Related papers: Fast Principal Component Analysis for Cryo-EM Imag…

Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role…

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…

We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new…

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…

We develop an efficient method to represent nuclear densities using basis functions extracted via Principal Component Analysis (PCA). Applying PCA to densities of 75 nuclei calculated with the relativistic continuum Hartree-Bogoliubov…

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…

We use Principal Component Analysis (PCA) to study the gas dynamics in numerical simulations of typical MCs. Our simulations account for the non-isothermal nature of the gas and include a simplified treatment of the time-dependent gas…

Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…

Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we…

Brillouin microscopy has recently emerged as a new bio-imaging modality that provides information on the micromechanical properties of biological materials, cells and tissues. The data collected in a typical Brillouin microscopy experiment…

In this paper, we study the problem of computing a Principal Component Analysis of data affected by Poisson noise. We assume samples are drawn from independent Poisson distributions. We want to estimate principle components of a fixed…

Principal component analysis (PCA) is widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA…

Single-particle cryo-electron microscopy (cryo-EM) is a leading technology to resolve the structure of molecules. Early in the process, the user detects potential particle images in the raw data. Typically, there are many false detections…

Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…

Particle Image Velocimetry (PIV) data processing procedures are adversely affected by light reflections and backgrounds as well as defects in the models and sticky particles that occlude the inner walls of the boundaries. In this paper, a…

Principal component analysis (PCA) is one of the most fundamental tools in machine learning with broad use as a dimensionality reduction and denoising tool. In the later setting, while PCA is known to be effective at subspace recovery and…

Principal Component Analysis (PCA) is a widely used technique in machine learning, data analysis and signal processing. With the increase in the size and complexity of datasets, it has become important to develop low-space usage algorithms…

We present a method using principal component analysis (PCA) to process x-ray pulses with severe shape variation where traditional optimal filter methods fail. We demonstrate that PCA is able to noise-filter and extract energy information…

We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success…

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…