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In this paper, a novel low-rank structural model is proposed for segmenting data drawn from a high-dimensional space. Our method is based on the fact that all groups clustered from a high-dimensional dataset are distributed in multiple low-rank subspaces. In general, it’s a very difficult task to find the low-rank structures hidden in data. Different from the classical sparse subspace clustering (SSC) and low-rank representation (LRR) which all take two steps including building the affinity matrix and spectral clustering, we introduce a new rank constraint into our model. This constraint allows our model to learn a subspace indicator which can capture different clusters directly from the data without any postprocessing. To further approximate the rank constraint, a piecewise function is utilized as the relaxing item for the proposed model. Besides, under the subspace indicator constraints, the integer programming problem is avoided, which makes our algorithm more efficient and scalable. In addition, we prove the convergence of the proposed algorithm in theory and further discuss the general case in which subspaces don’t pass through the origin. Experiment results on both synthetic and real-world datasets demonstrate that our algorithm significantly outperforms the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Fuzzy K-Means (FKM) clustering is of great importance for analyzing unlabeled data. FKM algorithms assign each data point to multiple clusters with some degree of certainty measured by the membership function. In these methods, the fuzzy membership degree matrix is obtained based on the calculation of the distance between data points in the original space. However, this operation may lead to suboptimal results because of the influence of noises and redundant features. Besides, some FKM clustering methods ignore the importance of the weighting exponent. In this paper, we propose a novel FKM method called Fuzzy K-Means Clustering With Discriminative Embedding. Within this method, we simultaneously conduct dimensionality reduction along with fuzzy membership degree learning. To retain most information in the embedding subspace and improve the robustness of this method, principal component analysis is incorporated into our framework. An iterative optimization algorithm is proposed to solve the model. To validate the efficacy of the proposed method, we perform comprehensive analyses, including convergence behavior, parameter determination and computational complexity. Moreover, we also match a appropriate weighting exponent for each data set. Experimental results on benchmark data sets show that the proposed method is more discriminative and effective for clustering tasks. [ABSTRACT FROM AUTHOR]

Due to the exponential growth of multimedia data, multi-modal hashing as a promising technique to make cross-view retrieval scalable is attracting more and more attention. However, most of the existing multi-modal hashing methods either divide the learning process unnaturally into two separate stages or treat the discrete optimization problem simplistically as a continuous one, which leads to suboptimal results. Recently, a few discrete multi-modal hashing methods that try to address such issues have emerged, but they still ignore several important discrete constraints (such as the balance and decorrelation of hash bits). In this paper, we overcome those limitations by proposing a novel method named “Enhanced Discrete Multi-modal Hashing (EDMH)” which learns binary codes and hashing functions simultaneously from the pairwise similarity matrix of data, under the aforementioned discrete constraints. Although the model of EDMH looks a lot more complex than the other models for multi-modal hashing, we are actually able to develop a fast iterative learning algorithm for it, since the subproblems of its optimization all have closed-form solutions after introducing a couple of auxiliary variables. Our experimental results on three real-world datasets have revealed the usefulness of those previously ignored discrete constraints and demonstrated that EDMH not only performs much better than state-of-the-art competitors according to several retrieval metrics but also runs much faster than most of them. [ABSTRACT FROM AUTHOR]

Feature selection is one of the most important techniques to deal with the high-dimensional data for a variety of machine learning and data mining tasks, such clustering, classification, and retrieval, etc. Fuzziness is a widespread nature of data in nature human society. However, most existing feature selection methods ignore the existence of fuzziness in the data, resulting in sub-optimal feature subsets. To address the problem, we propose a novel unsupervised feature selection method, called Unsupervised Discriminative Projection for Feature Selection (UDPFS) to select discriminative features by conducting fuzziness learning and sparse learning, simultaneously. Specifically, we use projection matrix transform data as its low-dimensional representation, which are partitioned into clusters by using membership matrix with sparse constraint. In addition, $\ell _{2, 1}$ ℓ 2 , 1 -norm regularization is applied to the projection matrix. Then, a discriminative projection matrix with row sparse is obtained by perform fuzziness learning and sparse learning, simultaneously. An effective alternative optimization algorithm is proposed to solve the objective function. Evaluate experimental results on several real-world datasets show the effectiveness and superiority of the proposed unsupervised feature selection method. [ABSTRACT FROM AUTHOR]

In many real-world applications, we are often confronted with high dimensional data which are represented by various heterogeneous views. How to cluster this kind of data is still a challenging problem due to the curse of dimensionality and effectively integration of different views. To address this problem, we propose two parameter-free weighted multi-view projected clustering methods which perform structured graph learning and dimensionality reduction simultaneously. We can use the obtained structured graph directly to extract the clustering indicators, without performing other discretization procedures as previous graph-based clustering methods have to do. Moreover, two parameter-free strategies are adopted to learn an optimal weight for each view automatically, without introducing a regularization parameter as previous methods do. Extensive experiments on several public datasets demonstrate that the proposed methods outperform other state-of-the-art approaches and can be used more practically. [ABSTRACT FROM AUTHOR]

Graph clustering plays an important role in data mining. Based on an input data graph, data points are partitioned into clusters. However, most existing methods keep the data graph fixed during the clustering procedure, so they are limited to exploit the implied data manifold and highly dependent on the initial graph construction. Inspired by the recent development on manifold learning, this paper proposes an Adaptive Consistency Propagation (ACP) method for graph clustering. In order to utilize the features captured from different perspectives, we further put forward the Multi-view version of the ACP model (MACP). The main contributions are threefold: (1) the manifold structure of input data is sufficiently exploited by propagating the topological connectivities between data points from near to far; (2) the optimal graph for clustering is learned by taking graph learning as a part of the optimization procedure; and (3) the negotiation among the heterogeneous features is captured by the multi-view clustering model. Extensive experiments on real-world datasets validate the effectiveness of the proposed methods on both single- and multi-view clustering, and show their superior performance over the state-of-the-arts. [ABSTRACT FROM AUTHOR]