Related papers: Graph Regularized PCA
This paper proposes a parameter collaborative optimization algorithm for large language models, enhanced with graph spectral analysis. The goal is to improve both fine-tuning efficiency and structural awareness during training. In the…
A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…
In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the…
In many CAD-based applications, complex geometries are defined by a high number of design parameters. This leads to high-dimensional design spaces that are challenging for downstream engineering processes like simulations, optimization, and…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…
Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…
Generalized principal component analysis (GLM-PCA) facilitates dimension reduction of non-normally distributed data. We provide a detailed derivation of GLM-PCA with a focus on optimization. We also demonstrate how to incorporate…
Bi-stochastic normalization provides an alternative normalization of graph Laplacians in graph-based data analysis and can be computed efficiently by Sinkhorn-Knopp (SK) iterations. This paper proves the convergence of bi-stochastically…
Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted…
Model-driven software engineering is a suitable method for dealing with the ever-increasing complexity of software development processes. Graphs and graph transformations have proven useful for representing such models and changes to them.…
This work studies the recursive robust principal components' analysis(PCA) problem. Here, "robust" refers to robustness to both independent and correlated sparse outliers. If the outlier is the signal-of-interest, this problem can be…
Multiview canonical correlation analysis (MCCA) seeks latent low-dimensional representations encountered with multiview data of shared entities (a.k.a. common sources). However, existing MCCA approaches do not exploit the geometry of the…
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 $n$''…
Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection.…
The graph Laplacian regularization term is usually used in semi-supervised representation learning to provide graph structure information for a model $f(X)$. However, with the recent popularity of graph neural networks (GNNs), directly…
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 often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the…
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…