54 research outputs found
Estimation in high dimensions: a geometric perspective
This tutorial provides an exposition of a flexible geometric framework for
high dimensional estimation problems with constraints. The tutorial develops
geometric intuition about high dimensional sets, justifies it with some results
of asymptotic convex geometry, and demonstrates connections between geometric
results and estimation problems. The theory is illustrated with applications to
sparse recovery, matrix completion, quantization, linear and logistic
regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change
A smooth introduction to the wavefront set
The wavefront set provides a precise description of the singularities of a
distribution. Because of its ability to control the product of distributions,
the wavefront set was a key element of recent progress in renormalized quantum
field theory in curved spacetime, quantum gravity, the discussion of time
machines or quantum energy inequalitites. However, the wavefront set is a
somewhat subtle concept whose standard definition is not easy to grasp. This
paper is a step by step introduction to the wavefront set, with examples and
motivation. Many different definitions and new interpretations of the wavefront
set are presented. Some of them involve a Radon transform.Comment: 29 pages, 7 figure
Tight p-fusion frames
Fusion frames enable signal decompositions into weighted linear subspace
components. For positive integers p, we introduce p-fusion frames, a sharpening
of the notion of fusion frames. Tight p-fusion frames are closely related to
the classical notions of designs and cubature formulas in Grassmann spaces and
are analyzed with methods from harmonic analysis in the Grassmannians. We
define the p-fusion frame potential, derive bounds for its value, and discuss
the connections to tight p-fusion frames
Investigating the use of space-time primitives to understand human movements
In this work we start investigating the use of appropriately learnt space-time primitives for modeling upper body human actions. As a study case we consider cooking activities which may undergo large intra class variations and are characterized by subtle details, observed by different view points. With a BoK procedure we quantize each video frame with respect to a dictionary of meaningful space-time primitives, then we derive time series that measure how the presence of different primitives evolves over time. The preliminary experiments we report are very encouraging on the discriminative power of the representation, also speaking in favor of the tolerance to view point changes
- …