Robust auto-weighted multi-view subspace clustering with common subspace representation matrix

Abstract

In many computer vision and machine learning applications, the data sets distribute on certain low-dimensional subspaces. Subspace clustering is a powerful technology to find the underlying subspaces and cluster data points correctly. However, traditional subspace clustering methods can only be applied on data from one source, and how to extend these methods and enable the extensions to combine information from various data sources has become a hot area of research. Previous multi-view subspace methods aim to learn multiple subspace representation matrices simultaneously and these learning task for different views are treated equally. After obtaining representation matrices, they stack up the learned representation matrices as the common underlying subspace structure. However, for many problems, the importance of sources and the importance of features in one source both can be varied, which makes the previous approaches ineffective. In this paper, we propose a novel method called Robust Auto-weighted Multi-view Subspace Clustering (RAMSC). In our method, the weight for both the sources and features can be learned automatically via utilizing a novel trick and introducing a sparse norm. More importantly, the objective of our method is a common representation matrix which directly reflects the common underlying subspace structure. A new efficient algorithm is derived to solve the formulated objective with rigorous theoretical proof on its convergency. Extensive experimental results on five benchmark multi-view datasets well demonstrate that the proposed method consistently outperforms the state-of-the-art methods.

Joint consensus and diversity for multi-view semi-supervised classification

“…-With the power mean incorporation strategy, the proposed JCD is robust against the lowquality views. And we show that the auto-weighted strategy (Huang et al 2019;Nie et al 2016;Shu et al 2017;Zhuge et al 2017) is a special case of power mean strategy. -We prove that the solution can be obtained by solving another problem with introduced variables and develop an efficient algorithm for optimization, which can be applied to large-scale multi-view semi-supervised classification.…”

“…The power mean strategy distinguishes the importance of various views according to the view loss, which enables the views with smaller losses to play more important roles in classification. The auto-weighted strategy has been widely adopted by recent works (Huang et al 2019;Nie et al 2016;Shu et al 2017;Zhuge et al 2017) to incorporate the losses of different views, which essentially is a special case of power mean strategy with p = 1 2 .…”

“…The adaptive parameter γ is tuned in the range of {1.1, 1.3, 1.5, 1.7, 1.9, 2.5, 3.3} and the balanced parameter λ is tuned from {10 −6 , 10 −5 , 10 −4 , 10 −3 , 10 −2 , 10 −1 , 10 0 }. Following (Huang et al 2019;Nie et al 2016Shu et al 2017;Zhuge et al 2017), the parameter p is set to be 1 2 . For the compared methods, we download their codes form authors' websites and determine the searching ranges of the parameters according to their papers.…”

Low-rank graph optimization for multi-view dimensionality reduction

“…However, all views are treated equally and the diversity among multi-view data is not explicitly considered in these methods [30–32]. Therefore, their performance may suffer from the graph of less informative views [34]. To overcome this limitation, Low-Rank Graph Optimization for Multi-View Dimensionality Reduction (LRGO-MVDR) is proposed in this section, which consists of the following two steps.…”

“…In fact, different views often contribute unequally in practice. Therefore, one challenge is how to aggregate the strengths of various heterogeneous graphs by exploring the rich information among them, which certainly can lead to more accurate and robust performance than by treating each individual type of graph equally [34].…”