Spectra, Euclidean representations and clusterings of hypergraphs

Bolla, Marianna

doi:10.1016/0012-365x(93)90322-k

Cited by 70 publications

(40 citation statements)

References 14 publications

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“…Bolla (Bolla, 1993) defines a Laplacian for an unweighted hypergraph in terms of the diagonal vertex degree matrix D v , the diagonal edge degree matrix D e , and the incidence matrix H, defined in Section 2.…”

Section: Bolla's Laplacianmentioning

confidence: 99%

Higher order learning with graphs

Agarwal

Branson

Belongie

2006

Proceedings of the 23rd International Conference on Machine Learning - ICML '06

315

293

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Recently there has been considerable interest in learning with higher order relations (i.e., three-way or higher) in the unsupervised and semi-supervised settings. Hypergraphs and tensors have been proposed as the natural way of representing these relations and their corresponding algebra as the natural tools for operating on them. In this paper we argue that hypergraphs are not a natural representation for higher order relations, indeed pairwise as well as higher order relations can be handled using graphs. We show that various formulations of the semi-supervised and the unsupervised learning problem on hypergraphs result in the same graph theoretic problem and can be analyzed using existing tools.

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Section: Bolla's Laplacianmentioning

confidence: 99%

Higher order learning with graphs

Agarwal

Branson

Belongie

2006

Proceedings of the 23rd International Conference on Machine Learning - ICML '06

315

293

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show abstract

“…The possible reasons that our proposed aMM method outperforms the other two reranking baselines are as follows: (1) due to the intrinsic limitation of the simple graph, learning on simple graph naturally cannot leverage higher-order relations among documents, which can only capture pairwise relations between documents [16,19,44,49]; (2) the baselines consider all modalities and views to have equal strength in representing the content of multi-modal documents, while in fact, they have query-specific contribution confidences [37,44];…”

Section: On Model Performance Comparisonmentioning

confidence: 98%

“…Answer. 1 We then issued them to Google Image search Engine. We manually selected a set of 20 verbose queries from the suggestion lists.…”

Section: Data Collectionmentioning

confidence: 99%

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aMM: Towards adaptive ranking of multi-modal documents

Akbari

Nie

Chua

2015

Int J Multimed Info Retr

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Information reranking aims to recover the true order of the initial search results. Traditional reranking approaches have achieved great success in uni-modal document retrieval. They, however, suffer from the following limitations when reranking multi-modal documents: (1) they are unable to capture and model the relations among multiple modalities within the same document; (2) they usually concatenate diverse features extracted from different modalities into one single vector, rather than adaptively fusing them by considering their discriminative capabilities with respect to the given query; and (3) most of them consider the pairwise relations among documents but discard their higher-order grouping relations, which leads to information loss. Towards this end, we propose an adaptive multi-modal multi-view (aMM) reranking model. This model is able to jointly regularize the relatedness among modalities, the effects of feature views extracted from different modalities, as well as the complex relations among multi-modal documents. Extensive experiments on three datasets well validated the effectiveness and robustness of our proposed model.

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“…To establish the adjacency matrix and Laplacian matrix for a hypergraph, an equivalent graph representation is required. Agarwal et al [2] have compared a number of alternative graph representations [4,13,23,27,39] for hypergraphs and explained their relationships with each other in machine learning. One common feature for these methods as well as the method in [1] is that a weight is assumed to be associated with each hyperedge.…”

Section: Introductionmentioning

confidence: 99%