scholarly journals Spectral Perturbation Meets Incomplete Multi-view Data

2019 ◽  
Author(s):  
Hao Wang ◽  
Linlin Zong ◽  
Bing Liu ◽  
Yan Yang ◽  
Wei Zhou
Keyword(s):  
Perturbation Theory ◽  
Spectral Clustering ◽  
Matrix Completion ◽  
Similarity Matrix ◽  
Spectral Perturbation Theory ◽  
Solid Fusion ◽  
Incomplete Similarity ◽  
Pic Method ◽  
Risk Bounds ◽  
Spectral Perturbation

Beyond existing multi-view clustering, this paper studies a more realistic clustering scenario, referred to as incomplete multi-view clustering, where a number of data instances are missing in certain views. To tackle this problem, we explore spectral perturbation theory. In this work, we show a strong link between perturbation risk bounds and incomplete multi-view clustering. That is, as the similarity matrix fed into spectral clustering is a quantity bounded in magnitude O(1), we transfer the missing problem from data to similarity and tailor a matrix completion method for incomplete similarity matrix. Moreover, we show that the minimization of perturbation risk bounds among different views maximizes the final fusion result across all views. This provides a solid fusion criteria for multi-view data. We motivate and propose a Perturbation-oriented Incomplete multi-view Clustering (PIC) method. Experimental results demonstrate the effectiveness of the proposed method.

VIBRATIONS OF A MEMBRANE WITH MANY CONCENTRATED MASSES NEAR THE BOUNDARY

1995 ◽  
Vol 05 (05) ◽  
pp. 565-585 ◽  
Author(s):  
MIGUEL LOBO ◽  
EUGENIA PÉREZ
Keyword(s):  
Perturbation Theory ◽  
Asymptotic Behavior ◽  
Small Parameter ◽  
Local Problem ◽  
Micro Structure ◽  
Spectral Perturbation Theory ◽  
Concentrated Masses ◽  
The Masses ◽  
Spectral Perturbation ◽  
Small Eigenvalues

We consider the asymptotic behavior of the vibrations of a membrane occupying a domain Ω ⊂ ℝ2. The density, which depends on a small parameter ε, is of order O(1) out of certain regions where it is O(ε−m) with m>0. These regions, the concentrated masses with diameter O(ε), are located near the boundary, at mutual distances O(η), with η=η(ε)→0. We impose Dirichlet (respectively Neumann) conditions at the points of ∂Ω in contact with (respectively, out of) the masses. Depending on the value of the parameter m(m>2, m=2 or m<2) we describe the asymptotic behavior of the eigenvalues. Small eigenvalues, of order O(εm−2) for m>2, are approached via those of a local problem obtained from the micro-structure of the problem, while the eigenvalues of order O(1) are approached through those of a homogenized problem, which depend on the relation between ε and η. Techniques of boundary homogenization and spectral perturbation theory are used to study this problem.

scholarly journals First order spectral perturbation theory of square singular matrix pencils

2008 ◽  
Vol 429 (2-3) ◽  
pp. 548-576 ◽  
Author(s):  
Fernando De Terán ◽  
Froilán M. Dopico ◽  
Julio Moro
Keyword(s):  
Perturbation Theory ◽  
Singular Matrix ◽  
First Order ◽  
Spectral Perturbation Theory ◽  
Matrix Pencils ◽  
Spectral Perturbation

Fast spectral clustering method based on graph similarity matrix completion

2021 ◽  
Vol 189 ◽  
pp. 108301
Author(s):  
Xu Ma ◽  
Shengen Zhang ◽  
Karelia Pena-Pena ◽  
Gonzalo R. Arce
Keyword(s):  
Spectral Clustering ◽  
Matrix Completion ◽  
Similarity Matrix ◽  
Clustering Method ◽  
Graph Similarity ◽  
Spectral Clustering Method

scholarly journals Spectral perturbation theory and the two weights problem

2014 ◽  
Vol 63 (5) ◽  
pp. 1349-1364
Author(s):  
Alexander Pushnitski ◽  
Alexander Volberg
Keyword(s):  
Perturbation Theory ◽  
Spectral Perturbation Theory ◽  
Spectral Perturbation

Fast affinity propagation clustering based on incomplete similarity matrix

2016 ◽  
Vol 51 (3) ◽  
pp. 941-963 ◽  
Author(s):  
Leilei Sun ◽  
Chonghui Guo ◽  
Chuanren Liu ◽  
Hui Xiong
Keyword(s):  
Affinity Propagation ◽  
Similarity Matrix ◽  
Affinity Propagation Clustering ◽  
Incomplete Similarity

scholarly journals A pareto ensemble based spectral clustering framework

2020 ◽  
Author(s):  
Juanjuan Luo ◽  
Huadong Ma ◽  
Dongqing Zhou
Keyword(s):  
Phase I ◽  
Phase Ii ◽  
Spectral Clustering ◽  
Clustering Algorithms ◽  
Divide And Conquer ◽  
Nonzero Entry ◽  
Similarity Matrix ◽  
Diversity Preservation ◽  
Two Phases ◽  
Matrix Construction

Abstract Similarity matrix has a significant effect on the performance of the spectral clustering, and how to determine the neighborhood in the similarity matrix effectively is one of its main difficulties. In this paper, a “divide and conquer” strategy is proposed to model the similarity matrix construction task by adopting Multiobjective evolutionary algorithm (MOEA). The whole procedure is divided into two phases, phase I aims to determine the nonzero entries of the similarity matrix, and Phase II aims to determine the value of the nonzero entries of the similarity matrix. In phase I, the main contribution is that we model the task as a biobjective dynamic optimization problem, which optimizes the diversity and the similarity at the same time. It makes each individual determine one nonzero entry for each sample, and the encoding length decreases to O(N) in contrast with the non-ensemble multiobjective spectral clustering. In addition, a specific initialization operator and diversity preservation strategy are proposed during this phase. In phase II, three ensemble strategies are designed to determine the value of the nonzero value of the similarity matrix. Furthermore, this Pareto ensemble framework is extended to semi-supervised clustering by transforming the semi-supervised information to constraints. In contrast with the previous multiobjective evolutionary-based spectral clustering algorithms, the proposed Pareto ensemble-based framework makes a balance between time cost and the clustering accuracy, which is demonstrated in the experiments section.

Joint Learning of Spectral Clustering Structure and Fuzzy Similarity Matrix of Data

2019 ◽  
Vol 27 (1) ◽  
pp. 31-44 ◽  
Author(s):  
Zekang Bian ◽  
Hisao Ishibuchi ◽  
Shitong Wang
Keyword(s):  
Spectral Clustering ◽  
Similarity Matrix ◽  
Joint Learning ◽  
Fuzzy Similarity
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