Related papers: Graph Regularized PCA
This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data. This problem, often dubbed as…
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…
We tackle the challenges of modeling high-dimensional data sets, particularly those with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships. Our approach enables a seamless integration of concepts…
Principal Component Analysis (PCA) is one of the most important unsupervised methods to handle high-dimensional data. However, due to the high computational complexity of its eigen decomposition solution, it hard to apply PCA to the…
Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…
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…
This paper presents a bias-variance tradeoff of graph Laplacian regularizer, which is widely used in graph signal processing and semi-supervised learning tasks. The scaling law of the optimal regularization parameter is specified in terms…
Graph is a fundamental mathematical structure in characterizing relations between different objects and has been widely used on various learning tasks. Most methods implicitly assume a given graph to be accurate and complete. However, real…
Independent component analysis (ICA) is popular in many applications, including cognitive neuroscience and signal processing. Due to computational constraints, principal component analysis is used for dimension reduction prior to ICA…
When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…
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,…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…
In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…
Low-dose computed tomography (LDCT) reconstruction faces a critical tradeoff between reconstruction quality and resource requirements. While recent deep learning methods achieve state-of-the-art performance, they typically rely on over…
High-dimensional data often contain low-dimensional signals obscured by structured background noise, which limits the effectiveness of standard PCA. Motivated by contrastive learning, we address the problem of recovering shared signal…
This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians. Graph Laplacians are a powerful, flexible method for…
We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those…
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…
Principal component regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide the…