Manifold-respecting discriminant nonnegative matrix factorization

An, Shounan; Yoo, Jun-Hyun; Choi, Seungjin

doi:10.1016/j.patrec.2011.01.012

Cited by 32 publications

(13 citation statements)

References 12 publications

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“…NMF on a manifold emerges when the data lies in a nonlinear low-dimensional submanifold ( Cai et al, 2008 ). Manifold Regularized Discriminative NMF ( Ana et al, 2011 ; Guan et al, 2011 ) were proposed with special constraints to preserve local invariance, so as to reflect the multilateral characteristics.…”

Section: Related Workmentioning

confidence: 99%

Computational Modeling of Hierarchically Polarized Groups by Structured Matrix Factorization

Sun¹,

Yang²,

Li³

et al. 2021

Front. Big Data

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The paper extends earlier work on modeling hierarchically polarized groups on social media. An algorithm is described that 1) detects points of agreement and disagreement between groups, and 2) divides them hierarchically to represent nested patterns of agreement and disagreement given a structural guide. For example, two opposing parties might disagree on core issues. Moreover, within a party, despite agreement on fundamentals, disagreement might occur on further details. We call such scenarios hierarchically polarized groups. An (enhanced) unsupervised Non-negative Matrix Factorization (NMF) algorithm is described for computational modeling of hierarchically polarized groups. It is enhanced with a language model, and with a proof of orthogonality of factorized components. We evaluate it on both synthetic and real-world datasets, demonstrating ability to hierarchically decompose overlapping beliefs. In the case where polarization is flat, we compare it to prior art and show that it outperforms state of the art approaches for polarization detection and stance separation. An ablation study further illustrates the value of individual components, including new enhancements.

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Section: Related Workmentioning

confidence: 99%

Computational Modeling of Hierarchically Polarized Groups by Structured Matrix Factorization

Sun¹,

Yang²,

Li³

et al. 2021

Front. Big Data

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“…In order to integrate manifold learning into NMF framework, a graph regularized NMF (GNMF) algorithm is firstly proposed in [6]; then some GNMF variants are introduced in [35][36][37][38].…”

Section: Related Workmentioning

confidence: 99%

Robust Structure Preserving Nonnegative Matrix Factorization for Dimensionality Reduction

Tang²,

Han³

2016

Mathematical Problems in Engineering

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As a linear dimensionality reduction method, nonnegative matrix factorization (NMF) has been widely used in many fields, such as machine learning and data mining. However, there are still two major drawbacks for NMF: (a) NMF can only perform semantic factorization in Euclidean space, and it fails to discover the intrinsic geometrical structure of high-dimensional data distribution. (b) NMF suffers from noisy data, which are commonly encountered in real-world applications. To address these issues, in this paper, we present a new robust structure preserving nonnegative matrix factorization (RSPNMF) framework. In RSPNMF, a local affinity graph and a distant repulsion graph are constructed to encode the geometrical information, and noisy data influence is alleviated by characterizing the data reconstruction term of NMF withl2,1-norm instead ofl2-norm. With incorporation of the local and distant structure preservation regularization term into the robust NMF framework, our algorithm can discover a low-dimensional embedding subspace with the nature of structure preservation. RSPNMF is formulated as an optimization problem and solved by an effective iterative multiplicative update algorithm. Experimental results on some facial image datasets clustering show significant performance improvement of RSPNMF in comparison with the state-of-the-art algorithms.

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“…We denote l i as the label of x i . Recent studies on spectral graph theory and manifold learning theory have demonstrated that the local geometric structure can be effectively modelled through a NN graph on a scatter of data points, so in order to exploit both the geometrical structure of data and label information, An et al [12] constructed the adjacency matrix for the intra-class K-NN graph W W by using binary weights indicating neighbourhood relationships as…”

Section: Standard Nmfmentioning

confidence: 99%

“…Moreover, the numerical value of K varied from 1 to 10. Also, because we want to compare the best average results between NMF-K-NN algorithm and our proposed algorithm, we chose the regularisation parameter α and the dimensionality of features with the same as the literature [12], that can be set by [0.01, 0.1, 1, 10, 100] and [200, 195, 190, … ,10, 5], respectively. Since X can be approximated by columnwise UV T , we can naturally project a sample x i from the original high-dimensional space to the low-dimensional space or equivalently y = U † x i , wherein the projection matrix U † = (U T U) − 1 U T is the pseudo-inverse of U.…”

Section: Face Recognitionmentioning

confidence: 99%

Non‐negative matrix factorisation based on fuzzy K nearest neighbour graph and its applications

2013

IET Computer Vision

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Non-negative matrix factorisation (NMF) has been widely used in pattern recognition problems. For the tasks of classification, however, most of the existing variants of NMF ignore both the discriminative information and the local geometry of data into the factorisation. The actual conditions of the problems will be affected by the change of the environmental factors to affect the recognition accuracy. In order to overcome these drawbacks, the authors regularised NMF by intra-class and inter-class fuzzy K nearest neighbour graphs, leading to NMF-FK-NN in this study. By introducing two novel fuzzy K nearest neighbour graphs, NMF-FK-NN can contract the intra-class neighbourhoods and expand the inter-class neighbourhoods in the decomposition. This method not only exploits the discriminative information and uses the geometric structure in the data effectively, but also reduces the influence of the external factors to improve recognition effect. In the factorisation, the authors minimised the approximation error whilst contracting intra-class fuzzy neighbourhoods and expanding inter-class fuzzy neighbourhoods. The authors develop simple multiplicative updates for NMF-FK-NN and present monotonic convergence results. Experiments of the text clustering on the CLUTO toolkit and face recognition on ORL and YALE datasets show the effectiveness of our proposed method.

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Manifold-respecting discriminant nonnegative matrix factorization

Cited by 32 publications

References 12 publications

Computational Modeling of Hierarchically Polarized Groups by Structured Matrix Factorization

Computational Modeling of Hierarchically Polarized Groups by Structured Matrix Factorization

Robust Structure Preserving Nonnegative Matrix Factorization for Dimensionality Reduction

Non‐negative matrix factorisation based on fuzzy K nearest neighbour graph and its applications

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