Besides as [12], [13] are some useful weighting techniques.

Besides the common
multi-view clustering, the feature selection can help to provide accurate model
in data clustering 6,7. Y.M. Xu et al. (2016) combined Weighted Multi-view
Clustering with Feature Selection in the 
WMCFS algorithm which in one way  performs
multi-view data clustering and feature selection in the other way6.  However, the feature selection calculation
may increase their objective function convergence. Their weighting scheme for
views and features can add an extra cost computation cost. The same idea have
been extended in 7  where an efficient gradient-based
optimization algorithm is embedded into k-means algorithm. H. Liu et al(2017)
used the weighted K-means clustering of a binary matrix to decrease the time from O(InrK) to O(n) and space complexities of
their Spectral Ensemble Clustering 8. Re-weighting such as 9; auto-weighting technique
such as 10 , 11; Bi-level weighting such as 12, 13 are some useful weighting
techniques.

1.1. 
Multi-view learning
methods

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ü 
Co-Training Style
Algorithms Co-training
style algorithms train alternately to maximize the mutual agreement on two
distinct views of the data. C. Lee and T. Liu (2016) introduced a new pairwise
co-training procedure in 14. They used the augmented view
to separately guide the improvement of each view, then updated the augmented
view and repeat this process iteratively. By this way, the proposed algorithm
overcomes the inefficiency of conventional co-training.

ü 
Multi-Kernel Learning multiple
kernel learning algorithms exploit kernels that naturally correspond to
different views and combine kernels either linearly or non-linearly to improve
learning performance. D. Guo et al.(2014) combined the kernel matrix
learning and the spectral clustering optimization into one15. The proposed
algorithm can not only detect the kernel weights but also cluster the
multi-view data simultaneously. Y. Ye et al.(2016) have proposed a three-step
alternative algorithm to tackle the multi-view clustering issues with respect
to the co-regularized Kernel k-means 16. According to the authors’
perspective, Kernel k-means clustering is trying to find the cluster assignment
that minimizes the sum-of-squares loss between the samples and the cluster
centroid. The main problem is formulated as follow:

Their algorithm
optimizes the consensus embedding and automatically determines the contribution
of each individual embedding to the consensus one.

ü  Multi-View Graph Clustering,

Multi-View Graph
Clustering recently reach lot of interest and an arsenal of algorithms 17-24
have been proposed. Limin Li (2014)
generalize a single-view penalized graph (SPGraph) clustering approach to a
Multiview penalized graph (MPGraph) version to integrate the structural and
chemical view of drug data in 17. They used the Laplacian eigenmaps with an extra
penalized term to cluster. Their proposed scheme is pretty similar to idea of
multi-view co-regularized spectral clustering. 18, X.
Zhang et al. (2016) solved the drawbacks of a nonnegative
matrix factorization (NMF) based multi-view clustering algorithms then proposed
the one via Graph Regularized Symmetric Nonnegative Matrix Factorization in 19. W. Zhuge et al (2017)
incorporated a new graph
learning mechanism into feature extraction and add an interaction between the
learned graph and the low-dimensional representations. The proposed feature
extraction with structured graph (FESG) scheme can learn both a transformation
matrix and an ideal structured graph containing the clustering information as
unsupervised single view 20. Furthermore, they
extended this framework to the multiple views feature extraction with
structured graph (MFESG), which learns an optimal weight for each view
automatically without requiring an additional parameter. More graph clustering are discussed in 21,
22,23,24.

ü 
Multi-View Subspace
Clustering subspace learning algorithms aim to obtain a
latent subspace shared by multiple views by assuming that the input views are
generated from this latent subspace then cluster the data points accordingly. H. Gao et al.(2015) proposed
an algorithm which can clustering on the subspace representation of
each view simultaneously in 25. X. Cao et al. (2015) extended the existing subspace clustering
into the multi-view domain, and used the Hilbert Schmidt Independence Criterion
(HSIC) as a diversity term to explore the complementarity of multi-view
representations26. More reading about
Subspace clustering can be find from27-32.

ü 
Multi-Task Multi-View
Clustering. X. Zhang et al.
(2016) proposed two multi-task multi-view clustering algorithms, the bipartite
graph based multi-task multi-view clustering algorithm (BMTMVC) for nonnegative
data, and the semi-nonnegative matrix tri-factorization based multi-task
multi-view clustering algorithm (SMTMVC) algorithm. for negative feature values 33. The proposed
algorithm’s framework is based on the co-clustering. A hierarchical clustering
multi-task learning (HC-MTL) have
been proposed in 34. Three challenges in
the area have motivated the authors: 1) Ignoring of the existence of latent
relatedness among actions, 2) Ignoring
of the grouping information among actions, 3) Difficulty in grouping
information discovery. They
formulated their objective function into the group-wise least square loss
regularized by low rank and sparsity with respect to two latent variables,
model parameters and grouping information, for joint optimization. However, the
proposed method cannot jointly leverage the multimodal and multi-view information
to discover even more latent correlations among different.

Background

2.1.  Multi-view Clustering

The
multi-view clustering consists of integrating multiple feature sets together to
perform clustering. One can say that, when clustering in multi-view data, we
can either perform a feature extraction or change the information interaction
process or make a consensus between many single view cluster. Generally
speaking, the multi-view clustering partitions a dataset into groups by
simultaneously considering multiple representations (views) for the same
instances. In real application k-means clustering, spectral clustering,
kernel-based clustering, graph-based clustering and hierarchical clustering
have been widely used.

• The correctness of views: How to know whether a view is correct is crucial for MvC.
Because MvC exploits all available views to help clustering performance, incorrect views are very harmful. Although some
work leverages these views with weights, errors could be propagated from a
misleading view to other views. Thus, this problem must be solved or mitigated
to a great extent to ensure that MvC is effective.