Multiview Clustering via Proximity Learning in Latent Representation Space

Author(s):  
Bao-Yu Liu ◽  
Ling Huang ◽  
Chang-Dong Wang ◽  
Jian-Huang Lai ◽  
Philip S. Yu
2006 ◽  
Vol 15 (12) ◽  
pp. 2267-2278 ◽  
Author(s):  
D. V. AHLUWALIA-KHALILOVA

Assuming the validity of the general relativistic description of gravitation on astrophysical and cosmological length scales, we analytically infer that the Friedmann–Robertson–Walker cosmology with Einsteinian cosmological constant, and a vanishing spatial curvature constant, unambiguously requires a significant amount of dark matter. This requirement is consistent with other indications for dark matter. The same space–time symmetries that underlie the freely falling frames of Einsteinian gravity also provide symmetries which, for the spin one half representation space, furnish a novel construct that carries extremely limited interactions with respect to the terrestrial detectors made of the standard model material. Both the "luminous" and "dark" matter turn out to be residents of the same representation space but they derive their respective "luminosity" and "darkness" from either belonging to the sector with (CPT)2 = +𝟙, or to the sector with (CPT)2 = -𝟙.


2018 ◽  
Vol 30 (4) ◽  
pp. 1080-1103 ◽  
Author(s):  
Kun Zhan ◽  
Jinhui Shi ◽  
Jing Wang ◽  
Haibo Wang ◽  
Yuange Xie

Most existing multiview clustering methods require that graph matrices in different views are computed beforehand and that each graph is obtained independently. However, this requirement ignores the correlation between multiple views. In this letter, we tackle the problem of multiview clustering by jointly optimizing the graph matrix to make full use of the data correlation between views. With the interview correlation, a concept factorization–based multiview clustering method is developed for data integration, and the adaptive method correlates the affinity weights of all views. This method differs from nonnegative matrix factorization–based clustering methods in that it can be applicable to data sets containing negative values. Experiments are conducted to demonstrate the effectiveness of the proposed method in comparison with state-of-the-art approaches in terms of accuracy, normalized mutual information, and purity.


2015 ◽  
Vol 15 (12) ◽  
pp. 8
Author(s):  
Marius Catalin Iordan ◽  
Michelle Greene ◽  
Diane Beck ◽  
Li Fei-Fei

2021 ◽  
Vol 27 (7) ◽  
pp. 667-692
Author(s):  
Lamia Berkani ◽  
Lylia Betit ◽  
Louiza Belarif

Clustering-based approaches have been demonstrated to be efficient and scalable to large-scale data sets. However, clustering-based recommender systems suffer from relatively low accuracy and coverage. To address these issues, we propose in this article an optimized multiview clustering approach for the recommendation of items in social networks. First, the selection of the initial medoids is optimized using the Bees Swarm optimization algorithm (BSO) in order to generate better partitions (i.e. refining the quality of medoids according to the objective function). Then, the multiview clustering (MV) is applied, where users are iteratively clustered from the views of both rating patterns and social information (i.e. friendships and trust). Finally, a framework is proposed for testing the different alternatives, namely: (1) the standard recommendation algorithms; (2) the clustering-based and the optimized clustering-based recommendation algorithms using BSO; and (3) the MV and the optimized MV (BSO-MV) algorithms. Experimental results conducted on two real-world datasets demonstrate the effectiveness of the proposed BSO-MV algorithm in terms of improving accuracy, as it outperforms the existing related approaches and baselines.


1997 ◽  
Vol 06 (06) ◽  
pp. 851-877 ◽  
Author(s):  
Weiping Li

Casson defined an invariant which can be thought of as the number of conjugacy classes of irreducible representations of π1(Y) into SU(2) counted with signs, where Y is an oriented integral homology 3-sphere. Lin defined a similar invariant (the signature of a knot) for a braid representative of a knot in S3. In this paper, we give a natural generalization of Casson-Lin's invariant. Our invariant is the symplectic Floer homology for the representation space of π1(S3 \ K) into SU(2) with trace-zero along all meridians. The symplectic Floer homology of braids is a new invariant of knots and its Euler number is the negative of Casson-Lin's invariant.


2008 ◽  
Vol 144 (3) ◽  
pp. 721-733 ◽  
Author(s):  
Olivier Serman

AbstractWe prove that, given a smooth projective curve C of genus g≥2, the forgetful morphism $\mathcal {M}_{\mathbf {O}_r} \longrightarrow \mathcal {M}_{\mathbf {GL}_r}$ (respectively $\mathcal M_{\mathbf {Sp}_{2r}}\longrightarrow \mathcal M_{\mathbf {GL}_{2r}}$) from the moduli space of orthogonal (respectively symplectic) bundles to the moduli space of all vector bundles over C is an embedding. Our proof relies on an explicit description of a set of generators for the polynomial invariants on the representation space of a quiver under the action of a product of classical groups.


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