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The aim of this paper is to design an algorithm based on nonsmooth optimization techniques to solve the minimum sum-of-squares clustering problems in very large data sets. First, the clustering problem is formulated as a nonsmooth optimization problem. Then the limited memory bundle method [Haarala et al., 2007] is modified and combined with an incremental approach to design a new clustering algorithm. The algorithm is evaluated using real world data sets with both the large number of attributes and the large number of data points. It is also compared with some other optimization based clustering algorithms. The numerical results demonstrate the efficiency of the proposed algorithm for clustering in very large data sets. [ABSTRACT FROM AUTHOR]

Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace representation by constructing affinity matrix shared among all views. Relying on the importance of both low-rank and sparsity constraints in the construction of the affinity matrix, we introduce the objective that balances between the agreement across different views, while at the same time encourages sparsity and low-rankness of the solution. Related low-rank and sparsity constrained optimization problem is for each view solved using the alternating direction method of multipliers. Furthermore, we extend our approach to cluster data drawn from nonlinear subspaces by solving the corresponding problem in a reproducing kernel Hilbert space. The proposed algorithm outperforms state-of-the-art multi-view subspace clustering algorithms on one synthetic and four real-world datasets. [ABSTRACT FROM AUTHOR]

Kernel possibilistic fuzzy C-means with local information (KWPFLICM) has important research significance of image segmentation, but it is very sensitive to high noise or outliers. To enhance the segmentation performance of the algorithm, this paper proposes a kernelized total Bregman divergence-driven possibilistic fuzzy clustering with local information (TKWPFLICM). Firstly, a polynomial kernel function is introduced to kernelize total Bregman divergence (TBD), and local neighborhood information of the pixel is used to modify it, which overcomes the shortcomings of Bregman divergence (BD) with rotation variability; Secondly, the modified kernelized TBD and possibilistic typicality are combined to further enhance the anti-noise ability of the algorithm; Finally, the modified kernelized TBD is introduced into the objective function of KWPFLICM algorithm, then a novel robust fuzzy clustering algorithm is derived by optimization theory. Experimental results show that compared with existing fuzzy clustering-related algorithms, the average SA improvement on TKWPFLICM algorithm is in the range of 0.791% to 33.237%. Therefore, TKWPFLICM algorithm has better anti-noise robustness and segmentation accuracy. [ABSTRACT FROM AUTHOR]

• An exclusivity term is introduced to enforce the diversity of different views. • Multi-view subspace representation is constrained to find the cluster structure. • An effective optimization algorithm is proposed to solve the objective function. • Experiments demonstrate that our algorithm outperforms state-of-the-art approaches. Multi-view subspace clustering algorithms have recently been developed to process multi-view dataset clustering by accurately depicting the essential characteristics of multi-view data. Most existing methods focus on conduct self-representation property using a consistent representation and a set of specific representations with well-designed regularization to learn the common and specific knowledge among different views. However, specific representations only contain the unique information of each individual view, which limits their ability to fully excavate the diversity of multi-view data to enhance the complementarity among different views. Moreover, when conducting multi-view subspace clustering, the learned subspace self-representation and clustering are sequential and independent, which lacks consideration of the interaction between representation learning and the final clustering calculation. In this paper, a novel method termed consistent and diverse multi-view subspace clustering with structure constraint (CDMSC 2) is proposed to overcome the above-described deficiencies. (1) An exclusivity constraint term is employed to enhance the diversity of specific representations among different views for modeling consistency and diversity in a unified framework. (2) A clustering structure constraint is imposed on the subspace self-representation by factorizing the learned subspace self-representation into the cluster centroids and the cluster assignments with the goal of obtaining a clustering-oriented subspace self-representation. In addition, we carefully designed an efficient optimization algorithm to solve the objective function through relaxation and alternating minimization. Extensive experiments on five benchmark datasets in terms of six evaluation metrics demonstrate that our method outperforms the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

• Our algorithm detects a low-dimensional manifold that lies within a set of bounds. • The bounds are derived using a given high-dimensional dataset of a point cloud. • A matrix representing the distances on a low-dimensional manifold is low-rank. • Our method recovers a partially observed distance matrix using fully observed entries. • Low-rank matrix completion is used to recover partially observed distance matrices. Nonlinear dimensionality reduction is an active area of research. In this paper, we present a thematically different approach to detect a low-dimensional manifold that lies within a set of bounds derived from a given point cloud. A matrix representing distances on a low-dimensional manifold is low-rank, and our method is based on current low-rank Matrix Completion (MC) techniques for recovering a partially observed matrix from fully observed entries. MC methods are currently used to solve challenging real-world problems such as image inpainting and recommender systems. Our MC scheme utilizes efficient optimization techniques that employ a nuclear norm convex relaxation as a surrogate for non-convex and discontinuous rank minimization. The method theoretically guarantees on detection of low-dimensional embeddings and is robust to non-uniformity in the sampling of the manifold. We validate the performance of this approach using both a theoretical analysis as well as synthetic and real-world benchmark datasets. [ABSTRACT FROM AUTHOR]

• A binary coyote optimization algorithm for feature selection problem is proposed. • The binarization method is based on hyperbolic transfer function. • We test the proposed wrapper with the Naïve Bayes classifier using seven data sets. • The wrapper presents high training accuracy. • The wrapper shows relatively low standard deviation and subsets with few features. The Coyote Optimization Algorithm (COA) is a bio-inspired optimization algorithm based on the intelligent behavior of coyotes. COA was proposed recently and it considers the social organization of the coyotes and its adaptation to the environment in order to solve continuous optimization problems. In addition, it is a population-based algorithm and it can be classified as both, swarm intelligence and evolutionary heuristics, because contributes with a different algorithmic structure. This paper proposes a binary version of the COA, named Binary COA (BCOA) applying to select the optimal feature subset for classification, based on the hyperbolic transfer function in a wrapper model. By this way, the features are selected based on the performance evaluation of a classification algorithm. We tested the effectiveness of the BCOA wrapper with the Naïve Bayes classifier and were used seven public domain benchmark datasets to compare the proposed approach in terms of classification accuracy, number of selected features and computational cost with other state-of-art algorithms of the literature. The results shown that BCOA was able to find subsets with few features while it still performs well in terms of classification accuracy. [ABSTRACT FROM AUTHOR]