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Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…

Principal Component Analysis (PCA) is an efficient tool to optimize the multiparameter tests of general relativity (GR) where one tests for simultaneous deviations in multiple post-Newtonian (PN) phasing coefficients by introducing…

In the second part of this two-paper series, the stability margin of a critical machine and that of the system are first proposed, and then the concept of non-global stability margin is illustrated. Based on the crucial statuses of the…

The reduction of overall system inertia in modern power systems due to the increasing deployment of distributed energy resources is generally recognized as a major issue for system stability. Consequently, real-time monitoring of system…

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…

Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…

In this paper we propose a novel optimization framework to systematically solve robust PCA problem with rigorous theoretical guarantee, based on which we investigate very computationally economic updating algorithms.

Principal Component Analysis (PCA) is widely used for dimensionality reduction and data analysis. However, PCA results are adversely affected by outliers often observed in real-world data. Existing robust PCA methods are often…

This paper proposes a novel sparse principal component analysis algorithm with self-learning ability for successive modes, where synaptic intelligence is employed to measure the importance of variables and a regularization term is added to…

Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…

Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…

Transient stability assessment is a critical tool for power system design and operation. With the emerging advanced synchrophasor measurement techniques, machine learning methods are playing an increasingly important role in power system…

This paper presents a novel method for transient stability analysis (TSA) that circumvents the limitations of sequential numerical integration and energy functions. The proposed method begins by constructing a trajectory-dependent stability…

We outline how principal component analysis (PCA) can be applied to particle configuration data to detect a variety of phase transitions in off-lattice systems, both in and out of equilibrium. Specifically, we discuss its application to…

Recent studies show that pattern-recognition-based transient stability assessment (PRTSA) is a promising approach for predicting the transient stability status of power systems. However, many of the current well-known PRTSA methods suffer…

In many domains, worst-case guarantees on the performance (e.g., prediction accuracy) of a decision function subject to distributional shifts and uncertainty about the environment are crucial. In this work we develop a method to quantify…

This paper demonstrates the concept of probabilistic stability assessment on large-signal stability in the use case of short circuits in an active distribution grid. Here, the concept of survivability is applied, which extends classical…

The principal component analysis (PCA) is a staple statistical and unsupervised machine learning technique in finance. The application of PCA in a financial setting is associated with several technical difficulties, such as numerical…

Numerical modeling of proton exchange membrane fuel cells is at the verge of becoming predictive. A crucial requisite for this, though, is that material properties of the membrane-electrode assembly and their functional dependence on the…