What is the role of memory efficiency in dimensionality reduction algorithms?

Memory efficiency ensures algorithms can handle large datasets without exhausting system resources.

Many dimensionality reduction methods require storing large matrices such as covariance matrices (d×d) or pairwise distance matrices (n×n). This becomes infeasible for large datasets. Memory-efficient approaches use sparse representations, randomized projections, or streaming updates. Techniques like randomized SVD reduce memory requirements significantly while maintaining approximation quality.