Robust C-Loss Kernel Classifiers

Xu, Guibiao; Hu, Bao-Gang; Prı́ncipe, José C.

doi:10.1109/tnnls.2016.2637351

Cited by 38 publications

(15 citation statements)

References 43 publications

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“…Moreover, in practice, the MCC can also be formulated as minimizing the following correntropy-induced loss (C-loss) function [36], [37]…”

Section: B Maximum Correntropy Criterionmentioning

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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“…Moreover, in practice, the MCC can also be formulated as minimizing the following correntropy-induced loss (C-loss) function [36], [37]…”

Section: B Maximum Correntropy Criterionmentioning

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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“…29is not a convex function, it can't be solved by a commonly used optimization method. According to the solution process in [23], we can effectively solve the optimization problem of nonconvex functions. (28)…”

Section: The Objective Function Of Csrgelmmentioning

confidence: 99%

“…Since the correntropy induced loss is a differentiable and smooth function, the gradient optimization algorithm can be employed [23]. However, the gradient-based optimization algorithm converges slowly, so we use the half-quadratic optimization algorithm to solve the optimization problem of CSRGELM.…”

Section: The Optimization Of Csrgelmmentioning

confidence: 99%

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Correntropy induced loss based sparse robust graph regularized extreme learning machine for cancer classification

et al. 2020

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Background As a machine learning method with high performance and excellent generalization ability, extreme learning machine (ELM) is gaining popularity in various studies. Various ELM-based methods for different fields have been proposed. However, the robustness to noise and outliers is always the main problem affecting the performance of ELM. Results In this paper, an integrated method named correntropy induced loss based sparse robust graph regularized extreme learning machine (CSRGELM) is proposed. The introduction of correntropy induced loss improves the robustness of ELM and weakens the negative effects of noise and outliers. By using the L2,1-norm to constrain the output weight matrix, we tend to obtain a sparse output weight matrix to construct a simpler single hidden layer feedforward neural network model. By introducing the graph regularization to preserve the local structural information of the data, the classification performance of the new method is further improved. Besides, we design an iterative optimization method based on the idea of half quadratic optimization to solve the non-convex problem of CSRGELM. Conclusions The classification results on the benchmark dataset show that CSRGELM can obtain better classification results compared with other methods. More importantly, we also apply the new method to the classification problems of cancer samples and get a good classification effect.

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“…The clipped square function (also known as the skipped-mean loss) was also used in [21] to estimate view relations, and in [14] to perform robust image restoration. Similar approaches have been taken for clipped loss functions, where they have been used for robust feature selection [9], regression [23,17], classification [19,16,22], and robust principal component analysis [18].…”

Section: Introductionmentioning

confidence: 99%

Minimizing a sum of clipped convex functions

2020

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We consider the problem of minimizing a sum of clipped convex functions; applications include clipped empirical risk minimization and clipped control. While the problem of minimizing the sum of clipped convex functions is NP-hard, we present some heuristics for approximately solving instances of these problems. These heuristics can be used to find good, if not global, solutions and appear to work well in practice. We also describe an alternative formulation, based on the perspective transformation, which makes the problem amenable to mixed-integer convex programming and yields computationally tractable lower bounds. We illustrate one of our heuristic methods by applying it to various examples and use the perspective transformation to certify that the solutions are relatively close to the global optimum. This paper is accompanied by an open-source implementation.

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Robust C-Loss Kernel Classifiers

Cited by 38 publications

References 43 publications

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

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

Correntropy induced loss based sparse robust graph regularized extreme learning machine for cancer classification

Minimizing a sum of clipped convex functions

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