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Jingya Chang

Publications and source records attributed to Jingya Chang.

9 recordsLinked to original sources
arXiv2023

A gradient projection method for semi-supervised hypergraph clustering problems

Semi-supervised clustering problems focus on clustering data with labels. In this paper,we consider the semi-supervised hypergraph problems. We use the hypergraph related tensor to construct an orthogonal constrained optimization model. The optimization problem is solved by a retraction method, which employs the polar decomposition to map the gradient direction in the tangent space to the Stefiel manifold. A nonmonotone curvilinear search is implemented to guarantee reduction in the objective function value. Convergence analysis demonstrates that the first order optimality condition is satisfied at the accumulation point. Experiments on synthetic hypergraph and hypergraph given by real data demonstrate the effectivity of our method.

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arXiv2023

Weighted structure tensor total variation for image denoising

For image denoising problems, the structure tensor total variation (STV)-based models show good performances when compared with other competing regularization approaches. However, the STV regularizer does not couple the local information of the image and may not maintain the image details. Therefore, we employ the anisotropic weighted matrix introduced in the anisotropic total variation (ATV) model to improve the STV model. By applying the weighted matrix to the discrete gradient of the patch-based Jacobian operator in STV, our proposed weighted STV (WSTV) model can effectively capture local information from images and maintain their details during the denoising process. The optimization problem in the model is solved by a fast first-order gradient projection algorithm with a complexity result of $O(1 / i^2)$. For images with different Gaussian noise levels, the experimental results demonstrate that the WSTV model can effectively improve the quality of restored images compared to other TV and STV-based models.

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arXiv2023

Hyperspectral super-resolution via low rank tensor triple decomposition

Hyperspectral image (HSI) and multispectral image (MSI) fusion aims at producing a super-resolution image (SRI). In this paper, we establish a nonconvex optimization model for image fusion problems through low-rank tensor triple decomposition. Using the L-BFGS approach, we develop a first-order optimization algorithm for obtaining the desired super-resolution image (TTDSR). Furthermore, two detailed methods are provided for calculating the gradient of the objective function. With the aid of the Kurdyka-Lojasiewicz property, the iterative sequence is proved to converge to a stationary point. Finally, experimental results on different datasets show the effectiveness of our proposed approach.

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arXiv2023

Multi-Linear Pseudo-PageRank for Hypergraph Partitioning

Motivated by the PageRank model for graph partitioning, we develop an extension of PageRank for partitioning uniform hypergraphs. Starting from adjacency tensors of uniform hypergraphs, we establish the multi-linear pseudo-PageRank (MLPPR) model, which is formulated as a multi-linear system with nonnegative constraints. The coefficient tensor of MLPPR is a kind of Laplacian tensors of uniform hypergraphs, which are almost as sparse as adjacency tensors since no dangling corrections are incorporated. Furthermore, all frontal slices of the coefficient tensor of MLPPR are M-matrices. Theoretically, MLPPR has a solution, which is unique under mild conditions. An error bound of the MLPPR solution is analyzed when the Laplacian tensor is slightly perturbed. Computationally, by exploiting the structural Laplacian tensor, we propose a tensor splitting algorithm, which converges linearly to a solution of MLPPR. Finally, numerical experiments illustrate that MLPPR is powerful and effective for hypergraph partitioning problems.

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arXiv2023

A tensor optimization algorithm for computing Lagrangians of hypergraphs

The Lagrangian of a hypergraph is a crucial tool for studying hypergraph extremal problems. Though Lagrangians of some special structure hypergraphs have closed-form solutions, it is a challenging problem to compute the Lagrangian of a general large scale hypergraph. In this paper, we exploit a fast computational scheme involving the adjacency tensor of a hypergraph. Furthermore, we propose to utilize the gradient projection method on a simplex from nonlinear optimization for solving the Lagrangian of a large scale hypergraph iteratively. Using the Lojasiewicz gradient inequality, we analyze the global and local convergence of the gradient projection method. Numerical experiments illustrate that the proposed numerical method could compute Lagrangians of large scale hypergraphs efficiently.

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arXiv2023

An adaptive weighted self-representation method for incomplete multi-view clustering

For multi-view data in reality, part of its elements may be missing because of human or machine error. Incomplete multi-view clustering (IMC) clusters the incomplete multi-view data according to the characters of various views of the instances. Recently, IMC has attracted much attention and many related methods have been proposed. However, the existing approaches still need to be developed and innovated in the following aspects: (1) Current methods only consider the differences of different views, while the different influences of instances, as well as distinguishes between missing values and completed values are ignored. (2) The updating scheme for weighting matrix in adaptive weighted algorithms usually relies on an optimization sub-problem, whose optimal solution may not be easy to achieve. (3) The adaptive weighted subspace algorithms that can recover the incomplete data are anchor types. The randomness of the anchor matrix may cause unreliability. To tackle these limitations, we propose an adaptive weighted self-representation (AWSR) subspace method for IMC. The AWSR method tunes the weighting matrix adaptively in accordance with the views of different instances and the recovery process of the missing values. The low rank and smoothness constraints on the representation matrix make the subspace reveal the underlying features of the dataset accurately. We also analyze the convergence property of the block coordinate method for our optimization model theoretically. Numerical performance on five real-world data shows that the AWSR method is effective and delivers superior results when compared to other eight widely-used approaches considering the clustering accuracy (ACC), normalized mutual information (NMI) and Purity.

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arXiv2017

Computing the $p$-Spectral Radii of Uniform Hypergraphs with Applications

The $p$-spectral radius of a uniform hypergraph covers many important concepts, such as Lagrangian and spectral radius of the hypergraph, and is crucial for solving spectral extremal problems of hypergraphs. In this paper, we establish a spherically constrained maximization model and propose a first-order conjugate gradient algorithm to compute the $p$-spectral radius of a uniform hypergraph (CSRH). By the semialgebraic nature of the adjacency tensor of a uniform hypergraph, CSRH is globally convergent and obtains the global maximizer with a high probability. When computing the spectral radius of the adjacency tensor of a uniform hypergraph, CSRH stands out among existing approaches. Furthermore, CSRH is competent to calculate the $p$-spectral radius of a hypergraph with millions of vertices and to approximate the Lagrangian of a hypergraph. Finally, we show that the CSRH method is capable of ranking real-world data set based on solutions generated by the $p$-spectral radius model.

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arXiv2016

Computing Eigenvalues of Large Scale Sparse Tensors Arising from a Hypergraph

The spectral theory of higher-order symmetric tensors is an important tool to reveal some important properties of a hypergraph via its adjacency tensor, Laplacian tensor, and signless Laplacian tensor. Owing to the sparsity of these tensors, we propose an efficient approach to calculate products of these tensors and any vectors. Using the state-of-the-art L-BFGS approach, we develop a first-order optimization algorithm for computing H- and Z-eigenvalues of these large scale sparse tensors (CEST). With the aid of the Kurdyka-Łojasiewicz property, we prove that the sequence of iterates generated by CEST converges to an eigenvector of the tensor.When CEST is started from multiple randomly initial points, the resulting best eigenvalue could touch the extreme eigenvalue with a high probability. Finally, numerical experiments on small hypergraphs show that CEST is efficient and promising. Moreover, CEST is capable of computing eigenvalues of tensors corresponding to a hypergraph with millions of vertices.

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