Related papers: Eigen component analysis: A quantum theory incorpo…

This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and…

Non-classical correlations can be regarded as resources for quantum information processing. However, the classification problem of non-classical correlations for quantum states remains a challenge, even for finite-size systems. Although…

The Intelligent Fault Diagnosis of rotating machinery currently proposes some captivating challenges. Although results achieved by artificial intelligence and deep learning constantly improve, this field is characterized by several open…

Perception, localization, planning, and control, high-level functions often organized in a so-called pipeline, are amongst the core building blocks of modern autonomous (ground, air, and underwater) vehicle architectures. These functions…

We present an unsupervised learning analysis of correlation hierarchies in the quarter-filled simple and extended Hubbard models by applying principal component analysis (PCA) to exact-diagonalization (ED) data on 3x4 and 4x4 cylindrical…

Independent component analysis (ICA) is a fundamental problem in the field of signal processing, and numerous algorithms have been developed to address this issue. The core principle of these algorithms is to find a transformation matrix…

Quantum Machine Learning algorithms based on Variational Quantum Circuits (VQCs) are important candidates for useful application of quantum computing. It is known that a VQC is a linear model in a feature space determined by its…

This paper examines several applications of principal component analysis (PCA) to physical systems. The first of these demonstrates that the principal components in a basis of appropriate system variables can be employed to identify…

In recent years, Artificial Intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised Machine Learning (ML) algorithm called Principal Component Analysis (PCA) as…

Distributed Principal Component Analysis (PCA) has been studied to deal with the case when data are stored across multiple machines and communication cost or privacy concerns prohibit the computation of PCA in a central location. However,…

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

We present a novel view on principal component analysis (PCA) as a competitive game in which each approximate eigenvector is controlled by a player whose goal is to maximize their own utility function. We analyze the properties of this PCA…

We revisit the problem of fair principal component analysis (PCA), where the goal is to learn the best low-rank linear approximation of the data that obfuscates demographic information. We propose a conceptually simple approach that allows…

A key element in defending computer networks is to recognize the types of cyber attacks based on the observed malicious activities. Obfuscation onto what could have been observed of an attack sequence may lead to mis-interpretation of its…

Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…

The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less…

A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and lower variance than the individual classifiers that…

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…

Learning-enabled components (LECs) are widely used in cyber-physical systems (CPS) since they can handle the uncertainty and variability of the environment and increase the level of autonomy. However, it has been shown that LECs such as…

Decision-making related to health is complex. Machine learning (ML) and patient generated data can identify patterns and insights at the individual level, where human cognition falls short, but not all ML-generated information is of equal…