Robust Nonnegative Matrix Factorization via Half-Quadratic Minimization

Du, Liang; Li, Xuan; Shen, Yi-Dong

doi:10.1109/icdm.2012.39

Cited by 94 publications

(72 citation statements)

References 30 publications

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“…The formulation of the above correntropy based optimization is closely related to [39] and [40]. In particular, when matrix X is fully observed (i.e.…”

Section: Proposed Algorithmsmentioning

confidence: 99%

Robust Matrix Completion via Maximum Correntropy Criterion and Half-Quadratic Optimization

Wang

et al. 2020

IEEE Trans. Signal Process.

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Robust matrix completion aims to recover a lowrank matrix from a subset of noisy entries perturbed by complex noises, where traditional methods for matrix completion may perform poorly due to utilizing l2 error norm in optimization. In this paper, we propose a novel and fast robust matrix completion method based on maximum correntropy criterion (MCC). The correntropy based error measure is utilized instead of using l2-based error norm to improve the robustness to noises. Using the half-quadratic optimization technique, the correntropy based optimization can be transformed to a weighted matrix factorization problem. Then, two efficient algorithms are derived, including alternating minimization based algorithm and alternating gradient descend based algorithm. The proposed algorithms do not need to calculate singular value decomposition (SVD) at each iteration. Further, the adaptive kernel selection strategy is proposed to accelerate the convergence speed as well as improve the performance. Comparison with existing robust matrix completion algorithms is provided by simulations, showing that the new methods can achieve better performance than existing state-of-the-art algorithms.

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“…The formulation of the above correntropy based optimization is closely related to [39] and [40]. In particular, when matrix X is fully observed (i.e.…”

Section: Proposed Algorithmsmentioning

confidence: 99%

Robust Matrix Completion via Maximum Correntropy Criterion and Half-Quadratic Optimization

Wang

et al. 2020

IEEE Trans. Signal Process.

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“…The Purdue AR dataset [22] contains 2600 frontal face images taken from 100 individuals comprising 50 males and 50 8. In this experiment, we compare with CauchyNMF to show the effect ot truncation.…”

Section: Contiguous Disguisementioning

confidence: 99%

Truncated Cauchy Non-Negative Matrix Factorization

Guan

Liu

Zhang

et al. 2019

IEEE Trans. Pattern Anal. Mach. Intell.

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Non-negative matrix factorization (NMF) minimizes the Euclidean distance between the data matrix and its low rank approximation, and it fails when applied to corrupted data because the loss function is sensitive to outliers. In this paper, we propose a Truncated Cauchy loss that handle outliers by truncating large errors, and develop a Truncated CauchyNMF to robustly learn the subspace on noisy datasets contaminated by outliers. We theoretically analyze the robustness of Truncated CauchyNMF comparing with the competing models and theoretically prove that Truncated CauchyNMF has a generalization bound which converges at a rate of order , where is the sample size. We evaluate Truncated CauchyNMF by image clustering on both simulated and real datasets. The experimental results on the datasets containing gross corruptions validate the effectiveness and robustness of Truncated CauchyNMF for learning robust subspaces.

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“…Recently, the correntropy induced metric (CIM ) proposed in [11] has achieved super robustness performance in face recognition [12], feature extraction [13] and nonnegative matrix factorization [14]. The formulation is defined below:…”

Section: The Model Of Multi-view Rnmfmentioning

confidence: 99%

“…Setting (14) to zero and utilizing the KKT conditions ψ kj H kj = 0, we can get following equation for H kj ,…”

Section: Algorithm For Multi-view Rnmfmentioning

confidence: 99%

Multi-view embedding learning via robust joint nonnegative matrix factorization

Zhang

You

et al. 2014

Proceedings 2014 IEEE International Conference on Security, Pattern Analysis, and Cybernetics (SPAC)

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Real data often are comprised of multiple modalities or different views, which provide complementary and consensus information to each other. Exploring those information is important for the multi-view data clustering and classification. Multiview embedding is an effective method for multiple view data which uncovers the common latent structure shared by different views. Previous studies assumed that each view is clean, or at least there are not contaminated by noises. However, in real tasks, it is often that every view might be suffered from noises or even some views are partially missing, which renders the traditional multi-view embedding algorithm fail to those cases. In this paper, we propose a novel multi-view embedding algorithm via robust joint nonnegative matrix factorization. We utilize the correntropy induced metric to measure the reconstruction error for each view, which are robust to the noises by assigning different weight for different entries. In order to uncover the common subspace shared by different views, we define a consensus matrix subspace to constrain the disagreement of different views. For the nonconvex objective function, we formulate it into half quadratic minimization and solve it via update scheme efficiently. The experiments results show its effectiveness and robustness in multiview clustering.

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Robust Nonnegative Matrix Factorization via Half-Quadratic Minimization

Cited by 94 publications

References 30 publications

Robust Matrix Completion via Maximum Correntropy Criterion and Half-Quadratic Optimization

Robust Matrix Completion via Maximum Correntropy Criterion and Half-Quadratic Optimization

Truncated Cauchy Non-Negative Matrix Factorization

Multi-view embedding learning via robust joint nonnegative matrix factorization

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