What is the role of scalability in dimensionality reduction for big data systems?

Scalability determines whether a dimensionality reduction method can handle large-scale datasets efficiently in time and memory.

In big data systems, dimensionality reduction must handle millions or billions of samples and high-dimensional feature spaces. Methods like PCA can become expensive due to covariance matrix computation, while techniques like randomized PCA, incremental PCA, and distributed SVD scale better. Nonlinear methods like t-SNE are often too expensive without approximations such as Barnes-Hut or FFT-based optimizations. Scalability involves both computational complexity (O(n·d²), O(n log n)) and memory footprint, as well as the ability to parallelize or distribute computation across clusters.