Sparsity Of Outliers Research Articles

Robust convex clustering

Objective-based clustering is a class of important clustering analysis techniques; however, these methods are easily beset by local minima due to the non-convexity of their objective functions involved, as a result, impacting final clustering performance. Recently, a convex clustering method (CC) has been on the spot light and enjoys the global optimality and independence on the initialization. However, one of its downsides is non-robustness to data contaminated with outliers, leading to a deviation of the clustering results. In order to improve its robustness, in this paper, an outlier-aware robust convex clustering algorithm, called as RCC, is proposed. Specifically, RCC extends the CC by modeling the contaminated data as the sum of the clean data and the sparse outliers and then adding a Lasso-type regularization term to the objective of the CC to reflect the sparsity of outliers. In this way, RCC can both resist the outliers to great extent and still maintain the advantages of CC, including the convexity of the objective. Further we develop a block coordinate descent approach with the convergence guarantee and find that RCC can usually converge just in a few iterations. Finally, the effectiveness and robustness of RCC are empirically corroborated by numerical experiments on both synthetic and real datasets.

Multimode process monitoring based on robust dictionary learning with application to aluminium electrolysis process

In modern process industries, many parameters or states can be acquired with sensors, and these parameters or states often have a close relationship with operation conditions. Unfortunately, the process often operates under different modes, and labels thereof are often unknown. In practice, labeling for sampled data is expensive and time-consuming, so identifying the operation conditions of the industrial process is difficult. In addition, sampled data from the industrial system are always contaminated by outliers or noise. Therefore, a robust process monitoring method for the multimode process is particularly important and challenging. In this paper, a robust dictionary learning method is proposed for processes with multiple unknown modes. Firstly, by taking the sparsity of outliers into account, a robust dictionary learning method is proposed to identify and remove the outliers and noise in the sampled training data. Secondly, an iterative minimization algorithm is designed for solving the dictionary learning optimization program. Thirdly, based on the sparsity of the sparse code, we partition the sparse code into different clusters via spectral clustering method, and then the dictionary is divided into some sub-dictionaries according to the cluster results of sparse code. Lastly, when a new sample is generated, we reconstruct it under different sub-dictionaries, and the smallest dictionary reconstruction error is calculated as a classifier for process monitoring and fault detection. To evaluate the validity and effectiveness of the proposed monitoring approach, we conduct extensive experiments on a numerical simulation, the continuous stirred tank heater (CSTH) process, and an industrial aluminum electrolysis process, in comparison with several state-of-the-art methods. The experimental results demonstrate that the proposed method is able to provide satisfying monitoring results, and it is also robust to outliers in the sampled training data. It is worth mentioning that the proposed method is an unsupervised learning method, therefore, it is more suitable for the process monitoring of real industrial systems.

Sparsity-Exploiting Robust Multidimensional Scaling

Multidimensional scaling (MDS) seeks an embedding of N objects in a p <; N dimensional space such that inter-vector distances approximate pairwise object dissimilarities. Despite their popularity, MDS algorithms are sensitive to outliers, yielding grossly erroneous embeddings even if few outliers contaminate the available dissimilarities. This work introduces robust MDS approaches exploiting the degree of sparsity in the outliers present. Links with compressive sampling lead to robust MDS solvers capable of coping with unstructured and structured outliers. The novel algorithms rely on a majorization-minimization approach to minimize a regularized stress function, whereby iterative MDS solvers involving Lasso and sparse group-Lasso operators are obtained. The resulting schemes identify outliers and obtain the desired embedding at computational cost comparable to that of their nonrobust MDS alternatives. The robust structured MDS algorithm considers outliers introduced by a sparse set of objects. In this case, two types of sparsity are exploited: i) sparsity of outliers in the dissimilarities; and ii) sparsity of the objects introducing outliers. Numerical tests on synthetic and real datasets illustrate the merits of the proposed algorithms.