A Comparative Analysis of Principal Component Analysis (PCA) and Singular Value Decomposition (SVD) as Dimensionality Reduction Techniques
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 (SVD). After the derivation of each algorithm from first principles, we assess their interpretability, numerical stability, and suitability for differing matrix shapes. We synthesize rule-of-thumb guidelines for choosing one out of the two algorithms without empirical benchmarking, building on classical and recent numerical literature. Limitations and directions for future experimental work are outlined at the end.
Code (0)
등록된 구현이 없습니다.
Tasks
BenchmarkingDimensionality ReductionSimilar Papers 제목 키워드 기반
Iterative Block Tensor Singular Value Thresholding for Extraction of Low Rank Component of Image Data
Tensor principal component analysis (TPCA) is a multi-linear extension of principal component analysis which converts a set of correlated measurements into several principal components. In this paper, we propose a new ro…
Modularity Component Analysis versus Principal Component Analysis
In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity com…
RelationPolar $n$-Complex and $n$-Bicomplex Singular Value Decomposition and Principal Component Pursuit
Informed by recent work on tensor singular value decomposition and circulant algebra matrices, this paper presents a new theoretical bridge that unifies the hypercomplex and tensor-based approaches to singular value deco…
Sparse principal component regression via singular value decomposition approach
Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by pr…
regressionTest-Time Adaptation with Principal Component Analysis
Machine Learning models are prone to fail when test data are different from training data, a situation often encountered in real applications known as distribution shift. While still valid, the training-time knowledge be…
Test-time Adaptationvalid