Generalized cohomology operations and $H$-spaces of low rank

Stable Operations in Generalized Cohomology

On the Cohomology of Generalized Homogeneous Spaces

We observe that work of Gugenheim and May on the cohomology of classical homogeneous spaces G/H of Lie groups applies verbatim to the calculation of the cohomology of generalized homogeneous spaces G/H, where G is a finite loop space or a p-compact group and H is a “subgroup” in the homotopical sense. We are interested in the cohomology H∗(G/H ; R) of a generalized homogeneous space G/H with co...

Generalized Low-Rank Approximations

We study the frequent problem of approximating a target matrix with a matrix of lower rank. We provide a simple and efficient (EM) algorithm for solving weighted low rank approximation problems, which, unlike simple matrix factorization problems, do not admit a closed form solution in general. We analyze, in addition, the nature of locally optimal solutions that arise in this context, demonstra...

The Cohomology of Classifying Spaces of H-spaces

Let G denote an associative iï-space with unit (e.g. a topological group). We will show that the relations between G and a classifying space B Q axe more readily displayed using a geometric analog of the resolutions of homological algebra. The analogy is quite sharp, the stages of the resolution, whose base is BQ, determine a filtration of BQ. The resulting spectral sequence for cohomology is i...

Generalized Low Rank Models

Principal components analysis (PCA) is a well-known technique for approximating a data set represented by a matrix by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as nonnegative matrix factorization, matrix...