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Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

Factor analysis and principal component analysis (PCA) are used in many application areas. The first step, choosing the number of components, remains a serious challenge. Our work proposes improved methods for this important problem. One of…

Intermittency analysis of factorial moments is a promising method used for the detection of power-law scaling in high-energy collision data. In particular, it has been employed in the search of fluctuations characteristic of the critical…

Sparse Principal Component Analysis (SPCA) is an important technique for high-dimensional data analysis, improving interpretability by imposing sparsity on principal components. However, existing methods often fail to simultaneously…

[Abridged] An increasing number of astronomical instruments (on Earth and space-based) provide hyperspectral images, that is three-dimensional data cubes with two spatial dimensions and one spectral dimension. The intrinsic limitation in…

Principal Component Analysis (PCA) is a commonly used tool for dimension reduction and denoising. Therefore, it is also widely used on the data prior to training a neural network. However, this approach can complicate the explanation of…

To deal with high-dimensional unlabeled datasets in many areas, principal component analysis (PCA) has become a rising technique for unsupervised feature selection (UFS). However, most existing PCA-based methods only consider the structure…

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

The beam position monitor (BPM) system is of most importance in a light source. The capability of the BPM depends on the resolution of the system. The traditional standard deviation on the raw data method merely gives the upper limit of the…

Fourier ptychography has attracted a wide range of focus for its ability of large space-bandwidth-produce, and quantative phase measurement. It is a typical computational imaging technique which refers to optimizing both the imaging…

The plug-and-play priors (PnP) framework has been recently shown to achieve state-of-the-art results in regularized image reconstruction by leveraging a sophisticated denoiser within an iterative algorithm. In this paper, we propose a new…

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…

We introduce a novel parameterization of complex unitary matrices, which allows for the efficient photonic implementation of arbitrary linear discrete unitary operators. The proposed architecture is built on factorizing an $N \times N$…

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…

Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…

Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection.…

In many optical metrology techniques, fringe pattern analysis is the central algorithm for recovering the underlying phase distribution from the recorded fringe patterns. Despite extensive research efforts for decades, how to extract the…

This paper is concerned with the computation of the principal components for a general tensor, known as the tensor principal component analysis (PCA) problem. We show that the general tensor PCA problem is reducible to its special case…

Searching for new physics~(NP) is one of the areas of high-energy physics that requires the most processing of large amounts of data. At the same time, quantum computing has huge potential advantages when dealing with large amounts of data.…

Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…