Robust Tensor Decomposition for Image Representation Based on Generalized Correntropy

Abstract

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.

Order Determination for Tensor-valued Observations Using Data Augmentation

“…The low-rank structure is usually thought to represent the signal/information of the original data tensor, whereas, if we manage to choose the rank appropriately, the difference between the original tensor and its low-rank approximation is pure noise. A comprehensive review of tensor decompositions is given by [9] and, for some recent uses of tensor decompositions in the context of image data, see [6,11,25].…”

Image representation and reconstruction by compositing Gaussian ellipses

“…Decomposing an image into representative components is a commonly used technique in image processing, computational imaging, and image representation [1][2][3][4]. Stroke-based rendering (SBR) [5] is a special approach to image decomposition and representation in nonphotorealistic rendering (NPR).…”

“…Because the equation of a Gaussian ellipse is parametric and differentiable, this study demonstrates herein that finding the derivative of a Gaussian ellipse is possible with alpha compositing. Given a set of Gaussian ellipses with arbitrary parameters, the gradient method can be used to automatically find the parameters of each Gaussian ellipse such that the 1 Girl with a Pearl Earring, Johannes Vermeer, 1665, public domain.…”

“…Figure 1 depicts an example of the proposed method. Figure 1a presents original image of Girl with a Pearl Earring 1 . Figures 1b and 1c display the results obtained through rendering with the proposed method with 50 and 2000 strokes, respectively.…”