In network code setting, a constant dimension code is a set of k-dimensional subspaces of F nq . If F_q n is a nondegenerated symlectic vector space with bilinear form f, an isotropic subspace U of F n q is a subspace that for all x, y ∈ U, f(x, y) = 0. We introduce isotropic subspace codes simply as a set of isotropic subspaces and show how the isotropic property use in decoding process, then...

The symmetric subpace has many applications in quantum information theory. This review article begins by explaining key background facts about the symmetric subspace from a quantum information perspective. Then we review, and in some places extend, work of Werner and Chiribella that connects the symmetric subspace to state estimation, optimal cloning, the de Finetti theorem and other topics. In...

We propose linear programming formulations of support vector machines (SVM). Unlike standard SVMs which use quadratic programs, our approach explores a fairly small dimensional subspace of a feature space to construct the nonlinear discriminator. This allows us to obtain the discriminator by solving a smaller sized linear program. We demonstrate that an orthonormal basis of the subspace can be ...

We consider the problem of clustering incomplete data drawn from a union of subspaces. Classical subspace clustering methods are not applicable to this problem because the data are incomplete, while classical low-rank matrix completion methods may not be applicable because data in multiple subspaces may not be low rank. This paper proposes and evaluates two new approaches for subspace clusterin...