Representations are at the heart of artificial intelligence. This talk addresses the problem of representation discovery: how can intelligent systems construct novel representations from their experience? Representation discovery re-parameterizes the data or state space -- prior to the application of machine learning, optimization, and search techniques -- by constructing a geometry and task-adaptive basis.
Two approaches to representation discovery will be described, based on generalizing classical Fourier and wavelet analysis to graphs and manifolds. Fourier analysis on graphs constructs global bases by diagonalization of a random walk operator; wavelet analysis constructs compact multiscale representations by dilation of the random walk operator. Efficient algorithms for basis extraction and representation will be presented by combining sampling, matrix compression, and domain knowledge.
A range of case studies will be used to illustrate the approach, including a novel paradigm for adaptive planning under uncertainty whereby both representation and control are learned simultaneously; a multiscale wavelet approach to clustering of text documents where the topic hierarchy is automatically constructed, and graph-based methods for compression of 3D objects in computer graphics using multiscale analysis of mesh geometry and topology.