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Register a new userRobust Tensor Decomposition for Image Representation Based on Generalized Correntropy
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Added by
Miaohua Zhang
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Traditional tensor decomposition methods, e.g., two dimensional principal component analysis and two dimensional singular value decomposition, that minimize mean square errors, are sensitive to outliers. To overcome this problem, in this paper we propose a new robust tensor decomposition method using generalized correntropy criterion (Corr-Tensor). A Lagrange multiplier method is used to effectively optimize the generalized correntropy objective function in an iterative manner. The Corr-Tensor can effectively improve the robustness of tensor decomposition with the existence of outliers without introducing any extra computational cost. Experimental results demonstrated that the proposed method significantly reduces the reconstruction error on face reconstruction and improves the accuracies on handwritten digit recognition and facial image clustering.
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Remote sensing image (RSI) inpainting plays an important role in real applications. Recently, fully-connected tensor network (FCTN) decomposition has been shown the remarkable ability to fully characterize the global correlation. Considering the global correlation and the nonlocal self-similarity (NSS) of RSIs, this paper introduces the FCTN decomposition to the whole RSI and its NSS groups, and proposes a novel nonlocal patch-based FCTN (NL-FCTN) decomposition for RSI inpainting. Different from other nonlocal patch-based methods, the NL-FCTN decomposition-based method, which increases tensor order by stacking similar small-sized patches to NSS groups, cleverly leverages the remarkable ability of FCTN decomposition to deal with higher-order tensors. Besides, we propose an efficient proximal alternating minimization-based algorithm to solve the proposed NL-FCTN decomposition-based model with a theoretical convergence guarantee. Extensive experiments on RSIs demonstrate that the proposed method achieves the state-of-the-art inpainting performance in all compared methods.
Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian samples and/or outliers often makes it unreliable in practice. To this end, a robust formulation of PCA is derived based on the maximum correntropy criterion (MCC) so as to maximise the expected likelihood of Gaussian distributed reconstruction errors. In this way, the proposed solution reduces to a generalised power iteration, whereby: (i) robust estimates of the principal components are obtained even in the presence of outliers; (ii) the number of principal components need not be specified in advance; and (iii) the entire set of principal components can be obtained, unlike existing approaches. The advantages of the proposed maximum correntropy power iteration (MCPI) are demonstrated through an intuitive numerical example.
Two-dimensional singular decomposition (2DSVD) has been widely used for image processing tasks, such as image reconstruction, classification, and clustering. However, traditional 2DSVD algorithm is based on the mean square error (MSE) loss, which is sensitive to outliers. To overcome this problem, we propose a robust 2DSVD framework based on a generalized kernel risk sensitive loss (GKRSL-2DSVD) which is more robust to noise and and outliers. Since the proposed objective function is non-convex, a majorization-minimization algorithm is developed to efficiently solve it with guaranteed convergence. The proposed framework has inherent properties of processing non-centered data, rotational invariant, being easily extended to higher order spaces. Experimental results on public databases demonstrate that the performance of the proposed method on different applications significantly outperforms that of all the benchmarks.
Video representation is a key challenge in many computer vision applications such as video classification, video captioning, and video surveillance. In this paper, we propose a novel approach for video representation that captures meaningful information including motion and appearance from a sequence of video frames and compacts it into a single image. To this end, we compute the optical flow and use it in a least squares optimization to find a new image, the so-called Flow Profile Image (FPI). This image encodes motions as well as foreground appearance information while background information is removed. The quality of this image is validated in activity recognition experiments and the results are compared with other video representation techniques such as dynamic images [1] and eigen images [2]. The experimental results as well as visual quality confirm that FPIs can be successfully used in video processing applications.
The problem of detecting anomalies in time series from network measurements has been widely studied and is a topic of fundamental importance. Many anomaly detection methods are based on packet inspection collected at the network core routers, with consequent disadvantages in terms of computational cost and privacy. We propose an alternative method in which packet header inspection is not needed. The method is based on the extraction of a normal subspace obtained by the tensor decomposition technique considering the correlation between different metrics. We propose a new approach for online tensor decomposition where changes in the normal subspace can be tracked efficiently. Another advantage of our proposal is the interpretability of the obtained models. The flexibility of the method is illustrated by applying it to two distinct examples, both using actual data collected on residential routers.
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