manifold (수가) 많은; 여러 가지의, 다방면
manifold hypothesis 란 ?
real-world high dimensional data (such as images) lie on low-dimensional manifolds embedded in the high-dimensional space.
For example, assume you have a dataset containing images with only two pixels, with each pixel having a value between 0 and 1. You could then plot this dataset in the high-dimensional space R^2. If all the images lie on a line (an embedded lower-dimensional manifold), then the manifold hypothesis would be proven true in this example.
The manifold hypothesis is important, since it partially explains why we are able to learn anything at all using deep learning. It also provides useful intuition when thinking about these types of problems, and has important implications if true (which I think to be the case)
nonlinear dimensionality reduction (NLDR)