1. Introduction

Clustering is one of the most critical unsupervised learning techniques, which has been widely applied for data analysis, such as social network analysis, gene expression analysis, heterogeneous data analysis, and market analysis. The goal of clustering is to partition a dataset into several groups such that data samples in the same group are more similar than those in

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

different groups. Clustering plays an important role in mining the hidden patterns. However, most of the existing clustering algorithms are designed for single-view data.

view clustering methods can be unified into the frameworks of these five methods. Therefore, when readers become familiar with these five multi-view clustering methods, they can capture the core ideas of other multi-view clustering methods easily. This chapter is self-contained, which follows a line of introduction from the preliminaries of these clustering methods for

New Approaches in Multi-View Clustering http://dx.doi.org/10.5772/intechopen.75598 197

The remainder of this chapter is organized as follows. Section 2 describes the benefits of multiview clustering. Section 3 details the aforementioned five multi-view clustering methods. Section 4 summarizes two kinds of popular open datasets. Several open issues are illustrated

Compared with the clustering methods that are implemented on single-view data, multi-view clustering is expected to obtain more robust and novel partitioning results by exploiting the redundant and complementary information in different views [5], as stated in the following

It is obvious that single-view data may contain incomplete knowledge, while multi-view data usually contains complementary and redundant information, which results in a more accurate description of the data. For example, it may fail to identify the intrinsic community structures of a social network via just leveraging the friendships. However, if more information such as users' demographics can be obtained, it is more inclined to find out the implicit relationships

Even when the information contained in single-view data is complete, there may exist some unavoidable noises. It is apparent that data cleaning is one critical issue in data analysis, which can tremendously affect the performance of clustering algorithms. It is quite hard and costly to remove all the noises of data, and thus single-view noisy data usually leads to unsatisfactory clustering results. On the other hand, multi-view clustering is able to circumvent the side effect of noises or corrupted data in each view and emphasize the common patterns shared by multi-

There is no doubt that all the multi-view clustering methods can be applied to single-view data. However, many clustering tasks are impossible to implement by single-view clustering due to its limitations. For example, data with multiple modalities is becoming more and more common and heterogeneous information networks are gaining increasing popularity as well.

single-view data to their variant forms for multi-view clustering.

in Section 5. Section 6 concludes this chapter.

2. Benefits of multi-view clustering

2.1. Benefit one: accurate description of data

2.2. Benefit two: reducing noises of data

2.3. Benefit three: wider range of applications

sections.

between users.

view data.

With the rapid development of Internet and communication technology (ICT), the accesses to extract data are dramatically extended. That is, data can be collected from multiple sources or multiple facets. In such setting, each datum is associated with much richer information, which results in the requirement that to mine the intrinsic and valuable patterns hidden in the data, it is a necessity to take full advantage of the information contained in multiple sources. This issue is formally referred to as multi-view learning. To be more specific, each view corresponds to one source of information. For example, web pages can be described by both the page-contents (one view) and the hyperlink information (another view). Besides, different facets of a datum can also be treated as different views. For instance, an image can be characterized by its shape, color, and location.

Obviously, integrating the information contained in multiple views can bring great benefits for data clustering. The most straightforward way to utilize the information of all views is to concatenate the data features of each view together and then perform the traditional clustering methods such as k-means. However, such a method lacks the ability to distinguish the different significance of different views. That is, the important views and less important views are treated equally, which may degrade the ultimate performance severely. To take better advantage of the multi-view information, the ideal approach is to simultaneously perform the clustering using each view of data features and integrate their results based on their importance to the clustering task. Formally, this approach is known as multi-view clustering.

As an emerging and effective paradigm in data mining and machine learning, multi-view clustering refers to the clustering of the same class of data samples with multi-view representations, either from various information sources or from different feature generators. It is clear that if the clustering method cannot cope appropriately with multi-views, these views may even degrade the performance of multi-view clustering. To make use of multi-view information to improve clustering results, there are two main challenges to overcome. The first one is how to naturally ensemble the multiple clustering results of all the views. The second one is how to learn the importance of different views to the clustering task. In addition, these two issues should be figured out simultaneously. Thus, to achieve these goals, new clustering objective function should be designed, followed by the new solving method.

Multi-view clustering was first studied by Bickel and Scheffer [1] in 2004. They extended the classic k-means and expectation maximization (EM) clustering methods to the multi-view environment to deal with text data with two conditionally independent views. Based on this seminal work, a variety of multi-view clustering methods have been proposed over the past two decades [2–4]. Since covering all the proposed methods in one chapter is hard, to provide a comprehensive review of the typical multi-view clustering methods and their corresponding recent developments, we summarize five kinds of popular clustering methods and their multiview learning versions, which include k-means, spectral clustering, matrix factorization, tensor decomposition, and deep learning. This is based on the consideration that these clustering methods are the most widely employed algorithms for single-view data, and lots of efforts have been devoted to extending them for multi-view clustering. Besides, many other multiview clustering methods can be unified into the frameworks of these five methods. Therefore, when readers become familiar with these five multi-view clustering methods, they can capture the core ideas of other multi-view clustering methods easily. This chapter is self-contained, which follows a line of introduction from the preliminaries of these clustering methods for single-view data to their variant forms for multi-view clustering.

The remainder of this chapter is organized as follows. Section 2 describes the benefits of multiview clustering. Section 3 details the aforementioned five multi-view clustering methods. Section 4 summarizes two kinds of popular open datasets. Several open issues are illustrated in Section 5. Section 6 concludes this chapter.
