Joint Projection Learning and Tensor Decomposition Based Incomplete
  Multi-view Clustering
Wei Lv Chao Zhang Huaxiong Li Xiuyi Jia Chunlin Chen
Incomplete multi-view clustering (IMVC) has received increasing attention
since it is often that some views of samples are incomplete in reality. Most
existing methods learn similarity subgraphs from original incomplete multi-view
data and seek complete graphs by exploring the incomplete subgraphs of each
view for spectral clustering. However, the graphs constructed on the original
high-dimensional data may be suboptimal due to feature redundancy and noise.
Besides, previous methods generally ignored the graph noise caused by the
inter-class and intra-class structure variation during the transformation of
incomplete graphs and complete graphs. To address these problems, we propose a
novel Joint Projection Learning and Tensor Decomposition Based method (JPLTD)
for IMVC. Specifically, to alleviate the influence of redundant features and
noise in high-dimensional data, JPLTD introduces an orthogonal projection
matrix to project the high-dimensional features into a lower-dimensional space
for compact feature learning.Meanwhile, based on the lower-dimensional space,
the similarity graphs corresponding to instances of different views are
learned, and JPLTD stacks these graphs into a third-order low-rank tensor to
explore the high-order correlations across different views. We further consider
the graph noise of projected data caused by missing samples and use a
tensor-decomposition based graph filter for robust clustering.JPLTD decomposes
the original tensor into an intrinsic tensor and a sparse tensor. The intrinsic
tensor models the true data similarities. An effective optimization algorithm
is adopted to solve the JPLTD model. Comprehensive experiments on several
benchmark datasets demonstrate that JPLTD outperforms the state-of-the-art
methods. The code of JPLTD is available at https://github.com/weilvNJU/JPLTD.