張雄軍作《Low-Rank Tensor Learning by Generalized Nonconvex Regularization》報(bào)告。In this talk, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding matrices of a tensor, which may be suboptimal. In order to explore the low-rankness of the underlying tensor effectively, we propose a nonconvex model based on transformed tensor nuclear norm for low-rank tensor learning. Specifically, a family of nonconvex functions are employed onto the singular values of all frontal slices of a tensor in the transformed domain to characterize the low-rankness of the underlying tensor. An error bound between the stationary point of the nonconvex model and the underlying tensor is established under restricted strong convexity on the loss function (such as least squares loss and logistic regression) and suitable regularity conditions on the nonconvex penalty function. By reformulating the nonconvex function into the difference of two convex functions, a proximal majorization-minimization (PMM) algorithm is designed to solve the resulting model. Then the global convergence and convergence rate of PMM are established under very mild conditions. Numerical experiments are conducted on tensor completion and binary classification to demonstrate the effectiveness of the proposed method over other state-of-the-art methods.
薛吉?jiǎng)t作《張量建模在高光譜圖像復(fù)原中的應(yīng)用》報(bào)告。高光譜圖像在采集過(guò)程中，受設(shè)備故障、硬件資源限制、環(huán)境干擾等因素影響，導(dǎo)致獲取的高光譜圖像存在退化現(xiàn)象，嚴(yán)重影響其后續(xù)使用。如何從退化的高光譜圖像中準(zhǔn)確復(fù)原原始信號(hào)，是有效利用高光譜圖像的前提。作為一種高維數(shù)據(jù)的表達(dá)框架，張量建模能夠保留高光譜圖像的多線(xiàn)性結(jié)構(gòu)，已成功應(yīng)用于高光譜圖像處理。因此，基于張量建模的高光譜圖像復(fù)原成為了計(jì)算機(jī)視覺(jué)和遙感領(lǐng)域的研究熱點(diǎn)之一。報(bào)告將介紹課題組在張量建模的高光譜圖像復(fù)原的研究成果。