Graph regularized multilayer concept factorization for data representation

Li, Xue; Shen, Xiaobo; Shu, Zhenqiu; Ye, Qiaolin; Zhao, Chenglin

doi:10.1016/j.neucom.2017.01.045

Cited by 32 publications

(22 citation statements)

References 32 publications

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“…Several methods of NMF are discussed here, which include: Semi supervised constrained NMF [19], semisupervised graph based discriminative NMF [20], Bayesian learning approach to reduce the generalization error in upper bound using NMF [21] and update rules [22], sparseness NMF, which provides better characterization of the features [23], sparse unmixing NMF [24], locally weighted sparse graph regularized NMF [25], graph-regularized NMF [26], graph dual regularization [27], multiple graph regularized NMF [28], graph regularized multilayer NMF [29], adaptive graph regularized NMF [30], hyper-graph regularized [31], graph regularization with sparse NMF [32], multi-view NMF [33], extended incremental NMF [34], incremental orthogonal projective NMF [35], correntropy induced metric NMF [36], multi-view NMF [37], patch based NMF [38], MMNMF [39], regularized NMF [40], FR conjugate gradient NMF [41]. However, these methods failed to address the problems associated with non-orthogonality due to the presence of nonnegative elements in NMF.…”

Section: Related Workmentioning

confidence: 99%

Reducing Dimensionality in Text Mining using Conjugate Gradients and Hybrid Cholesky Decomposition

Alostad¹

2017

ijacsa

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Abstract-Generally, data mining in larger datasets consists of certain limitations in identifying the relevant datasets for the given queries. The limitations include: lack of interaction in the required objective space, inability to handle the data sets or discrete variables in datasets, especially in the presence of missing variables and inability to classify the records as per the given query, and finally poor generation of explicit knowledge for a query increases the dimensionality of the data. Hence, this paper aims at resolving the problems with increasing data dimensionality in datasets using modified non-integer matrix factorization (NMF). Further, the increased dimensionality arising due to non-orthogonally of NMF is resolved with Cholesky decomposition (cdNMF). Initially, the structuring of datasets is carried out to form a well-defined geometric structure. Further, the complex conjugate values are extracted and conjugate gradient algorithm is applied to reduce the sparse matrix from the data vector. The cdNMF is used to extract the feature vector from the dataset and the data vector is linearly mapped from upper triangular matrix obtained from the Cholesky decomposition. The experiment is validated against accuracy and normalized mutual information (NMI) metrics over three text databases of varied patterns. Further, the results prove that the proposed technique fits well with larger instances in finding the documents as per the query, than NMF, neighborhood preserving: nonnegative matrix factorization (NPNMF), multiple manifolds non-negative matrix factorization (MMNMF), robust non-negative matrix factorization (RNMF), graph regularized non-negative matrix factorization (GNMF), hierarchical non-negative matrix factorization (HNMF) and cdNMF.

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Section: Related Workmentioning

confidence: 99%

Reducing Dimensionality in Text Mining using Conjugate Gradients and Hybrid Cholesky Decomposition

Alostad¹

2017

ijacsa

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“…Nonnegative matrix factorization with local similarity learning (KLS-NMF) [44] introduced self-expressiveness mechanism into matrix factorization to learn the local similarity of the data in the kernel space. Chen et al [49] performed the multilayer concept factorization by exploiting the local structure. Qian et al [50] combined sparse graph learning into NMF for solving the feature matrix.…”

Section: Introductionmentioning

confidence: 99%

Robust Structured Convex Nonnegative Matrix Factorization for Data Representation

et al. 2021

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Nonnegative Matrix Factorization (NMF) is a popular technique for machine learning. Its power is that it can decompose a nonnegative matrix into two nonnegative factors whose product well approximates the nonnegative matrix. However, the nonnegative constraint of the data matrix limits its application. Additionally, the representations learned by NMF fail to respect the intrinsic geometric structure of the data. In this paper, we propose a novel unsupervised matrix factorization method, called Robust Structured Convex Nonnegative Matrix Factorization (RSCNMF). RSCNMF not only achieves meaningful factorizations of the mixed-sign data, but also learns a discriminative representation by leveraging local and global structures of the data. Moreover, it introduces the L 2,1 -norm loss function to deal with noise and outliers, and exploits the L 2,1 -norm feature regularizer to select discriminative features across all the samples. We develop an alternate iterative scheme to solve such a new model. The convergence of RSCNMF is proven theoretically and verified empirically. The experimental results on eight real-world data sets show that our RSCNMF algorithm matches or outperforms the state-of-the-art methods.INDEX TERMS Convex nonnegative matrix factorization, global structure, L 2,1 norm, clustering.

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“…Therefore, how to extract effective information from high-dimensional data becomes very significant. In recent years, data representation plays an important role in pattern recognition and image processing [1]- [3]. A suitable data representation is helpful to reveal the potential information structure of the data very well, which is convenient for the next processing.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Graph Regularization Discriminant Nonnegative Matrix Factorization for Data Representation

Zhang

Wang

et al. 2019

IEEE Access

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Nonnegative matrix factorization, as a classical part-based representation method, has been widely used in pattern recognition, data mining and other fields. However, the traditional nonnegative matrix factorization directly factoring decomposes the original data, and the original data often contains a lot of redundancy and noise, which seriously affect the subsequent processing of the data. In this work, we propose an adaptive graph regularization discriminant nonnegative matrix factorization (AGDNMF) for image clustering. The AGDNMF algorithm makes full use of local structure information and a small amount of label information. In AGDNMF, the local structure information can be more accurate and the label information can prevent the points with the same label from being merged into one point. These two items are combined into the objective function of NMF. In addition, we provide the update rules for the corresponding optimization functions and prove its convergence. A large number of experiments on different data sets show that the proposed algorithm has good clustering performance.

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Graph regularized multilayer concept factorization for data representation

Cited by 32 publications

References 32 publications

Reducing Dimensionality in Text Mining using Conjugate Gradients and Hybrid Cholesky Decomposition

Reducing Dimensionality in Text Mining using Conjugate Gradients and Hybrid Cholesky Decomposition

Robust Structured Convex Nonnegative Matrix Factorization for Data Representation

Adaptive Graph Regularization Discriminant Nonnegative Matrix Factorization for Data Representation

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