Multi-view clustering via neighbor domain correlation learning

Abstract

With the development of data science, more and more data are presented in the form of multi-view. Compared with single-view feature learning, multi-view feature learning is more effective, and it has been successfully applied in many fields. Clustering is a core technology of computer science. Thus, many researchers start to study multi-view clustering. Recently, combining with multi-view feature learning techniques, some multi-view clustering methods have been presented. These methods mainly focus on the multiple features fusion, while most of them ignore the correlations among multiple views. Therefore, it cannot make full use of the advantages of multiple view features. In this paper, we propose a novel approach, named multi-view clustering via neighbor domain correlation learning (MCNDCL) approach. Specifically, MCNDCL learns a discriminant common space for multiple view features. Under the learned common space, the correlations of the consistent neighbor domain are maximized, and the correlations of specific neighbor domain are minimized at the same time. Extensive experimental results on four typical benchmarks, i.e., UCI Digits, Caltech7, BBCSport and CCV, validate the high effectiveness of our proposed approach.

Appendix

Proof

$$\begin{aligned} \begin{aligned} S^T=&\left( \frac{1}{N}\sum _{i=1}^{N}\frac{1}{|P_i|}\sum _{m=1}^{M}\sum _{n=1}^{M}\sum _{s=1}^{|P_i|}\sum _{t=1}^{|P_i|}(p^m_s)(p^n_t)^T\right) ^T\\&-\left( \frac{\lambda }{N}\sum _{i=1}^{N}\frac{1}{|Q_i|}\sum _{m=1}^{M}\sum _{n=1}^{M}\sum _{s=1}^{|Q_i|}\sum _{t=1}^{|Q_i|}(q^m_s)(q^n_t)^T\right) ^T\\ =&\frac{1}{N}\sum _{i=1}^{N}\frac{1}{|P_i|}\sum _{n=1}^{M}\sum _{m=1}^{M}\sum _{t=1}^{|P_i|}\sum _{s=1}^{|P_i|}(p^n_t)(p^m_s)^T\\&-\frac{\lambda }{N}\sum _{i=1}^{N}\frac{1}{|Q_i|}\sum _{n=1}^{M}\sum _{m=1}^{M}\sum _{t=1}^{|Q_i|}\sum _{s=1}^{|Q_i|}(q^n_t)(q^m_s)^T\\&=S \end{aligned}, \end{aligned}$$

$\square$