A comprehensive review of Principal Component Analysis
DOI:
https://doi.org/10.54097/5mmrkr11Keywords:
Principal component analysis, Dimensionality Reduction, Correlation Variance, Data analysis, Kernel PCA.Abstract
PCA (Principal Component Analysis) is a method aiming to reduce the dimensions among data analysis, with various applications in neurosciences, finance, and beyond. Data normalization, covariance matrix decomposition, eigenvalue-driven component selection, and other mathematical underpinnings of PCA will be methodically covered in this article. A comparison with SVD decomposition will also be made due to the similarities between the two methods. Additionally, we will discuss contemporary developments like sparse PCA, kernel PCA, and robust PCA that tackle nonlinearity and sparsity by integrating trends like PCA's integration with deep learning, the variation in applied circumstances, and its use in high-dimensional data presentation. Furthermore, this review will also highlight the inherent limits, such as nonlinearity issues, massive datasets, and data contamination. Throughout investigation, this review serves as a map for the researchers tackling with increasingly complex data environments requiring dimensionality reduction and are not certain with the specific PCA type selected to apply.
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