Low-rank Sparse Matrix Research Articles

Multiple Faults Detection for Rotating Machinery Based on Bicomponent Sparse Low-Rank Matrix Separation Approach

Multifault detection of rotating machinery at the incipient fault stage presents a challenging issue due to its interaction feature, complexity, and coupling characteristics. Aiming at the concern of identifying the multiple faults pattern of rotating machinery, a novel multiple faults detection approach based on Bi-component sparse low-rank matrix separation is proposed in this paper. The core idea of the proposed method is that the measured vibration signal typically shows as the sum of transient component and oscillatory component, meanwhile, the multi-fault identification problem with regularization terms can be transformed into a sparse optimization formulation that could be solved by the alternating direction method of multipliers algorithm. The proposed approach is applied by simulated synthetic signal, experimental data including rolling bearing and gearbox with weak multiple faults, and its effectiveness and superiority are verified by comparing to some state-of-the-art methods such as L1-norm fused lasso optimization, maximum correlated kurtosis deconvolution, and ensemble empirical mode decomposition.

Incipient Fault Diagnosis for Large Reducer Taper Roller Bearings Based on Non-convex Penalty Regularization Sparse Low-rank Matrix Approach

Incipient Fault Diagnosis for Large Reducer Taper Roller Bearings Based on Non-convex Penalty Regularization Sparse Low-rank Matrix Approach

Spike and slab biclustering

Biclustering refers to the problem of simultaneously clustering the rows and columns of a given data matrix, with the goal of obtaining submatrices where the selected rows present a coherent behaviour in the selected columns, and vice-versa. To face this intrinsically difficult problem, we propose a novel generative model, where biclustering is approached from a sparse low-rank matrix factorization perspective. The main idea is to design a probabilistic model describing the factorization of a given data matrix in two other matrices, from which information about rows and columns belonging to the sought for biclusters can be obtained. One crucial ingredient in the proposed model is the use of a spike and slab sparsity-inducing prior, thus we term the approach spike and slab biclustering (SSBi). To estimate the parameters of the SSBi model, we propose an expectation-maximization (EM) algorithm, termed SSBiEM, which solves a low-rank factorization problem at each iteration, using a recently proposed augmented Lagrangian algorithm. Experiments with both synthetic and real data show that the SSBi approach compares favorably with the state-of-the-art.

Improved sparse low-rank matrix estimation

We address the problem of estimating a sparse low-rank matrix from its noisy observation. We propose an objective function consisting of a data-fidelity term and two parameterized non-convex penalty functions. Further, we show how to set the parameters of the non-convex penalty functions, in order to ensure that the objective function is strictly convex. The proposed objective function better estimates sparse low-rank matrices than a convex method which utilizes the sum of the nuclear norm and the ℓ1 norm. We derive an algorithm (as an instance of ADMM) to solve the proposed problem, and guarantee its convergence provided the scalar augmented Lagrangian parameter is set appropriately. We demonstrate the proposed method for denoising an audio signal and an adjacency matrix representing protein interactions in the ‘Escherichia coli’ bacteria.

Laser induced breakdown spectroscopy for quantitative analysis based on low-rank matrix approximations

In this paper, a novel and quantitative LIBS analysis method based on a sparse low-rank matrix approximation via convex optimization is proposed.

Estimation of a sparse and spiked covariance matrix

We suggest a method for estimating a covariance matrix that can be represented as a sum of a sparse low-rank matrix and a diagonal matrix. Our formulation is based on penalized quadratic loss, which is a convex problem that can be solved via incremental gradient and proximal method. In contrast to other spiked covariance matrix estimation approaches that are related to principal component analysis and factor analysis, our method has a simple formulation and does not constrain entire rows and columns of the matrix to be zero. We further discuss a penalized entropy loss method that is nevertheless nonconvex and necessitates a majorization-minimization algorithm in combination with the incremental gradient and proximal method. We carry out simulations to demonstrate the finite-sample properties focusing on high-dimensional covariance matrices. Finally, the proposed method is illustrated using a gene expression data set.

Exemplar-based low-rank matrix decomposition for data clustering

Today, digital data is accumulated at a faster than ever speed in science, engineering, biomedicine, and real-world sensing. The ubiquitous phenomenon of massive data and sparse information imposes considerable challenges in data mining research. In this paper, we propose a theoretical framework, Exemplar-based low-rank sparse matrix decomposition (EMD), to cluster large-scale datasets. Capitalizing on recent advances in matrix approximation and decomposition, EMD can partition datasets with large dimensions and scalable sizes efficiently. Specifically, given a data matrix, EMD first computes a representative data subspace and a near-optimal low-rank approximation. Then, the cluster centroids and indicators are obtained through matrix decomposition, in which we require that the cluster centroids lie within the representative data subspace. By selecting the representative exemplars, we obtain a compact "sketch"of the data. This makes the clustering highly efficient and robust to noise. In addition, the clustering results are sparse and easy for interpretation. From a theoretical perspective, we prove the correctness and convergence of the EMD algorithm, and provide detailed analysis on its efficiency, including running time and spatial requirements. Through extensive experiments performed on both synthetic and real datasets, we demonstrate the performance of EMD for clustering large-scale data.