A Survey: Potential Dimensionality Reduction Methods

Abstract: Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis (PCA), Kernel PCA (KPCA), Sparse Kernel PCA, t-Distributed Stochastic Neighbor Embedding (t-SNE), and Uniform Manifold Approximation and Projection (UMAP). PCA provides a linear approach to capturing variance, whereas KPCA and Sparse KPCA extend this concept to non-linear structures using kernel functions. Meanwhile, t-SNE and UMAP focus on preserving local relationships, making them effective for data visualization. Each method is examined in terms of its mathematical formulation, computational complexity, strengths, and limitations. The trade-offs between global structure preservation, computational efficiency, and interpretability are discussed to guide practitioners in selecting the appropriate technique based on their application needs.