Hearing the clusters in a graph: A distributed algorithm

We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of the Laplacian matrix, thus providing clustering information. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to spectral clustering and derive convergence rates. We demonstrate the benefit of using this decentralized clustering algorithm for community detection in social graphs, accelerating distributed estimation in sensor networks and efficient computation of distributed multi-agent search strategies

Relevance-driven acquisition and rapid on-site analysis of 3d geospatial data

One central problem in geospatial applications using 3D models is the tradeoff between detail and acquisition cost during acquisition, as well as processing speed during use. Commonly used laser-scanning technology can be used to record spatial data in various levels of detail. Much detail, even on a small scale, requires the complete scan to be conducted at high resolution and leads to long acquisition time, as well as a great amount of data and complex processing. Therefore, we propose a new scheme for the generation of geospatial 3D models that is driven by relevance rather than data. As part of that scheme we present a novel acquisition and analysis workflow, as well as supporting data-models. The workflow includes on-site data evaluation (e.g. quality of the scan) and presentation (e.g. visualization of the quality), which demands fast data processing. Thus, we employ high performance graphics cards (GPGPU) to effectively process and analyze large volumes of LIDAR data. In particular we present a density calculation based on k-nearest-neighbor determination using OpenCL. The presented GPGPU-accelerated workflow enables a fast data acquisition with highly detailed relevant objects and minimal storage requirements.State of Lower-SaxonyVolkswagen Foundatio

Geometry-Oblivious FMM for Compressing Dense SPD Matrices

We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate matrix-vector multiplication in $N \log N$ or even $N$ time, where $N$ is the matrix size. Compression requires $N \log N$ storage and work. In general, our scheme belongs to the family of hierarchical matrix approximation methods. In particular, it generalizes the fast multipole method (FMM) to a purely algebraic setting by only requiring the ability to sample matrix entries. Neither geometric information (i.e., point coordinates) nor knowledge of how the matrix entries have been generated is required, thus the term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme for hierarchical matrix computations that reduces synchronization barriers. We present results on the Intel Knights Landing and Haswell architectures, and on the NVIDIA Pascal architecture for a variety of matrices.Comment: 13 pages, accepted by SC'1