arXiv research

Study connects Morse theory with cluster variables for wall-crossing in Cerf diagrams.

This study considers that the collective route choices of travelers en route represent a resolution of their competition on network routes. Well understanding this competition and coordinating their route choices help mitigate urban traffic congestion. Even though existing studies have developed such mechanisms (e.g., …

Geometric model of unbounded sl3 laminations with tropical coordinates.

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…

Concept Factorization (CF) and its variants may produce inaccurate representation and clustering results due to the sensitivity to noise, hard constraint on the reconstruction error and pre-obtained approximate similarities. To improve the representation ability, a novel unsupervised Robust Flexible Auto-weighted Local…

Characterizes pseudo-Anosov mapping classes using cluster algebra techniques.

New spectral clustering method for graphs with uneven node degrees.

Natural coordinates for SL3-webs on surfaces are shown to be consistent under triangulation changes.

To answer the existence of optimal swimmer learning/teaching strategies, this work introduces a two-level clustering in order to analyze temporal dynamics of motor learning in breaststroke swimming. Each level have been performed through Sparse Fisher-EM, a unsupervised framework which can be applied efficiently on lar…

Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and partially observed signals respectively. We combine the distance preserving measur…

Paper tackles Byzantine attacks in Federated Learning by clustering and robustifying.

We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow …

High dimensional data often contain multiple facets, and several clustering patterns can co-exist under different variable subspaces, also known as the views. While multi-view clustering algorithms were proposed, the uncertainty quantification remains difficult --- a particular challenge is in the high complexity of es…

This paper proposes a decentralized reinforcement learning method for multi-agent resource allocation.

Robustly computes intrinsic coordinates on point clouds using resampling and averaging.

Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms and implementations are critical to efficiently solving these problems. Building…

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 meaningfulness is more prominent (e.g. the Euclidean distance between images). In this…

Unified 3D R-matrices from quantum cluster algebra.

In this paper we develop and analyze Hydra: HYbriD cooRdinAte descent method for solving loss minimization problems with big data. We initially partition the coordinates (features) and assign each partition to a different node of a cluster. At every iteration, each node picks a random subset of the coordinates from tho…

Complete construction for Lie groups of types F4, E6, E7, E8.

We show that the Borel sums of the Voros symbols considered in the theory of exact WKB analysis arise naturally as Fock-Goncharov coordinates of framed $PGL_2(\mathbb{C})$-local systems on a marked bordered surface. Using this result, we show that these Borel sums can be meromorphically continued to any point of $\math…

Real-time advertising allows advertisers to bid for each impression for a visiting user. To optimize specific goals such as maximizing revenue and return on investment (ROI) led by ad placements, advertisers not only need to estimate the relevance between the ads and user's interests, but most importantly require a str…

Integrable dynamics explained via geometric maps and cluster algebras.

We propose a penalized likelihood method to jointly estimate multiple precision matrices for use in quadratic discriminant analysis and model based clustering. A ridge penalty and a ridge fusion penalty are used to introduce shrinkage and promote similarity between precision matrix estimates. Block-wise coordinate desc…

We introduce coordinates on the spaces of framed and decorated representations of the fundamental group of a surface with nonempty boundary into the symplectic group $Sp(2n,\mathbf R)$. These coordinates provide a noncommutative generalization of the parametrizations of the spaces of representations into $SL(2,\mathbf …

Meta clustering categorizes learners for collaborative learning.

We describe the Fast Greedy Sparse Subspace Clustering (FGSSC) algorithm providing an efficient method for clustering data belonging to a few low-dimensional linear or affine subspaces. The main difference of our algorithm from predecessors is its ability to work with noisy data having a high rate of erasures (missed e…

Interprets SL3-web intersections on surfaces.

BIGUE algorithm provides credible intervals for hyperbolic network embeddings.

We define new coordinates for Fock-Goncharov's higher Teichmüller spaces for a surface with holes, which are the moduli spaces of representations of the fundamental group into a reductive Lie group $G$. Some additional data on the boundary leads to two closely related moduli spaces, the $\mathscr{X}$-space and the $\ma…

Given a similarity graph between items, correlation clustering (CC) groups similar items together and dissimilar ones apart. One of the most popular CC algorithms is KwikCluster: an algorithm that serially clusters neighborhoods of vertices, and obtains a 3-approximation ratio. Unfortunately, KwikCluster in practice re…

K-means clustering improved for robustness to outliers and distribution shifts.

Selective clustering annotated using modes of projections (SCAMP) is a new clustering algorithm for data in $\mathbb{R}^p$. SCAMP is motivated from the point of view of non-parametric mixture modeling. Rather than maximizing a classification likelihood to determine cluster assignments, SCAMP casts clustering as a searc…

Notwithstanding the popularity of conventional clustering algorithms such as K-means and probabilistic clustering, their clustering results are sensitive to the presence of outliers in the data. Even a few outliers can compromise the ability of these algorithms to identify meaningful hidden structures rendering their o…

Many powerful machine learning models are based on the composition of multiple processing layers, such as deep nets, which gives rise to nonconvex objective functions. A general, recent approach to optimise such "nested" functions is the method of auxiliary coordinates (MAC). MAC introduces an auxiliary coordinate for …

Orthogonal Matching Pursuit (OMP) plays an important role in data science and its applications such as sparse subspace clustering and image processing. However, the existing OMP-based approaches lack of data adaptiveness so that the data cannot be represented well enough and may lose the accuracy. This paper proposes a…

Clusterpath estimator simplifies graphical model interpretation for large datasets.

Given a symmetric nonnegative matrix $A$, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix $H$, usually with much fewer columns than $A$, such that $A \approx HH^T$. SymNMF can be used for data analysis and in particular for various clustering tasks. In this paper, we p…

Analysis of 'big data' characterized by high-dimensionality such as word vectors and complex networks requires often their representation in a geometrical space by embedding. Recent developments in machine learning and network geometry have pointed out the hyperbolic space as a useful framework for the representation o…

We propose a method for estimating coefficients in multivariate regression when there is a clustering structure to the response variables. The proposed method includes a fusion penalty, to shrink the difference in fitted values from responses in the same cluster, and an L1 penalty for simultaneous variable selection an…

Bracelets and theta bases match in various cluster algebras.

We recall the fat-graph description of Riemann surfaces $Σ_{g,s,n}$ and the corresponding Teichmüller spaces $\mathfrak T_{g,s,n}$ with $s>0$ holes and $n>0$ bordered cusps in the hyperbolic geometry setting. If $n>0$, we have a bijection between the set of Thurston shear coordinates and Penner's $λ$-lengths and we can…

Ankle sprains and instability are major public health concerns. Up to 70% of individuals do not fully recover from a single ankle sprain and eventually develop chronic ankle instability (CAI). The diagnosis of CAI has been mainly based on self-report rather than objective biomechanical measures. The goal of this study …

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…

Online retail, eCommerce, frequently falls victim to fraud conducted by malicious customers (fraudsters) who obtain goods or services through deception. Fraud coordinated by groups of professional fraudsters that place several fraudulent orders to maximize their gain is referred to as organized fraud. Existing approach…

A new FL algorithm reduces communication overhead by selectively updating model parameters.

Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often results in challenging high-dimensional estimation problems where only a minority of t…

The paper connects knot theory and cluster algebras via dimer face polynomials.