arXiv research

Develops a new weighted Laplacian method for graph problems.

Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced $k$-cut of the graph, are either based on greedy techniques or heuristics which have weak connection to th…

It has been recently shown that a large class of balanced graph cuts allows for an exact relaxation into a nonlinear eigenproblem. We review briefly some of these results and propose a family of algorithms to compute nonlinear eigenvectors which encompasses previous work as special cases. We provide a detailed analysis…

Paper provides a performance guarantee for spectral clustering.

Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data since they tend to emphasize cut sizes over cut values. We propose a graph partit…

Let φ(G) be the minimum conductance of an undirected graph G, and let 0=λ_1 <= λ_2 <=... <= λ_n <= 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k >= 2, φ(G) = O(k) λ_2 / \sqrt{λ_k}, and this performance guarantee is achieved by the spectral partitioning algorithm. …

Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced cluster sizes sin…

New Karger-like algorithms solve graph cuts, useful for image segmentation.

A novel hypergraph partitioning method using tensor eigenvalue decomposition captures super-dyadic interactions.

Study shows convergence rates for Cheeger cuts on data clouds.

New 2-spheres of revolution with simple cut locus structures.

New algorithm for multiway spectral clustering on Grassmann manifolds.

When it comes to clustering nonconvex shapes, two paradigms are used to find the most suitable clustering: minimum cut and maximum density. The most popular algorithms incorporating these paradigms are Spectral Clustering and DBSCAN. Both paradigms have their pros and cons. While minimum cut clusterings are sensitive t…

We determine the minimum number of vertices needed to provide balanced triangulations of $\mathbb S^{d-2}$-bundles over $\mathbb S^1$. If $d$ is odd and the bundle is orientable, or $d$ is even and the bundle is non-orientable, the minimum number of vertices is $3d$; otherwise, it is $3d+2$. Similar results apply to al…

We study the problem of partitioning a small sample of $n$ individuals from a mixture of $k$ product distributions over a Boolean cube $\{0, 1\}^K$ according to their distributions. Each distribution is described by a vector of allele frequencies in $\R^K$. Given two distributions, we use $γ$ to denote the average $\el…

Graph cuts find global optima for Potts models in slight perturbations.

Paper studies gradient fields from discrete Morse functions for watershed-cut computation.

New algorithm solves large cardinality-constrained clustering problems.

Disk pairings with zero signature are related to topological surfaces.

Study optimal adjustment sets for causal policies with hidden variables.

Paper proposes quantum methods for optimizing machine learning functions.

Optimizes balanced treatment assignment for experiments.

This paper studies the large sample asymptotics of data analysis procedures based on the optimization of functionals defined on $k$-NN graphs on point clouds. The paper is framed in the context of minimization of balanced cut functionals, but our techniques, ideas and results can be adapted to other functionals of rele…

The paper optimizes spatial experimental designs to improve causal effect estimation.

Paper simplifies balancing weights by relaxing outcome assumptions.

Optimal student loan repayment strategies vary based on loan size.

Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, $ε$-graphs and $k$-NN graphs can lead to poor performance in the presence of proximal and unbalanced data. This is because spectral methods based…

This work proposes an adaptive trace lasso regularized L1-norm based graph cut method for dimensionality reduction of Hyperspectral images, called as `Trace Lasso-L1 Graph Cut' (TL-L1GC). The underlying idea of this method is to generate the optimal projection matrix by considering both the sparsity as well as the corr…

OCmst detects anomalies using CNN features and MSTs.

One of the main issues affecting the Italian NHS is the healthcare deficit: according to current agreements between the Italian State and its Regions, public funding of regional NHS is now limited to the amount of regional deficit and is subject to previous assessment of strict adherence to constraint on regional healt…

We provide a new proof of a result of X.X.Chen and G.Tian : for a polarized extremal Kähler manifold, an extremal metric attains the minimum of the modified K-energy. The proof uses an idea of C.Li adapted to the extremal metrics using some weighted balanced metrics.

A well-known Lemma in Riemannian geometry by Klingenberg says that if $x_0$ is a minimum point of the distance function $d(p,\cdot)$ to $p$ in the cut locus $C_p$ of $p$, then either there is a minimal geodesic from $p$ to $x_0$ along which they are conjugate, or there is a geodesic loop at $p$ that smoothly goes throu…

This paper studies knots in sutured manifolds achieving minimum instanton homology rank.

New algorithm tackles high-dimensional contextual bandits without sparsity.

Unified framework for PDF estimation using MDL-based binning and tensor factorization.

In Minkowski geometry the unit ball is a compact convex body $K$ containing the origin in its interior. The boundary of the body is formed by the unit vectors. We also have a so-called Minkowski functional to measure the length of vectors. By changing the origin in the interior of the body we have a smoothly varying fa…

A new classifier improves one-class predictions on unevenly sampled data.

Novel technique reduces Bayesian network complexity while preserving inference accuracy.

A method is given for calculating the strict minimum message length (SMML) estimator for 1-dimensional exponential families with continuous sufficient statistics. A set of $n$ equations are found that the $n$ cut-points of the SMML estimator must satisfy. These equations can be solved using Newton's method and this app…

A new algorithm solves semidefinite programs using Langevin diffusion.

Proposes a new graph trend filtering model for inhomogeneous graph signals.

CBDA improves active learning for semantic segmentation, especially with imbalanced classes.

Random walk constructs Morse functions on surfaces.

SCORE technique reduces BO's high-dimensional search costs.

Improves scalability of Bayesian optimization for combinatorial spaces.

NeuralCut learns to select cutting planes by looking ahead, outperforming traditional methods.

Differentiable cutting-plane layers solve parametric mixed-integer linear optimization problems.

NeVI-Cut uses neural networks to efficiently propagate uncertainty without feedback.