Related papers: Structure-preserving non-linear PCA for matrices
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 $n$''…
The signal to noise ratio (SNR) fundamentally limits the information accessible by magnetic resonance imaging (MRI). This limitation has been addressed by a host of denoising techniques, recently including so-called MPPCA: Principal…
The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation…
A novel decomposition scheme to solve parametric non-convex programs as they arise in Nonlinear Model Predictive Control (NMPC) is presented. It consists of a fixed number of alternating proximal gradient steps and a dual update per time…
In this paper, we apply the Logistic PCA (LPCA) as a dimensionality reduction tool for visualizing patterns and characterizing the relevance of mathematics abilities from a given population measured by a large-scale assessment. We establish…
Dynamic inner principal component analysis (DiPCA) is a powerful method for the analysis of time-dependent multivariate data. DiPCA extracts dynamic latent variables that capture the most dominant temporal trends by solving a large-scale,…
Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank…
Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…
This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to…
Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…
Commonly used in computer vision and other applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into…
Multiple Correspondence Analysis (MCA) is a dimension reduction method which plays a large role in the analysis of tables with categorical nominal variables such as survey data. Though it is usually motivated and derived using geometric…
To do dimensionality reduction on the datasets with outliers, the $\ell_1$-norm principal component analysis (L1-PCA) as a typical robust alternative of the conventional PCA has enjoyed great popularity over the past years. In this work, we…
Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Lo\`{e}ve expansion, which assumes a linear structure of the…
Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be…
High-dimensional image data often require dimensionality reduction before further analysis. This paper provides a purely analytical comparison of two linear techniques-Principal Component Analysis (PCA) and Singular Value Decomposition…
High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…