CSC321:

Extra Lecture (not on the exam)
Non-linear dimensionality reduction

Linear methods of reducing dimensionality

Other non-linear methods of reducing dimensionality

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IsoMap: Local MDS without local optima

How Isomap measures intrinsic distances

Using Isomap to discover the intrinsic manifold in a set of face images

A probabilistic version of local MDS

Computing affinities between datapoints

Turning conditional probabilities into pairwise probabilities

Throwing away the raw data

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

Data from sne paper

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