Grassmannian diffusion maps based surrogate modeling via geometric harmonics

AFRL-RY-WP-TP-2007-1223, V2 DIFFUSION MAPS AND GEOMETRIC HARMONICS FOR AUTOMATIC TARGET RECOGNITION (ATR) Volume 2: Appendices

Data fusion and multi-cue data matching are fundamental tasks of high-dimensional data analysis. In this paper, we apply the recently introduced diffusion framework to address these tasks. Our contribution is three-fold. First, we present the Laplace-Beltrami approach for computing density invariant embeddings which are essential for integrating different sources of data. Second, we describe a ...

Activity Recognition Via Classification Constrained Diffusion Maps

Clustering Mixed Data via Diffusion Maps

Data clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, customer segmentation, trend analysis, pattern recognition and image analysis. Although many clustering algorithms have been proposed most of them deal with clustering of numerical data. Finding the similarity between numeric objects usually relies on a com...

Crystals via the Affine Grassmannian

Let G be a connected reductive group over C and let g be the Langlands dual Lie algebra. Crystals for g are combinatoral objects, that were introduced by Kashiwara (cf. for example [5]) as certain “combinatorial skeletons” of finite-dimensional representations of g. For every dominant weight λ of g Kashiwara constructed a crystal B(λ) by considering the corresponding finite-dimensional represen...

Augmenting topology-based maps with geometric information

Topology-based maps are a new representation of the workspace of a mobile robot, which capture the structure of the free space in the environment in terms of the basic topological notions of connectivity and adjacency. A topology-based map can represent the environment in terms of open spaces (rooms and corridors) connected by narrow passages (doors and junctions). In this paper, we show how to...