[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

The minimum Covariance Determinant (MCD) scatter estimator is a highly robust estimator for the dispersion matrix of a multivariate, elliptically symmetric distribution. It is fast to compute and intuitively appealing. In this note we derive its influence function and compute the asymptotic variances of its elements. A comparison with the one step reweighted MCD and with S-estimators is made. Also finite-sample results are reported.

Influence Function and Efficiency of the Minimum Covariance Determinant Scatter MAtrix Estimator

Process monitoring is crucial for maintaining favorable operating conditions and has received considerable attention in previous decades. Currently, a plant-wide process generally consists of multiple operational units and a large number of measured variables. The correlation among the variables and units is complex and results in the imperative but challenging monitoring of such plant-wide processes. With the rapid advancement of industrial sensing techniques, process data with meaningful process information are collected. Data-driven multivariate statistical plant-wide process monitoring (DMSPPM) has become popular. The key idea of DMSPPM is first decomposing a plant-wide process into multiple subprocesses and then establishing a data-driven model for monitoring the process, in which process variable decomposition is important for guaranteeing the monitoring performance. In the current review, we first introduce the basics of multivariate statistical process monitoring and highlight the necessity of des...

Review and Perspectives of Data-Driven Distributed Monitoring for Industrial Plant-Wide Processes

Review and big data perspectives on robust data mining approaches for industrial process modeling with outliers and missing data

Traditional spectral-based methods such as PCA are popular for anomaly detection in a variety of problems and domains. However, if data includes tensor (multiway) structure (e.g. space-time-measurements), some meaningful anomalies may remain invisible with these methods. Although tensor-based anomaly detection (TAD) has been applied within a variety of disciplines over the last twenty years, it is not yet recognized as a formal category in anomaly detection. This survey aims to highlight the potential of tensor-based techniques as a novel approach for detection and identification of abnormalities and failures. We survey the interdisciplinary works in which TAD is reported and characterize the learning strategies, methods and applications; extract the important open issues in TAD and provide the corresponding existing solutions according to the state-of-the-art.

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Tensor-based anomaly detection

A novel dimensionality reduction algorithm named “global–local preserving projections” (GLPP) is proposed. Different from locality preserving projections (LPP) and principal component analysis (PCA), GLPP aims at preserving both global and local structures of the data set by solving a dual-objective optimization function. A weighted coefficient is introduced to adjust the trade-off between global and local structures, and an efficient selection strategy of this parameter is proposed. Compared with PCA and LPP, GLPP is more general and flexible in practical applications. Both LPP and PCA can be interpreted under the GLPP framework. A GLPP-based online process monitoring approach is then developed. Two monitoring statistics, i.e., D and Q statistics, are constructed for fault detection and diagnosis. The case study on the Tennessee Eastman process illustrates the effectiveness and advantages of the GLPP-based monitoring method.

Process Monitoring with Global–Local Preserving Projections

Nonlinear process monitoring based on kernel global–local preserving projections

Quality prediction and quality-relevant monitoring with multilinear PLS for batch processes

A novel process monitoring method is proposed based on sparse principal component analysis (SpPCA). To reveal meaningful variable correlations from process data, the SpPCA is developed to sequentially extract a set of sparse loading vectors from process data. To build a high-performance monitoring model, a fault detectability matrix is applied to select the sparse loading vectors used for process modeling from all sparse loading vectors obtained by SpPCA. The fault detectability matrix ensures that the faults related to any monitored process variable are detectable in the principal component subspace and no overlapped (or redundant) loading vectors are involved in the monitoring model. Moreover, the selected sparse loading vectors classify all process variables into nonoverlapping groups according to variable correlations. Two-level contribution plots, which consist of group-wise and group-variable-wise contribution plots, are used for fault diagnosis. The first-level group-wise contribution plot describe...

Fault Detection and Diagnosis Based on Sparse PCA and Two-Level Contribution Plots

Principal component analysis (PCA) is a popular method for modeling and analysis of high-dimensional data. In spite of its advantages, classical PCA also has two drawbacks. First, it is very sensitive to outliers in the data. Second, it cannot yield interpretable PCs because most of the loadings are nonzero. To overcome these drawbacks, we propose a new PCA method that has the properties of robustness and sparsity at the same time, called sparse robust PCA (SRPCA). The robustness is achieved by taking a robust covariance matrix instead of the classical covariance matrix used in PCA. Meanwhile, an additional penalty is imposed on the number of nonzero loadings to achieve the sparsity. SRPCA is not only robust against outliers, but also can yield interpretable PCs. A robust process monitoring method is developed using SRPCA. A cumulative percent contribution criterion is proposed for selecting the optimal PCs for process monitoring. The selected PCs are used to define two fault detection indices. Based on t...

Lijia Luo

Papers

Process Monitoring with Global–Local Preserving Projections

Nonlinear process monitoring based on kernel global–local preserving projections

Quality prediction and quality-relevant monitoring with multilinear PLS for batch processes

Fault Detection and Diagnosis Based on Sparse PCA and Two-Level Contribution Plots

Sparse Robust Principal Component Analysis with Applications to Fault Detection and Diagnosis