Recent authors have investigated the use of manifolds and Lie group methods for independent component analysis (ICA), including the Stiefel and the Grassmann manifolds and the orthogonal group O(n). In this paper we introduce a new class of manifold, the generalized flag manifold, which is suitable for independent subspace analysis. The generalized flag manifold is a set of subspaces which are ...

2. Statement of results. We will be concerned with cohomology groups having as coefficients the integers, Z, or the integers mod 2, Z2. If Mn is an w-dimensional differentiable manifold, then WíElH'ÍM", Z2) denotes the îth Stiefel-Whitney class of the tangent bundle, and WiGH^M", Z2) denotes the ith dual Stiefel-Whitney class. Our first theorem gives a necessary condition for the existence of a...

The main objective of this paper is to propose a new method to generate smooth interpolating curves on Stiefel manifolds. This method is obtained from a modification of the geometric Casteljau algorithm on manifolds and is based on successive quasi-geodesic interpolation. The quasi-geodesics introduced here for Stiefel manifolds have constant speed, constant covariant acceleration and constant ...

This note demonstrates that it is possible to bound the expectation of an arbitrary norm of a random matrix drawn from the Stiefel manifold in terms of the expected norm of a standard Gaussian matrix with the same dimensions. A related comparison holds for any convex function of a random matrix drawn from the Stiefel manifold. For certain norms, a reversed inequality is also valid. Mathematics ...

In this paper rolling maps for real Stiefel manifolds are studied. Real Stiefel manifolds being the set of all orthonormal k-frames of an n-dimensional real Euclidean space are compact manifolds. They are considered here as rigid bodies embedded in a suitable Euclidean space such that the corresponding Euclidean group acts on the rigid body by rotations and translations in the usual way. We der...

We give an efficient, quick algorithm for the minimization of a quadratic function over Stiefel manifold. We reduce the original (nonconvex) problem, to an SDP, by computing a convex hull of the certain set of matrices.

Based on the one-bit-matching principle and by turning the de-mixing matrix into an orthogonal matrix via certain normalization, Ma et al proposed a one-bit-matching learning algorithm on the Stiefel manifold for independent component analysis [8]. But this algorithm is not adaptive. In this paper, an algorithm which can extract kurtosis and its sign of each independent source component directl...

We give a short elementary proof for a formula for the Hopf–Stiefel function that was found recently by Plagne via additive number theory. c © 2006 Elsevier Ltd. All rights reserved. The Hopf–Stiefel function ◦, introduced by Hopf [3] and Stiefel [8], plays an important role in additive number theory and bilinear algebra; see e.g. Plagne [6] for an overview and many references, for example [5] ...

Associated to a compact Lie group G is the abelian group P(G) of total Stiefel-Whitney classes of representations. In certain cases the rank of P(G) is equal to the number of conjugacy classes of involutions in G. For the symmetric groups Sn, the total Stiefel-Whitney class of the regular representation is highly divisible in P(Sn) and this implies the existence of 'global' Dickson invariants i...