### STATISTICAL LEARNING or NON-LINEAR DIMENSION-REDUCTION ALGORITHM:

From this MMDS lecture, an this parallel presentation.

Manifold learning addresses the problem of high-dimensional data. Dimensionality reduction improves computational analysis, and it is beneficial as long as it preserves most of the important information.

An $$n = 698$$ dataset of $$64 \times 64$$ gray images of faces, where the faces only vary in terms of the head moving up and down or left to right, a 2D manifold is defined. In this case the different orientations are shown on an isomap embedding: