Principal Component Analysis (PCA) is a fundamental unsupervised learning technique used for dimensionality reduction. Its primary goal is to transform a high-dimensional dataset into a lower-dimensional space by identifying a new set of orthogonal axes, known as principal components. These components are ordered such that the first few retain most of the variation present in the original data. By discarding the components that capture the least variance, PCA reduces the number of features while minimizing information loss. This is invaluable for data visualization, noise filtering, and improving the efficiency of subsequent machine learning models.

B. Classification is a supervised learning task for predicting categorical labels; PCA is an unsupervised transformation technique, not a predictive model.

C. Regression is a supervised learning task for predicting continuous numerical values, which is not the direct purpose of PCA.

D. While PCA can be a preprocessing step in some recommendation systems, its core function is data reduction, not the recommendation logic itself.

1. Ng

A. (n.d.). CS229 Lecture Notes: Principal Component Analysis. Stanford University. Retrieved from http://cs229.stanford.edu/notes/cs229-notes10.pdf. In Section 1

"Application 1: Dimensionality reduction" (p. 2)

the notes explicitly state

"By far the most common application of PCA is for dimensionality reduction."

2. Shlens

J. (2014). A Tutorial on Principal Component Analysis. arXiv:1404.1100 [cs.LG]. In the Abstract (p. 1)

the author states

"Principal component analysis (PCA) is a mainstay of modern data analysis - a black box that is widely used but poorly understood. The goal of this paper is to dispel the magic behind this black box. This manuscript focuses on building a solid intuition for how and why principal component analysis works. This is accomplished by forging connections between the underlying statistics and geometry of PCA. This tutorial avoids the use of heavy mathematical notation and instead focuses on building a visual

intuitive framework for what PCA is actually doing. With minimal additional effort

PCA provides a roadmap for how to reduce a complex data set to a lower dimension to reveal the sometimes hidden

simplified dynamics that often underlie it."

3. Scikit-learn Developers. (n.d.). 2.5. Decomposing signals in components (matrix factorization problems). Scikit-learn 1.4.2 documentation. In Section 2.5.1

"Principal component analysis (PCA)

" the documentation introduces PCA as a method to "...decompose a multivariate dataset in a set of successive orthogonal components that explain a maximum amount of the variance." This decomposition is the basis for its use in dimensionality reduction.