SIAM Journal on Applied Algebra and Geometry最新文献_第4页

The Maximum Likelihood Degree of Sparse Polynomial Systems 稀疏多项式系统的最大似然度

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-05-16 DOI: 10.1137/21m1422550

J. Lindberg, Nathan Nicholson, J. Rodriguez, Zinan Wang

引用次数: 3

On the Central Path of Semidefinite Optimization: Degree and Worst-Case Convergence Rate 半确定优化的中心路径:程度和最坏情况下的收敛速度

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-05-14 DOI: 10.1137/21m1419933

S. Basu, Ali Mohammad Nezhad

引用次数: 2

Galois/monodromy groups for decomposing minimal problems in 3D reconstruction 三维重建中分解最小问题的伽罗瓦/单群

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-05-10 DOI: 10.1137/21m1422872

Timothy Duff, Viktor Korotynskiy, T. Pajdla, Margaret H. Regan

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引用次数: 11

Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sums maxout网络的区域数目和Minkowski和的顶点数目的尖锐界限

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-04-16 DOI: 10.1137/21m1413699

Guido Montúfar, Yue Ren, Leon Zhang

引用次数: 23

Symmetry Reduction to Optimize a Graph-based Polynomial From Queueing Theory 基于排队论优化图多项式的对称约简

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-04-16 DOI: 10.1137/21M1413298

Sven Polak

引用次数: 5

On Tensors That Are Determined by Their Singular Tuples 在由奇异元组决定的张量上

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-04-08 DOI: 10.1137/21M1412980

Ettore Teixeira Turatti

引用次数: 7

On the Density of Eigenvalues on Periodic Graphs 周期图上特征值的密度

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-03-23 DOI: 10.1137/22m1505268

C. Kravaris

引用次数: 1

Geometric Approaches on Persistent Homology 关于持久同调的几何方法

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-03-11 DOI: 10.1137/21M1422914

Henry Adams, Baris Coskunuzer

引用次数: 9

A New Bound for the Waring Rank of Monomials 单项式警戒秩的一个新界

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-01-08 DOI: 10.1137/21M1390736

Kangjin Han, Hyunsuk Moon

引用次数: 2

Robust Hierarchical Clustering for Directed Networks: An Axiomatic Approach 有向网络的鲁棒分层聚类:一种公理方法

IF 1.2 2区数学

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-01-01 DOI: 10.1137/20m1359201

G. Carlsson, Facundo M'emoli, Santiago Segarra

{"title":"Robust Hierarchical Clustering for Directed Networks: An Axiomatic Approach","authors":"G. Carlsson, Facundo M'emoli, Santiago Segarra","doi":"10.1137/20m1359201","DOIUrl":"https://doi.org/10.1137/20m1359201","url":null,"abstract":"We provide a complete taxonomic characterization of robust hierarchical clustering methods for directed networks following an axiomatic approach. We begin by introducing three practical properties associated with the notion of robustness in hierarchical clustering: linear scale preservation, stability, and excisiveness. Linear scale preservation enforces imperviousness to change in units of measure whereas stability ensures that a bounded perturbation in the input network entails a bounded perturbation in the clustering output. Excisiveness refers to the local consistency of the clustering outcome. Algorithmically, excisiveness implies that we can reduce computational complexity by only clustering a subset of our data while theoretically guaranteeing that the same hierarchical outcome would be observed when clustering the whole dataset. In parallel to these three properties, we introduce the concept of representability, a generative model for describing clustering methods through the specification of their action on a collection of networks. Our main result is to leverage this generative model to give a precise characterization of all robust -- i.e., excisive, linear scale preserving, and stable -- hierarchical clustering methods for directed networks. We also address the implementation of our methods and describe an application to real data.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78884685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1