Related papers: HyperPCA: a Powerful Tool to Extract Elemental Map…

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…

This paper presents a new approach of applying partial least squares method combined with a physical principle based dominant factor. The characteristic line intensity of the specific element was taken to build up the dominant factor to…

Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components…

Hyperspectral pansharpening aims to synthesize a low-resolution hyperspectral image (LR-HSI) with a registered panchromatic image (PAN) to generate an enhanced HSI with high spectral and spatial resolution. Recently proposed HS…

We study a practical algorithm for sparse principal component analysis (PCA) of incomplete and noisy data. Our algorithm is based on the semidefinite program (SDP) relaxation of the non-convex $l_1$-regularized PCA problem. We provide…

The internal linear combination (ILC) method is a popular approach for constructing component-separated maps in cosmic microwave background (CMB) analyses. It optimally combines observed maps at different frequencies to produce an unbiased…

Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…

The recent development of more sophisticated spectroscopic methods allows acqui- sition of high dimensional datasets from which valuable information may be extracted using multivariate statistical analyses, such as dimensionality reduction…

Principal component analysis has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the…

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 $n$''…

In this paper, we propose a new method to perform Sparse Kernel Principal Component Analysis (SKPCA) and also mathematically analyze the validity of SKPCA. We formulate SKPCA as a constrained optimization problem with elastic net…

Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatio-temporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable tradeoff between frequency…

Our main objective is to develop a denoising strategy to increase the signal to noise ratio of individual spectral lines of stellar spectropolarimetric observations. We use a multivariate statistics technique called Principal Component…

The Herschel Space Observatory of ESA was launched in May 2009 and is in operation since. From its distant orbit around L2 it needs to transmit a huge quantity of information through a very limited bandwidth. This is especially true for the…

One of the current trends of laser applications in material science is using high-intensity lasers to provide fast and efficient surface or volume modifications for achieving controllable material properties, synthesis of novel materials…

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

For many modern applications in science and engineering, data are collected in a streaming fashion carrying time-varying information, and practitioners need to process them with a limited amount of memory and computational resources in a…

This article focuses on the robust principal component analysis (PCA) of high-dimensional data with elliptical distributions. We investigate the PCA of the sample spatial-sign covariance matrix in both nonsparse and sparse contexts,…

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…

Deep learning based semi-supervised learning (SSL) methods have achieved strong performance in medical image segmentation, which can alleviate doctors' expensive annotation by utilizing a large amount of unlabeled data. Unlike most existing…