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As graph technology is widely used in unsupervised dimensionality reduction, many methods automatically construct a full connection graph to learn the structure of data, and then preserve critical information on data in subspace. The construction of a full connection graph with heavy computational complexity, however, is separated from the optimization of transformation matrix. In order to solve significant computational burden, we design anchor-based graph and unify the construction of graph and optimization of transformation matrix into a framework called fast unsupervised embedding learning with anchor-based graph (FUAG) which not only can avoid the impact of noises and redundant features in original space, but also can capture local structure of data in subspace precisely. Our method additionally incorporates the discriminant information of data captured by using trace difference form. Meanwhile, it optimizes the anchor-based graph partitioning problem with Constrained Laplacian Rank in order to ensure that the number of connected components is exactly equal to the number of classes. We also impose ℓ 0 norm constraint on each point to avoid trivial solutions and propose an efficient iterative algorithm. Experimental results on both synthetic and real-world datasets demonstrate the promising performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• The proposed model is built on Grassmann manifold. • The proposed model can fully mine the subspace information of views. • The proposed model can get clustering results directly without postprocessing. • The proposed model can ensure the inconsistency of different views. • The proposed model with effectiveness and efficiency can be applied to practice. Multi-view clustering plays an important role in a wide spectrum of applications. In this article, we propose a multi-view clustering approach with adaptive Procrustes on Grassmann manifold (MC-APGM) to overcome the three demerits in existing graph-based multi-view clustering methods, namely, insufficient mining of subspace information of views, a requirement for post-processing, and high computational complexity. Specifically, in the proposed model, the indicator matrix is directly learned from multiple orthogonal spectral embeddings, avoiding the random clustering results caused by post-processing; The orthogonal form of the indicator matrix approximates multiple orthogonal spectral embeddings on the Grassmann manifold, fully uncovering subspace information of views and thus improving clustering performance; Both implicitly and explicitly weighted learning mechanisms are established to capture inconsistencies among different views. Moreover, an efficient algorithm with rigorous convergence guarantee is derived to optimize the proposed model. Finally, experimental results on both toy and real-world datasets demonstrate the effectiveness and efficiency of this proposed method. [ABSTRACT FROM AUTHOR]

Linear Discriminant Analysis (LDA) is one of most important methods in dimensionality reduction domain, which is limited with Gaussian assumption. Because of the complexity of real data, data often presents non-Gaussian distribution that points in same class can be divided into several sub-clusters and center point is not enough to describe the distribution of data. In order to solve non-Gaussian data, LDA-based methods consider local structure information through measuring each pairwise distance of full connection graph. However, the strategy of establishing fully-connected graph is at expense of high computational complexity and limits it practical and industrial applications. We propose a Fast Local Representation Learning (FLRL) method which leverages anchor points to establish anchor-based graph and uses similarity matrix to depict the relationships of each pairwise connections. Notably, to avoid the affect of noises and redundant features in original space, anchor points and similarity matrix are updated alternately in subspace that local structure of data will be more precise to learn. Extensive pattern classification and image retrieval experiments on several synthetic datasets, well-known datasets and deep features datasets demonstrate the advantages of our method over the state-of-the-art methods. Our source code available on : https://github.com/superzcy/FLRL. [ABSTRACT FROM AUTHOR]