CSC 2535: Lecture
10
Non-parametric, non-linear dimensionality reduction
Dimensionality reduction: Some Assumptions
The basic idea of non-parameteric dimensionality reduction
Two types of dimensionality reduction
Linear methods of reducing dimensionality
Metric Multi-Dimensional Scaling
Other non-linear methods of reducing dimensionality
IsoMap: Local MDS without local optima
How Isomap measures intrinsic distances
Using Isomap to discover the intrinsic manifold in a set of face images
Maps that preserve local geometry
A sensible but inefficient way to use the local weights
Local Linear Embedding: A less sensible but more efficient way to use local weights
Evaluating an arrangement of the data in a low-dimensional space
The cost function for a low-dimensional representation
The forces acting on the low-dimensional points
Picking the radius of the gaussian that is used to compute the p’s
Computing the p’s for symmetric SNE
Turning conditional probabilities into pairwise probabilities
Evaluating an arrangement of the points in the low-dimensional space
The cost function for a low-dimensional representation
The forces acting on the low-dimensional points
More optimization tricks for SNE
A more interesting variation that uses the probabilistic foundation of SNE
A nice dataset for testing “Aspect maps”
The relationship between aspect maps and clustering
A weird behaviour of aspect maps