Maximum Correntropy Criterion-Based Robust Semisupervised Concept Factorization for Image Representation

Modal Regression-Based Graph Representation for Noise Robust Face Hallucination

Manifold learning-based face hallucination technologies have been widely developed during the past decades. However, the conventional learning methods always become ineffective in noise environment due to the least-square regression, which usually generates distorted representations for noisy inputs they employed for error modeling. To solve this problem, in this article, we propose a modal regression-based graph representation (MRGR) model for noisy face hallucination. In MRGR, the modal regression-based function is incorporated into graph learning framework to improve the resolution of noisy face images. Specifically, the modal regression-induced metric is used instead of the least-square metric to regularize the encoding errors, which admits the MRGR to robust against noise with uncertain distribution. Moreover, a graph representation is learned from feature space to exploit the inherent typological structure of patch manifold for data representation, resulting in more accurate reconstruction coefficients. Besides, for noisy color face hallucination, the MRGR is extended into quaternion (MRGR-Q) space, where the abundant correlations among different color channels can be well preserved. Experimental results on both the grayscale and color face images demonstrate the superiority of MRGR and MRGR-Q compared with several state-of-the-art methods.

Noise Robust Face Hallucination Based on Smooth Correntropy Representation

Face hallucination technologies have been widely developed during the past decades, among which the sparse manifold learning (SML)-based approaches have become the popular ones and achieved promising performance. However, these SML methods always failed in handling noisy images due to the least-square regression (LSR) they used for error approximation. To this end, we propose, in this article, a smooth correntropy representation (SCR) model for noisy face hallucination. In SCR, the correntropy regularization and smooth constraint are combined into one unified framework to improve the resolution of noisy face images. Specifically, we introduce the correntropy induced metric (CIM) rather than the LSR to regularize the encoding errors, which admits the proposed method robust to noise with uncertain distributions. Besides, the fused LASSO penalty is added into the feature space to ensure similar training samples holding similar representation coefficients. This encourages the SCR not only robust to noise but also can well exploit the inherent typological structure of patch manifold, resulting in more accurate representations in noise environment. Comparison experiments against several state-of-the-art methods demonstrate the superiority of SCR in super-resolving noisy low-resolution (LR) face images.

Correntropy based semi-supervised concept factorization with adaptive neighbors for clustering

Concept factorization (CF) has shown the effectiveness in the field of data clustering. In this paper, a novel and robust semi-supervised CF method, called correntropy based semi-supervised concept factorization with adaptive neighbors (CSCF), is proposed with improved performance in clustering applications. Specifically, on the one hand, the CSCF method adopts correntropy as the cost function to increase the robustness for non-Gaussian noise and outliers, and combines two different types of supervised information simultaneously for obtaining a compact low-dimensional representation of the original data. On the other hand, CSCF assigns the adaptive neighbors for each data point to construct a good data similarity matrix for reducing the sensitiveness of data. Moreover, a generalized version of CSCF is derived for enlarging the clustering application ranges. Analysis is also presented for the relationship of CSCF with several typical CF methods. Experimental results have shown that CSCF has better clustering performance than several state-of-the-art CF methods.

Mixture Correntropy-Based Kernel Extreme Learning Machines

Kernel-based extreme learning machine (KELM), as a natural extension of ELM to kernel learning, has achieved outstanding performance in addressing various regression and classification problems. Compared with the basic ELM, KELM has a better generalization ability owing to no needs of the number of hidden nodes given beforehand and random projection mechanism. Since KELM is derived under the minimum mean square error (MMSE) criterion for the Gaussian assumption of noise, its performance may deteriorate under the non-Gaussian cases, seriously. To improve the robustness of KELM, this article proposes a mixture correntropy-based KELM (MC-KELM), which adopts the recently proposed maximum mixture correntropy criterion as the optimization criterion, instead of using the MMSE criterion. In addition, an online sequential version of MC-KELM (MCOS-KELM) is developed to deal with the case that the data arrive sequentially (one-by-one or chunk-by-chunk). Experimental results on regression and classification data sets are reported to validate the performance superiorities of the new methods.