arXiv research

New method clusters non-spherical Gaussian mixtures with fewer samples and time.

Proposes a new clustering method based on expectiles for non-spherical clusters.

We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical Gaussian components, where the clusters are distinguished by only a few relevant dimens…

Identifying a set of homogeneous clusters in a heterogeneous dataset is one of the most important classes of problems in statistical modeling. In the realm of unsupervised partitional clustering, k-means is a very important algorithm for this. In this technical report, we develop a new k-means variant called Augmented …

Generalizes string-net modular functors to non-spherical categories.

A string-net model associates a vector space to a surface in terms of graphs decorated by objects and morphisms of a pivotal fusion category modulo local relations. String-net models are usually considered for spherical fusion categories, and in this case the vector spaces agree with the state spaces of the correspondi…

Robustly clusters mixtures of Gaussians even with outliers.

Study perturbs mean curvature flow near non-spherical shrinkers.

Deep neural networks are a family of computational models that have led to a dramatical improvement of the state of the art in several domains such as image, voice or text analysis. These methods provide a framework to model complex, non-linear interactions in large datasets, and are naturally suited to the analysis of…

We use purely topological methods to prove the semicontinuity of the mod 2 spectrum of local isolated hypersurface singularities in $\mathbb{C}^{n+1}$, using Seifert forms of high-dimensional non-spherical links, the Levine--Tristram signatures and the generalized Murasugi--Kawauchi inequality obtained in earlier work …

It is shown that the qc Yamabe problem has a solution on any compact qc manifold which is non-locally qc equivalent to the standard 3-Sasakian sphere. Namely, it is proved that on a compact non-locally spherical qc manifold there exists a qc conformal qc structure with constant qc scalar curvature

New solutions for soft materials' nonlinear behavior in growing spheroidal inclusions.

Researchers set entropy limits for specific types of self-shrinkers.

The horizon and geodesic structure of static configurations generated by anisotropic conformal transforms of the Schwarzschild metric is analyzed. We construct the maximal analytic extension of such off--diagonal vacuum metrics and conclude that for small deformations there are different classes of vacuum solutions of …

Study on naked singularities without symmetry, forming incomplete future null infinity and singular inner Cauchy horizon.

Paper proves Łojasiewicz inequalities near simple bubble trees on surfaces.

Study shows instability of naked singularities in perfect fluid models.

Algorithm distinguishes Gaussian mixtures from pure Gaussians in quasi-polynomial time.

The paper proves smoothness of mean curvature flow for generic initial data in 3D and 4D.

We solve the dynamics of large spherical Minority Games (MG) in the presence of non-negligible time dependent external contributions to the overall market bid. The latter represent the actions of market regulators, or other major natural or political events that impact on the market. In contrast to non-spherical MGs, t…

Estimates shared linear subspace from noisy data with multiple users.

We construct large families of initial data sets for the vacuum Einstein equations with positive cosmological constant which contain exactly Delaunay ends; these are non-trivial initial data sets which coincide with those for the Kottler-Schwarzschild-de Sitter metrics in regions of infinite extent. From the purely Rie…

We solve Einstein vacuum equations in a spacetime region up to the "center" of gravitational collapse. Within this region, we construct a sequence of marginally outer trapped surfaces (MOTS) with areas going to zero. These MOTS form a marginally outer trapped tube (apparent horizon). It emerges from a point and is smoo…

Matveev and Piergallini independently showed that, with a small number of known exceptions, any triangulation of a three-manifold can be transformed into any other triangulation of the same three-manifold with the same number of vertices, via a sequence of 2-3 and 3-2 moves. We can interpret this as showing that the Pa…

We prove a homological version of a conjecture about the homotopy type of diffeomorphism spaces of reducible 3-manifolds.

New PL-invariants defined for 4-manifolds with boundary.

Classifies low-energy harmonic maps from curved surfaces to spheres.

Two classification results for stationary surfaces of least moment of inertia.

We study Riemannian metrics on compact, torsionless, non-geometric $3$-manifolds, i.e. whose interior does not support any of the eight model geometries. We prove a lower bound "à la Margulis" for the systole and a volume estimate for these manifolds, only in terms of an upper bound of entropy and diameter. We then ded…

The so-called Mom-structures on hyperbolic cusped 3-manifolds without boundary were introduced by Gabai, Meyerhoff, and Milley, and used by them to identify the smallest closed hyperbolic manifold. In this work we extend the notion of a Mom-structure to include the case of 3-manifolds with non-empty boundary that does …

Polynomial-time algorithm for estimating covariance in corrupted Gaussian data.

A representation for compact 3-manifolds with non-empty non-spherical boundary via 4-colored graphs (i.e., 4-regular graphs endowed with a proper edge-coloration with four colors) has been recently introduced by two of the authors, and an initial classification of such manifolds has been obtained up to 8 vertices of th…

Study of CR twistor model $Q^{2,2}$ and its sections.

The paper explores properties of CR hypersurfaces and their flatness.

Constructs initial data leading to apparent horizons and tests Penrose Inequality.

Improved estimation of concentration using half-spaces for adversarial vulnerability.

Positive mass theorem for tori with scalar curvature bounds.

Convex clustering can only learn convex clusters, with significant gaps between clusters.

CCMM efficiently solves large-scale convex clustering problems.

A multi-neck spacetime wormhole is constructed with a simple metric tensor.

Discussing issues in robust clustering, especially with Gaussian models.

New indices for determining cluster compactness and separability.

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 …

Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. For most applications, applying clustering is only appropriate when cluster structure is present. As such, the study of clusterability, which evaluates whether data possesses such structure, is an integral part of clus…

In this paper, a similarity-driven cluster merging method is proposed for unsuper-vised fuzzy clustering. The cluster merging method is used to resolve the problem of cluster validation. Starting with an overspecified number of clusters in the data, pairs of similar clusters are merged based on the proposed similarity-…

Clustering ensemble, or consensus clustering, has emerged as a powerful tool for improving both the robustness and the stability of results from individual clustering methods. Weighted clustering ensemble arises naturally from clustering ensemble. One of the arguments for weighted clustering ensemble is that elements (…

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…

Study examines how cluster number affects short-text clustering, introducing a stability metric.