Multiview clustering partitions data into different groups according to their heterogeneous features. Most existing methods degenerate the applicability of models due to their intractable hyper-parameters triggered by various regularization terms. Moreover, traditional spectral based methods always encounter the expensive time overheads and fail in exploring the explicit clusters from graphs. In this paper, we present a scalable and parameter-free graph fusion framework for multiview clustering, seeking for a joint graph compatible across multiple views in a self-supervised weighting manner. Our formulation coalesces multiple view-wise graphs straightforward and learns the weights as well as the joint graph interactively, which could actively release the model from any weight-related hyper-parameters. Meanwhile, we manipulate the joint graph by a connectivity constraint such that the connected components indicate clusters directly. The designed algorithm is initialization-independent and time-economical which obtains the stable performance and scales well with the data size. Substantial experiments on toy data as well as real datasets are conducted that verify the superiority of the proposed method compared to the state-of-the-arts over the clustering performance and time expenditure.

The rapid growth of the number of data brings great challenges to clustering, especially the introduction of multi-view data, which collected from multiple sources or represented by multiple features, makes these challenges more arduous. How to clustering large-scale data efficiently has become the hottest topic of current large-scale clustering tasks. Although several accelerated multi-view methods have been proposed to improve the efficiency of clustering large-scale data, they still cannot be applied to some scenarios that require high efficiency because of the high computational complexity. To cope with the issue of high computational complexity of existing multi-view methods when dealing with large-scale data, a fast multi-view clustering model via nonnegative and orthogonal factorization (FMCNOF) is proposed in this paper. Instead of constraining the factor matrices to be nonnegative as traditional nonnegative and orthogonal factorization (NOF), we constrain a factor matrix of this model to be cluster indicator matrix which can assign cluster labels to data directly without extra post-processing step to extract cluster structures from the factor matrix. Meanwhile, the F-norm instead of the L2-norm is utilized on the FMCNOF model, which makes the model very easy to optimize. Furthermore, an efficient optimization algorithm is proposed to solve the FMCNOF model. Different from the traditional NOF optimization algorithm requiring dense matrix multiplications, our algorithm can divide the optimization problem into three decoupled small size subproblems that can be solved by much less matrix multiplications. Combined with the FMCNOF model and the corresponding fast optimization method, the efficiency of the clustering process can be significantly improved, and the computational complexity is nearly O(n). Extensive experiments on various benchmark data sets validate our approach can greatly improve the efficiency when achieve acceptable performance.

The large-scale hyperspectral image (HSI) clustering problem has attracted significant attention in the field of remote sensing. Most traditional graph-based clustering methods still face challenges in the successful application of the large-scale HSI clustering problem mainly due to their high computational complexity. In this letter, we propose a novel approach, called fast spectral clustering with anchor graph (FSCAG), to efficiently deal with the large-scale HSI clustering problem. Specifically, we consider the spectral and spatial properties of HSI in the anchor graph construction. The proposed FSCAG algorithm first constructs anchor graph and then performs spectral analysis on the graph. With this, the computational complexity can be reduced to O(ndm), which is a significant improvement compared to conventional graph-based clustering methods that need at least O(n²d), where n, d, and m are the number of samples, features, and anchors, respectively. Several experiments are conducted to demonstrate the efficiency and effectiveness of the proposed FSCAG algorithm.

K-means is one of the most simple and popular clustering algorithms, which implemented as a standard clustering method in most of machine learning researches. The goal of K-means clustering aims to find a set of cluster centers and minimize the sum of squared distances between each sample and its nearest clustering center. In this paper, we proposed a novel K-means clustering method, which reformulate the classical K-Means objective function as a trace maximization problem and then replace it with a new formulation. The proposed method does not need to calculate the cluster centers in each iteration and requires fewer additional intermediate variables during the optimization process. In addition, we propose an efficient iterative re-weighted algorithm to solve the involved optimization problem and provide the corresponding convergence analysis. The proposed method keeps a consistent computational complexity as Lloyd's algorithm, O(ndk), but shows a faster convergence rate in experiments. Extensive experimental results on a series real benchmark datasets show the effectiveness of the proposed method.

The locality preserving projections (LPP) algorithm is a recently developed linear dimensionality reduction algorithm that has been frequently used in face recognition and other applications. However, the projection matrix in LPP is not orthogonal, thus creating difficulties for both reconstruction and other applications. As the orthogonality property is desirable, orthogonal LPP (OLPP) has been proposed so that an orthogonal projection matrix can be obtained based on a step by step procedure; however, this makes the algorithm computationally more expensive. Therefore, in this paper, we propose a fast and orthogonal version of LPP, called FOLPP, which simultaneously minimizes the locality and maximizes the globality under the orthogonal constraint. As a result, the computation burden of the proposed algorithm can be effectively alleviated compared with the OLPP algorithm. Experimental results on two face recognition data sets and two hyperspectral data sets are presented to demonstrate the effectiveness of the proposed algorithm.