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Speaker: Dr. Anna Little

Abstract: This talk addresses multiple topics related to robust
statistical procedures for clustering in high dimensions, including
path-based spectral clustering (a new method), classical
multidimensional scaling (an old method), and clustering in signal
processing. Path-based spectral clustering is a novel approach which
combines a data driven metric with graph-based clustering. Using a data
driven metric allows for fast algorithms and strong theoretical
guarantees when clusters concentrate around low-dimensional sets.
Another approach to high-dimensional clustering is classical
multidimensional scaling (CMDS), a dimension reduction technique widely
popular across disciplines due to its simplicity and generality. CMDS
followed by a simple clustering algorithm can exactly recover all
cluster labels with high probability when the signal to noise ratio is
high enough. However, scaling conditions become increasingly restrictive
as the ambient dimension increases, illustrating the need for robust
unbiasing procedures in high dimensions.  Clustering in signal
processing is the final topic; in this context each data point
corresponds to a corrupted signal. The classic multireference alignment
problem is generalized to include random dilation in addition to random
translation and additive noise, and a wavelet based approach is used to
define an unbiased representation of the target signal(s) which is
robust to high frequency perturbations.