Related papers: Adaptive Principal Component Regression with Appli…
We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…
In areas of application, including actuarial science and demography, it is increasingly common to consider a time series of curves; an example of this is age-specific mortality rates observed over a period of years. Given that age can be…
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 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 (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…
Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…
Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…
In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at $p$ locations and $n$ time points with the possibility that $p>n$. While principal component analysis…
We propose a supervised principal component regression method for relating functional responses with high dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected…
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…
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…
It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…
Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…
A promising technique for the spectral design of acoustic metamaterials is based on the formulation of suitable constrained nonlinear optimization problems. Unfortunately, the straightforward application of classical gradient-based…
Functional principal component regression (PCR) can fail to provide good prediction if the response is highly correlated with some excluded functional principal component(s). This situation is common since the construction of functional…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…
Domain adaptation is a popular paradigm in modern machine learning which aims at tackling the problem of divergence (or shift) between the labeled training and validation datasets (source domain) and a potentially large unlabeled dataset…
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general,…