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.
Study of Legendrian links using Floer theory and cluster varieties.
We use Bonahon-Wong's trace map to study character varieties of the once-punctured torus and of the 4-punctured sphere. We clarify a relationship with cluster algebra associated with ideal triangulations of surfaces, and we show that the Goldman Poisson algebra of loops on surfaces is recovered from the Poisson structu…
The paper connects Legendrian links to cluster theory and exact Lagrangian fillings.
Cluster varieties are geometric objects that have recently found applications in several areas of mathematics and mathematical physics. This thesis studies the geometry of a large class of cluster varieties associated to compact oriented surfaces with boundary. The main original contribution of this thesis is to develo…
A positive space is a space with a positive atlas, i.e. a collection of rational coordinate systems with subtraction free transition functions. The set of positive real points of a positive space is well defined. We define a tropical compactification of the latter. We show that it generalizes the Thurston compactificat…
We consider two interesting spaces associated to a quiver with potential: a space of stability conditions and a cluster variety. In the case where the quiver with potential arises from an ideal triangulation of a marked bordered surface, we construct a natural map from a dense subset of the space of stability condition…
We describe a natural -deformation of Fock and Goncharov's canonical basis for the algebra of regular functions on a cluster variety associated to a quiver of type . We then describe an extension of this construction involving a cluster variety called the symplectic double.
We define a canonical map from a certain space of laminations on a punctured surface into the quantized algebra of functions on a cluster variety. We show that this map satisfies a number of special properties conjectured by Fock and Goncharov. Our construction is based on the "quantum trace" map introduced by Bonahon …
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density estimator. This paper addresses the basic question of quantifying our uncertainty by ass…
A cluster variety of Fock and Goncharov is a scheme constructed from the data related to the cluster algebras of Fomin and Zelevinsky. A seed is a combinatorial data which can be encoded as an matrix with integer entries, or as a quiver in special cases, together with formal variables. A mutation is a c…
Large multi-tenant production clusters often have to handle a variety of jobs and applications with a variety of complex resource usage characteristics. It is non-trivial and non-optimal to manually create placement rules for scheduling that would decide which applications should co-locate. In this paper, we present De…
Many interesting spaces --- including all positroid strata and wild character varieties --- are moduli of constructible sheaves on a surface with microsupport in a Legendrian link. We show that the existence of cluster structures on these spaces may be deduced in a uniform, systematic fashion by constructing and taking…
The paper proposes a parallelizable clustering method for multivariate data.
Research connects geometric structures to knot theory and algebraic combinatorics.
Study connects Morse theory with cluster variables for wall-crossing in Cerf diagrams.
The paper constructs bases for cluster varieties using -webs and laminations.
Bracelets and theta bases match in various cluster algebras.
Proves conjecture linking cluster algebras and skein algebras for surfaces with punctures.
PEA improves PCA and k-means for non-linear data and complex clusters.
The paper connects knot theory and cluster algebras via dimer face polynomials.
A Bernoulli Mixture Model (BMM) is a finite mixture of random binary vectors with independent dimensions. The problem of clustering BMM data arises in a variety of real-world applications, ranging from population genetics to activity analysis in social networks. In this paper, we analyze the clusterability of BMMs from…
In many practical applications of clustering, the objects to be clustered evolve over time, and a clustering result is desired at each time step. In such applications, evolutionary clustering typically outperforms traditional static clustering by producing clustering results that reflect long-term trends while being ro…
Cluster analysis is widely used in the areas of machine learning and data mining. Fuzzy clustering is a particular method that considers that a data point can belong to more than one cluster. Fuzzy clustering helps obtain flexible clusters, as needed in such applications as text categorization. The performance of a clu…
New method fills cluster seeds with exact Lagrangian structures.
In this paper, we propose a model-based clustering method (TVClust) that robustly incorporates noisy side information as soft-constraints and aims to seek a consensus between side information and the observed data. Our method is based on a nonparametric Bayesian hierarchical model that combines the probabilistic model …
We perform a large-scale analysis of language diatopic variation using geotagged microblogging datasets. By collecting all Twitter messages written in Spanish over more than two years, we build a corpus from which a carefully selected list of concepts allows us to characterize Spanish varieties on a global scale. A clu…
The paper generalizes Thurston's earthquake map to cluster algebras of finite type.
Cluster analysis methods seek to partition a data set into homogeneous subgroups. It is useful in a wide variety of applications, including document processing and modern genetics. Conventional clustering methods are unsupervised, meaning that there is no outcome variable nor is anything known about the relationship be…
BalLOT uses optimal transport for balanced k-means clustering.
Geometric model of unbounded sl3 laminations with tropical coordinates.
Clustering is an extensive research area in data science. The aim of clustering is to discover groups and to identify interesting patterns in datasets. Crisp (hard) clustering considers that each data point belongs to one and only one cluster. However, it is inadequate as some data points may belong to several clusters…
New method clusters hypergraphs using weighted random walks and Laplacians.
Convex clustering, a convex relaxation of k-means clustering and hierarchical clustering, has drawn recent attentions since it nicely addresses the instability issue of traditional nonconvex clustering methods. Although its computational and statistical properties have been recently studied, the performance of convex c…
Quantizes moduli space of 3D gravity metrics.
Detecting stellar clusters have always been an important research problem in Astronomy. Although images do not convey very detailed information in detecting stellar density enhancements, we attempt to understand if new machine learning techniques can reveal patterns that would assist in drawing better inferences from t…
We introduce a novel end-to-end approach for learning to cluster in the absence of labeled examples. Our clustering objective is based on optimizing normalized cuts, a criterion which measures both intra-cluster similarity as well as inter-cluster dissimilarity. We define a differentiable loss function equivalent to th…
We describe a probabilistic (generative) view of affinity matrices along with inference algorithms for a subclass of problems associated with data clustering. This probabilistic view is helpful in understanding different models and algorithms that are based on affinity functions OF the data. IN particular, we show how(…
Paper introduces scalable clustering for large datasets with outliers.
Study of quantum decorated character stacks and their quantizations.
Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density. Leveraging on properties of pairwise differences between data points, we propose a…
Community detection is a fundamental unsupervised learning problem for unlabeled networks which has a broad range of applications. Many community detection algorithms assume that the number of clusters is known apriori. In this paper, we propose an approach based on semi-definite relaxations, which does not require…
Unsupervised clustering of curves according to their shapes is an important problem with broad scientific applications. The existing model-based clustering techniques either rely on simple probability models (e.g., Gaussian) that are not generally valid for shape analysis or assume the number of clusters. We develop an…
Develops a framework for consistent clustering algorithm benchmarking.
Characterizes pseudo-Anosov mapping classes on general marked surfaces.
We consider the stochastic multi-armed bandit problem and the contextual bandit problem with historical observations and pre-clustered arms. The historical observations can contain any number of instances for each arm, and the pre-clustering information is a fixed clustering of arms provided as part of the input. We de…
Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input. Dirichlet process mixture models are appealing as they can infer the number of clu…
Adapts manifold structure for better clustering performance.
A cluster variety of Fock and Goncharov is a scheme constructed by gluing split algebraic tori, called seed tori, via birational gluing maps called mutations. In quantum theory, the ring of functions on seed tori are deformed to non-commutative rings, represented as operators on Hilbert spaces. Mutations are quantized …