Real-world visual data is often corrupted and requires the use of estimation techniques that are robust to noise and outliers. Robust methods are well studied for Euclidean spaces and their use has also been extended to Riemannian spaces. In this chapter, we present the necessary mathematical constructs for Grassmann manifolds, followed by two different algorithms that can perform robust estima...

Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite, number of loss functions. In this paper, we propose a novel Riemannian extension of the Euclidean stochastic variance reduced gradient algorithm (R-SVRG) to a compact manifold search space. To this end, we show the developments on the Grassmann manifold. The key challenges of...

We present a graphical representation of the supersymmetry and the graphical calculation. Calculation is demonstrated for 4D Wess-Zumino model and for Super QED. The chiral operators are graphically expressed in an illuminating way. The tedious part of SUSY calculation, due to manipulating chiral suffixes, reduces considerably. The application is diverse. PACS. 02.10.Ox Copmbinatorics, graph th...

Some recent results (and a conjecture) concerning the polynomial degree of the Grassmannian G1;n;2 of the lines of PG(n; 2) are shown to be equivalent to results (and a conjecture) concerning certain kinds of subgraphs of any (simple) graph = (V; E) which is of order jVj = n+ 1: It turns out that those graphs of size jEj = n = jVj 1 are of particular signi…cance. Somewhat similarly, results con...

We introduce and analyze a natural geometric version of Renegar’s condition number R, which we call Grassmann condition number, for the homogeneous convex feasibility problem associated with a regular cone C ⊆ R. Let Grn,m denote the Grassmann manifold of m-dimensional linear subspaces of R with the Riemannian distance metric dg. The set of ill-posed instances Σm ⊂ Grn,m consists of the linear ...

The existence of characteristic structure, or shape, in complex data sets has been recognized as increasingly important for mathematical data analysis. This realization has motivated the development of new tools such as persistent homology for exploring topological invariants, or features, in data large sets. In this paper we apply persistent homology to the characterization of gas plumes in ti...

Domain adaptation aims to leverage information from the source domain improve classification performance in target domain. It mainly utilizes two schemes: sample reweighting and feature matching. While first scheme allocates different weights individual samples, second matches of domains using global structural statistics. The schemes are complementary with each other, which expected jointly wo...