Low-Rank Common Subspace for Multi-view Learning

Abstract

Multi-view data is very popular in real-world applications, as different view-points and various types of sensors help to better represent data when fused across views or modalities. Samples from different views of the same class are less similar than those with the same view but different class. We consider a more general case that prior view information of testing data is inaccessible in multi-view learning. Traditional multiview learning algorithms were designed to obtain multiple viewspecific linear projections and would fail without this prior information available. That was because they assumed the probe and gallery views were known in advance, so the correct viewspecific projections were to be applied in order to better learn low-dimensional features. To address this, we propose a LowRank Common Subspace (LRCS) for multi-view data analysis, which seeks a common low-rank linear projection to mitigate the semantic gap among different views. The low-rank common projection is able to capture compatible intrinsic information across different views and also well-align the within-class samples from different views. Furthermore, with a low-rank constraint on the view-specific projected data and that transformed by the common subspace, the within-class samples from multiple views would concentrate together. Different from the traditional supervised multi-view algorithms, our LRCS works in a weakly supervised way, where only the view information gets observed. Such a common projection can make our model more flexible when dealing with the problem of lacking prior view information of testing data. Two scenarios of experiments, robust subspace learning and transfer learning, are conducted to evaluate our algorithm. Experimental results on several multi-view datasets reveal that our proposed method outperforms state-of-the-art, even when compared with some supervised learning methods.

Low-Rank Representation with Graph Constraints for Robust Visual Tracking

“…By choosing an appropriate dictionary A, LRR can recover the underlying row space so as to reveal the true segmentation of data. Recently, low-rank representation has been incorporated with subspace learning, e.g., Low-rank Transfer Subspace Learning (LTSL) [22], Supervised Regularization based Robust Subspace (SRRS) [18], Low-Rank Common Subspace (LRCS) [23] and Low-Rank Discriminate Embedding (LRDE) [19], aiming to find a more robust subspace with low-rank constraint.…”

“…To optimize the variables in Eq. (15), we use the Alternating Direction Method of Multiplier (ADMM) [29] since previous work [18] and [23] have demonstrated that ADMM works well in solving similar problems. By using ADMM, we can alternately update variables one by one with an iterative method.…”

Regularized deep learning for fashion and social media data analysis

“…We remove other irrelevant parts to D as: 24) where the rank minimization problem is replaced with minimizing the nuclear norm problem [66,135,78]. And problem (5.24) can be effectively solved by the singular value thresholding (SVT)…”

“…To effectively capture the common information shared by them, we propose to adopt low-rank sparse decomposition to further decompose B andB [66,134,135,78]. As shown in Figure 5.1, we assume the two rating patterns B andB share a common patterns D and also preserve domain-specific patterns E andẼ [136].…”

“…Since there are more than one variables to be optimized, it is hard to update them jointly [135,78]. However, we could solve the variables one by one, meaning we optimize one variable by fixing others.…”