Projection pursuit is concerned with finding interesting lowdimensional subspace of multivariate data. In this paper we proposed a genetic optimization approach to find the globally optimal orthogonal subspace given training data and user defined criterion on what subspaces are interesting. We then applied this approach to human face recognition. Suppose face recognition is done by simple corre...

We define a new notion of affine subspace concentration conditions for lattice polytopes, and prove that they hold smooth reflexive polytopes with barycenter at the origin. Our proof involves considering slope stability canonical extension tangent bundle by trivial line class $c_1(\mathcal{T}_X)$ on Fano toric varieties.

Obtaining a good similarity matrix is extremely important in subspace clustering. Current state-of-the-art methods learn the through self-expressive strategy. However, these directly adopt original samples as set of basis to represent itself linearly. It difficult accurately describe linear relation between real-world applications, and thus hard find an ideal matrix. To better samples, we prese...

Subspace clustering tries to find groups of similar objects from the given dataset such that the objects are projected on only a subset of the feature space. It finds meaningful clusters in all possible subspaces. However, when it comes to the quality of the resultant subspace clusters most of the subspace clusters are redundant. These redundant subspace clusters don’t provide new information. ...

This paper presents a new approach to deriving statistically optimal weights for weighted subspace fitting (WSF) algorithms. The approach uses a formula called a “subspace perturbation expansion,” which shows how the subspaces of a matrix change when the matrix elements are perturbed. The perturbation expansion is used to derive an optimal WSF algorithm for estimating directions of arrival in a...