To cluster data that are not linearly separable in the original feature space, @math -means clustering was extended to the kernel version. However, the performance of kernel @math -means clustering largely depends on the choice of kernel function. To mitigate this problem, multiple kernel learning has been introduced into the @math -means clustering to obtain an optimal kernel combination for clustering. Despite the success of multiple kernel @math -means clustering in various scenarios, few of the existing work update the combination coefficients based on the diversity of kernels, which leads to the result that the selected kernels contain high redundancy and would degrade the clustering performance and efficiency. In this paper, we propose a simple but efficient strategy that selects a diverse subset from the pre-specified kernels as the representative kernels, and then incorporate the subset selection process into the framework of multiple @math -means clustering. The representative kernels can be indicated as the significant combination weights. Due to the non-convexity of the obtained objective function, we develop an alternating minimization method to optimize the combination coefficients of the selected kernels and the cluster membership alternatively. We evaluate the proposed approach on several benchmark and real-world datasets. The experimental results demonstrate the competitiveness of our approach in comparison with the state-of-the-art methods.
We propose a spectral clustering algorithm for the multi-view setting where we have access to multiple views of the data, each of which can be independently used for clustering. Our spectral clustering algorithm has a flavor of co-training, which is already a widely used idea in semi-supervised learning. We work on the assumption that the true underlying clustering would assign a point to the same cluster irrespective of the view. Hence, we constrain our approach to only search for the clusterings that agree across the views. Our algorithm does not have any hyperparameters to set, which is a major advantage in unsupervised learning. We empirically compare with a number of baseline methods on synthetic and real-world datasets to show the efficacy of the proposed algorithm. Combining information from various data sources has become an important research topic in machine learning with many scientific applications. Most previous studies employ kernels or graphs to integrate different types of features, which routinely assume one weight for one type of features. However, for many problems, the importance of features in one source to an individual cluster of data can be varied, which makes the previous approaches ineffective. In this paper, we propose a novel multi-view learning model to integrate all features and learn the weight for every feature with respect to each cluster individually via new joint structured sparsity-inducing norms. The proposed multi-view learning framework allows us not only to perform clustering tasks, but also to deal with classification tasks by an extension when the labeling knowledge is available. A new efficient algorithm is derived to solve the formulated objective with rigorous theoretical proof on its convergence. We applied our new data fusion method to five broadly used multi-view data sets for both clustering and classification. In all experimental results, our method clearly outperforms other related state-of-the-art methods.  Clustering data in high dimensions is believed to be a hard problem in general. A number of efficient clustering algorithms developed in recent years address this problem by projecting the data into a lower-dimensional subspace, e.g. via Principal Components Analysis (PCA) or random projections, before clustering. Here, we consider constructing such projections using multiple views of the data, via Canonical Correlation Analysis (CCA). Under the assumption that the views are un-correlated given the cluster label, we show that the separation conditions required for the algorithm to be successful are significantly weaker than prior results in the literature. We provide results for mixtures of Gaussians and mixtures of log concave distributions. We also provide empirical support from audio-visual speaker clustering (where we desire the clusters to correspond to speaker ID) and from hierarchical Wikipedia document clustering (where one view is the words in the document and the other is the link structure). With advances in information acquisition technologies, multi-view data become ubiquitous. Multi-view learning has thus become more and more popular in machine learning and data mining fields. Multi-view unsupervised or semi-supervised learning, such as co-training, co-regularization has gained considerable attention. Although recently, multi-view clustering (MVC) methods have been developed rapidly, there has not been a survey to summarize and analyze the current progress. Therefore, this paper reviews the common strategies for combining multiple views of data and based on this summary we propose a novel taxonomy of the MVC approaches. We further discuss the relationships between MVC and multi-view representation, ensemble clustering, multi-task clustering, multi-view supervised and semi-supervised learning. Several representative real-world applications are elaborated. To promote future development of MVC, we envision several open problems that may require further investigation and thorough examination.