clustering with adaptive resonance theory and validity indices.
New theory for clustering in geometric and adaptive settings.
The Wisdom of Crowds (WOC), as a theory in the social science, gets a new paradigm in computer science. The WOC theory explains that the aggregate decision made by a group is often better than those of its individual members if specific conditions are satisfied. This paper presents a novel framework for unsupervised an…
We propose a novel method for clustering data which is grounded in information-theoretic principles and requires no parametric assumptions. Previous attempts to use information theory to define clusters in an assumption-free way are based on maximizing mutual information between data and cluster labels. We demonstrate …
Quantum cluster algebras for surfaces with coefficients defined using skein theory.
The paper connects Legendrian links to cluster theory and exact Lagrangian fillings.
We classify elements of a cluster modular group into three types. We characterize them in terms of fixed point property of the action on the tropical compactifications associated with the corresponding cluster ensemble. The characterization gives an analogue of the Nielsen-Thurston classification theory on the mapping …
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…
Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by developing a probabilistic framework based on the theory of random labeled point…
This paper analyzes various graph clustering methods and their applications.
New link polynomials linked to cluster theory.
Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on this theory, we demonstrate the efficiency of Subspace Clustering in fairly broad…
New method uses dendrograms for better mixture model selection and clustering.
An adaptive clustering algorithm learns from evolving data without manual tuning.
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…
The paper develops a Galois theory for cluster algebras and Riemann surfaces.
Study of Legendrian links using Floer theory and cluster varieties.
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…
It is proved that the K_0-group of a cluster C*-algebra is isomorphic to the corresponding cluster algebra. As a corollary, one gets a shorter proof of the positivity conjecture for cluster algebras. As an example, we consider a cluster C*-algebra A(1,1) coming from triangulation of an annulus with one marked point on …
The paper connects knot theory and cluster algebras via dimer face polynomials.
Develops clustering methods based on likelihood and convergence proved.
Solves Riemann-Hilbert problems on surface triangulations.
This work draws inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping clustering of Jardine and Sibson, the functorial approach of Carlsson and Mémoli to par…
Adjusted for chance measures are widely used to compare partitions/clusterings of the same data set. In particular, the Adjusted Rand Index (ARI) based on pair-counting, and the Adjusted Mutual Information (AMI) based on Shannon information theory are very popular in the clustering community. Nonetheless it is an open …
New concept of mixture complexity helps detect gradual clustering changes.
Study finds the cutoff for exact recovery in Gaussian mixture models.
Transformers learn to cluster Gaussian mixtures as well as the EM algorithm.
The paper addresses uncertainties in spectral clustering of corrupted data.
The paper connects Legendrian links to cluster algebras via microlocal methods.
Spectral clustering identifies clusters of multivariate extremes.
A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found using mean-shift algorithms. We describe the theory and practice behind clustering…
Machine learning predicts liquid water properties from cluster data.
Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern Recognition, CVPR (2009) 2790-27…
New algorithm clusters GRBs into two groups: short and long duration.
We focus on spectral clustering of unlabeled graphs and review some results on clustering methods which achieve weak or strong consistent identification in data generated by such models. We also present a new algorithm which appears to perform optimally both theoretically using asymptotic theory and empirically.
The R Package CEC performs clustering based on the cross-entropy clustering (CEC) method, which was recently developed with the use of information theory. The main advantage of CEC is that it combines the speed and simplicity of -means with the ability to use various Gaussian mixture models and reduce unnecessary cl…
In this work we develop a theory of hierarchical clustering for graphs. Our modeling assumption is that graphs are sampled from a graphon, which is a powerful and general model for generating graphs and analyzing large networks. Graphons are a far richer class of graph models than stochastic blockmodels, the primary se…
The paper proposes a new portfolio allocation method combining RMT and machine learning.
DMFAW improves multi-view clustering with adaptive weights and feature selection.
Motivated by social balance theory, we develop a theory of link classification in signed networks using the correlation clustering index as measure of label regularity. We derive learning bounds in terms of correlation clustering within three fundamental transductive learning settings: online, batch and active. Our mai…
New method clusters large datasets using geometric properties.
Tangles improve clustering in various datasets.
Kleinberg introduced three natural clustering properties, or axioms, and showed they cannot be simultaneously satisfied by any clustering algorithm. We present a new clustering property, Monotonic Consistency, which avoids the well-known problematic behaviour of Kleinberg's Consistency axiom, and the impossibility resu…
New method preserves spectral clustering performance under aggressive sparsification and quantization.
New insights into spectral clustering reveal strong connections within eigenvectors.