论文笔记：Multiview Subspace Clustering via Tensorial t-Product Representation

motivation

High-order statistics that can only be captured by simultaneously utilizing all views are often overlooked. This paper proposed a novel multiview clustering method by using t-product in the third-order tensor space.

contributions

• Presenting an innovative construction method by organizing the multiview data set into the third-order tensorial data. As such, multiple views can be simultaneously exploited, rather than only set of pairwise information.

 

• It is the first attempt to propose a low-rank multiview clustering in the third-order tensor space via t-linear combination ( the t-product).

Algorithms

objective function:

they are sparse term, low-rank term, represen- tation term, and consensus terms respectively. The objective function's augmented Lagrangian formulation is formulated as

 

which can be solved with ADMM:

C* can be regarded as a new representation learned from multiview data. After solving problem (8), the next step is to segment C* to find the final subspace clusters.

This algorithm is called subspace clustering for multiview data in the third-order tensor space, namely SCMV-3DT, which is outlined in Algorithm 2. 

experiment results and conclusions

Test data sets used in this work:

• The proposed method significantly outperforms those of the comparisons on all criteria, for all types of data including facial image, object image, digits image, and text data.  
• It's concluded that the proposed method is relatively insensitive to its parameters as long as the parameters are in a suitable range. 

• Multiview can be employed to comprehensively and accurately describe the data wherever possible.

Drawback

The proposed method cannot be directly applied to very large data sets unless parallelization or random sampling is used.

 

论文信息

Ming, Yin, Junbin, et al. Multiview Subspace Clustering via Tensorial t-Product Representation.[J]. IEEE Transactions on Neural Networks & Learning Systems, 2018.