Related papers: Sparse and Functional Principal Components Analysi…

In this paper, we study the problem of recovering a low-rank matrix (the principal components) from a high-dimensional data matrix despite both small entry-wise noise and gross sparse errors. Recently, it has been shown that a convex…

In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension $n\times p$ and seek to reconstruct it under additional sparsity assumptions. In particular, we assume here each of the principal…

With the development of high-throughput technologies, principal component analysis (PCA) in the high-dimensional regime is of great interest. Most of the existing theoretical and methodological results for high-dimensional PCA are based on…

Sparse Principal Component Analysis (SPCA) and Sparse Linear Regression (SLR) have a wide range of applications and have attracted a tremendous amount of attention in the last two decades as canonical examples of statistical problems in…

We present novel analysis and algorithms for solving sparse phase retrieval and sparse principal component analysis (PCA) with convex lifted matrix formulations. The key innovation is a new mixed atomic matrix norm that, when used as…

Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of…

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.…

This work introduces a variant of resolvent analysis that identifies forcing and response modes that are sparse in both space and time. This is achieved through the use of a sparse principal component analysis (PCA) algorithm, which…

We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors…

Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…

Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar…

A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the…

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…

Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…

This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low…

Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…

Over the years, Principal Component Analysis (PCA) has served as the baseline approach for dimensionality reduction in gene expression data analysis. It primary objective is to identify a subset of disease-causing genes from a vast pool of…

In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…

Dimensionality reduction represents a critical preprocessing step in order to increase the efficiency and the performance of many hyperspectral imaging algorithms. However, dimensionality reduction algorithms, such as the Principal…

Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…