# SPRING 2007: CMPSCI 791BB: Representation Learning

## Principal Instructor: Sridhar Mahadevan

### Room 140, Friday 1:25-3:55 (tentative)

### PREREQUISITE: CMPSCI 689 (or permission of instructor)

###
Note: If you took 791BB before, you can still take this class for
credit as it covers new topics

### SUMMARY

This course will explore new frontiers of research in machine learning
that may have a fundamental and far-reaching impact on AI and computer
science over the next decade. In particular, we will explore recent
methods that dynamically construct feature spaces facilitating the
solution of not just a specific problem, but rather of an entire suite
of related problems across multiple learning modalities.
Representation learning fundamentally differs from previous
formulations of learning, in that it is both modality and task
independent. The goal of representation learning is to "understand"
the data or state space, or more precisely, estimate the underlying
* geometry * or manifold structure of a data space through the
construction of * basis functions *. These basis functions can
then be used in conjunction with standard learning techniques, such as
clustering, regression, reinforcement learning, or supervised
learning, to solve not just a single problem, but many problems. This
course will provide a gentle introduction to both the theory and
applications of representation learning.

The course will be organize into three sections. Part 1 will cover
elementary techniques of representation learning, beginning with
classical linear algebraic methods such as principal components
analysis (PCA). Part 2 will introduce more recent nonlinear
graph-theoretic methods, including global "Fourier" methods, such as
Laplacian eigenmaps, and multi-scale "Wavelet" methods, such as
diffusion wavelets. Finally, Part 3 will explore advanced topics,
including the representation theory of finite and infinite groups, Lie
groups, and Riemannian manifolds.
The underlying theory and algorithms will be illustrated using a
diverse set of applications, such as compression of 3D objects in
computer graphics (see above), ranking (IR), document clustering,
analysis of Markov chains and Markov decision processes, sensor
networks, computer vision, robotics, networking, and web search.