arXiv research

Bayesian approach for multifile record linkage and duplicate detection.

The study limits how many parts regular simplicial partitions can overlap.

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received …

In this paper, we propose a family of graph partition similarity measures that take the topology of the graph into account. These graph-aware measures are alternatives to using set partition similarity measures that are not specifically designed for graph partitions. The two types of measures, graph-aware and set parti…

The study examines the balancedness of random partition models and finds the rich-get-richer characteristic is a result of model assumptions.

The paper develops mixed-integer formulations for neural networks using partitioning.

New partition designs reduce star discrepancy in high-dimensional sampling.

The paper constructs Markov partitions for geodesic flow on hyperbolic surfaces.

Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including variants of multi-level methods and spectral clustering. We propose GAP, a Generaliz…

Survey of mass partition problems in geometry and topology.

New method unifies and formalizes data partitioning using a single vector.

Locally isoperimetric partitions minimize perimeter in space.

Online BSP-Forest improves space partitioning for large-scale classification and regression.

Space partitions of $\mathbb{R}^d$ underlie a vast and important class of fast nearest neighbor search (NNS) algorithms. Inspired by recent theoretical work on NNS for general metric spaces [Andoni, Naor, Nikolov, Razenshteyn, Waingarten STOC 2018, FOCS 2018], we develop a new framework for building space partitions re…

Study of Torelli groups of partitioned surfaces with bounds and asymptotic lengths.

Efficiently calculates PL model likelihood for partitioned preference data.

We argue that the standard graph Laplacian is preferable for spectral partitioning of signed graphs compared to the signed Laplacian. Simple examples demonstrate that partitioning based on signs of components of the leading eigenvectors of the signed Laplacian may be meaningless, in contrast to partitioning based on th…

New proof of a unique 3-part partition in 8D space.

Paper recovers lattice signal partitions efficiently.

Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different p…

We prove that the least-perimeter partition of the sphere into four regions of equal area is a tetrahedral partition.

Maps discrete manifolds to partitions to define new manifolds.

Standard bubbles and partitions are stable in various model spaces.

To devise efficient solutions for approximating a mean partition in consensus clustering, Dimitriadou et al. [3] presented a necessary condition of optimality for a consensus function based on least square distances. We show that their result is pivotal for deriving interesting properties of consensus clustering beyond…

Algorithms learn and test variable partitions in various groups and error metrics.

This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or tertiary predictors and allows the number of predictors to exceed the size of the sa…

The study explores continuous noncrossing partitions and their relation to weighted circular factorizations.

Proves an Euler-type formula for Möbius strip partitions.

Although consistency is a minimum requirement of any estimator, little is known about consistency of the mean partition approach in consensus clustering. This contribution studies the asymptotic behavior of mean partitions. We show that under normal assumptions, the mean partition approach is consistent and asymptotic …

Homology of partition algebras matches symmetric group homology under certain conditions.

Both supervised and unsupervised machine learning algorithms have been used to learn partition-based index structures for approximate nearest neighbor (ANN) search. Existing supervised algorithms formulate the learning task as finding a partition in which the nearest neighbors of a training set point belong to the same…

Topological recursion recovers a specific partition function for colored knots.

New model of vague knowledge without strict partitions or transitivity.

Stochastic partition models divide a multi-dimensional space into a number of rectangular regions, such that the data within each region exhibit certain types of homogeneity. Due to the nature of their partition strategy, existing partition models may create many unnecessary divisions in sparse regions when trying to d…

This thesis classifies pseudo-Anosov homeomorphisms using geometric Markov partitions.

POUnets combine partitions of unity and monomials for efficient deep learning.

Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of regions and region-specific models. This paper proposes novel convex region-specific…

Study on detecting hierarchical community structures in networks.

Proposes SPFB method for optimizing partition functions in stochastic learning.

Bayesian nonparametric method partitions shapes using curves.

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit using distributed algorithms. The dataset can be partitioned either horizontally (i…

Extends partitioned local depth concept with probabilistic considerations.

In this paper we relate the partition function to the max-statistics of random variables. In particular, we provide a novel framework for approximating and bounding the partition function using MAP inference on randomly perturbed models. As a result, we can use efficient MAP solvers such as graph-cuts to evaluate the c…

We investigate the minimal number of links and knots in complete partite graphs. We provide exact values or bounds on the minimal number of links for all complete partite graphs with all but 4 vertices in one partition, or with 9 vertices in total. In particular, we find that the minimal number of links for $K_{4,4,1}$…

Study on optimal partitions and nodal solutions for the Yamabe equation.

Recently, locality sensitive hashing (LSH) was shown to be effective for MIPS and several algorithms including $L_2$-ALSH, Sign-ALSH and Simple-LSH have been proposed. In this paper, we introduce the norm-range partition technique, which partitions the original dataset into sub-datasets containing items with similar 2-…

Condorcet's Jury Theorem has been invoked for ensemble classifiers to indicate that the combination of many classifiers can have better predictive performance than a single classifier. Such a theoretical underpinning is unknown for consensus clustering. This article extends Condorcet's Jury Theorem to the mean partitio…

Improved neural network robustness certification through tighter convex relaxations.