Dimensionality Reduction: Trade-offs and Techniques Dimensionality Reduction: Trade-offs and Techniques In this blog, we discuss some trade-offs involved when choosing a Dimensionality Reduction (DR) technique. Dimensionality reduction aims to represent high-dimensional data in a lower-dimensional space while preserving as much meaningful structure as possible. $$ f : \mathbb{R}^n \to \mathbb{R}^k, \quad k The goal is to find a mapping \( f \) that captures the essential relationships among the data points in \( \mathbb{R}^n \) within a lower-dimensional space \( \mathbb{R}^k \). However, depending on the technique used, distortions such as artificial clusters or misplaced neighbors may appear. We will focus on three widely used methods: t-SNE , UMAP , and TriMap . 1. t-SNE (t-distributed Stochastic Neighbor Embedding) t-SNE models the pairwise similarities between points in both the high-dimensional and low-dimensional spaces u...
Math intensive