Multi-view clustering (MVC) holds a significant role in domains like machine learning, data mining, and pattern recognition. Despite the development of numerous new MVC approaches employing various techniques, there remains a gap in comprehensive studies evaluating the characteristics and performance of these approaches. This gap hinders the in-depth understanding and rational utilization of the recently developed MVC techniques. This study formalizes the basic concepts of MVC and analyzes their techniques. It then introduces a novel taxonomy for MVC approaches and presents the working mechanisms and characteristics of representative MVC approaches developed in recent years. Moreover, it summarizes representative datasets and performance metrics commonly employed for evaluating MVC approaches. Furthermore, we have meticulously chosen 35 representative MVC approaches to conduct an empirical evaluation across seven real-world benchmark datasets, offering valuable insights into the realm of MVC approaches.

Spatial co-location pattern mining is an interesting and important task in spatial data mining which discovers the subsets of spatial features frequently observed together in nearby geographic space. However, the traditional framework of mining prevalent co-location patterns produces numerous redundant co-location patterns, which makes it hard for users to understand or apply. To address this issue, in this paper, we study the problem of reducing redundancy in a collection of prevalent co-location patterns by utilizing the spatial distribution information of co-location instances. We first introduce the concept of semantic distance between a co-location pattern and its super-patterns, and then define redundant co-locations by introducing the concept of δ-covered, where $\delta \,(0\leq \delta \leq 1)$ is a coverage measure. We develop two algorithms RRclosed and RRnull to perform the redundancy reduction for prevalent co-location patterns. The former adopts the post-mining framework that is commonly used by existing redundancy reduction techniques, while the latter employs the mine-and-reduce framework that pushes redundancy reduction into the co-location mining process. Our performance studies on the synthetic and real-world data sets demonstrate that our method effectively reduces the size of the original collection of closed co-location patterns by about 50 percent. Furthermore, the RRnull method runs much faster than the related closed co-location pattern mining algorithm.

Multi-view clustering (MVC), which aims to explore the underlying structure of data by leveraging heterogeneous information of different views, has brought along a growth of attention. Multi-view clustering algorithms based on different theories have been proposed and extended in various applications. However, most existing MVC algorithms are shallow models, which learn structure information of multi-view data by mapping multi-view data to low-dimensional representation space directly, ignoring the nonlinear structure information hidden in each view, and thus, the performance of multi-view clustering is weakened to a certain extent. In this paper, we propose a deep multi-view clustering algorithm based on multiple auto-encoder, termed MVC-MAE, to cluster multi-view data. MVC-MAE adopts auto-encoder to capture the nonlinear structure information of each view in a layer-wise manner and incorporate the local invariance within each view and consistent as well as complementary information between any two views together. Besides, we integrate the representation learning and clustering into a unified framework, such that two tasks can be jointly optimized. Extensive experiments on six real-world datasets demonstrate the promising performance of our algorithm compared with 15 baseline algorithms in terms of two evaluation metrics.

Multiview subspace clustering has turned into a promising technique due to its encouraging ability to discover the underlying subspace structure. In recent studies, a lot of subspace clustering methods have been developed to strengthen the clustering performance of multiview data, but these methods rarely consider simultaneously the nonlinear structure and multilevel representation (MLR) information in multiview data as well as the data distribution of latent representation. To address these problems, we develop a new Multiview Subspace Clustering with MLRs and Adversarial Regularization (MvSC-MRAR), where multiple deep auto-encoders are utilized to model nonlinear structure information of multiview data, multiple self-expressive layers are introduced into each deep auto-encoder to extract multilevel latent representations of each view data, and diversity regularizations are designed to preserve complementary information contained in different layers and different views. Furthermore, a universal discriminator based on adversarial training is developed to enforce the output of each encoder to obey a given prior distribution, so that the affinity matrix for spectral clustering (SPC) is more realistic. Comprehensive empirical evaluation with nine real-world multiview datasets indicates that our proposed MvSC-MRAR achieves significant improvements than several state-of-the-art methods in terms of clustering accuracy (ACC) and normalized mutual information (NMI).

The spatial co-location pattern is a collection of spatial features in which instances of features prevalently appear in neighboring spatial regions. Due to the heterogeneity of spatial data distribution, the instances of some patterns appear prevalently in the global region (i.e., Global Prevalent Co-location Patterns, GPCPs), while some patterns are not prevalent globally, and their instances are clustered only in some local regions (i.e., Local Prevalent Co-location Patterns, LPCPs). Multi-level co-location pattern mining aims to mine these two types of patterns simultaneously, but existing methods cannot accurately judge the spatial distribution of patterns in a certain region, leading to unsuitable judgment of both GPCPs and LPCPs. To overcome this problem, this paper firstly proposes the relative distribution coefficient to identify the spatial distribution form of patterns, and provides a more refined way for discovering both GPCPs and LPCPs. Secondly, a novel multi-level co-location pattern mining algorithm is proposed by using the relative distribution coefficient as the interest metrics, and some pruning strategies are suggested to improve the mining efficiency. Finally, extensive experiments are conducted on both real and synthetic datasets to verify the effectiveness and efficiency of the proposed method.