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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…

Principal component analysis (PCA) is a widely used dimension reduction method, but its performance is known to be non-robust to outliers. Recently, product-PCA (PPCA) has been shown to possess the efficiency-loss free ordering-robustness…

Anomaly detection is critical in industrial manufacturing for ensuring product quality and improving efficiency in automated processes. The scarcity of anomalous samples limits traditional detection methods, making anomaly generation…

Unmanned Aerial Vehicles (UAVs) are widely used and meet many demands in military and civilian fields. With the continuous enrichment and extensive expansion of application scenarios, the safety of UAVs is constantly being challenged. To…

Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…

We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse…

With the development of Earth observation technology, very-high-resolution (VHR) image has become an important data source of change detection. Nowadays, deep learning methods have achieved conspicuous performance in the change detection of…

We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…

Analyzing principal components for multivariate data from its spatial sign covariance matrix (SCM) has been proposed as a computationally simple and robust alternative to normal PCA, but it suffers from poor efficiency properties and is…

In this work we apply the principal component analysis (PCA) method with kernel trick to study classification of phases and phase transition in classical XY models in frustrated lattices. Comparing to our previous work with linear PCA…

The problem of quickest anomaly detection in networks with unlabeled samples is studied. At some unknown time, an anomaly emerges in the network and changes the data-generating distribution of some unknown sensor. The data vector received…

Anomaly detection methods have demonstrated remarkable success across various applications. However, assessing their performance, particularly at the pixel-level, presents a complex challenge due to the severe imbalance that is most…

Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…

We develop quantum protocols for anomaly detection and apply them to the task of credit card fraud detection (FD). First, we establish classical benchmarks based on supervised and unsupervised machine learning methods, where average…

Acceleration processes that occur in astrophysical plasmas produce cosmic rays that are observed on Earth. To study particle acceleration, fully-kinetic particle-in-cell (PIC) simulations are often used as they can unveil the microphysics…

Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations…

The application of machine learning techniques for anomaly detection in particle accelerators has gained popularity in recent years. These efforts have ranged from the analysis of quenches in radio frequency cavities and superconducting…

Network anomaly detection is a very relevant research area nowadays, especially due to its multiple applications in the field of network security. The boost of new models based on variational autoencoders and generative adversarial networks…

Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…

Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…