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

Comparison Jaccard similarity, Cosine Similarity and Combined Both of the Data Clustering With Shared Nearest Neighbor Method

Text Mining is the excavations carried out by the computer to get something new that comes from information extracted automatically from data sources of different text. Clustering technique itself is a grouping technique that is widely used in data mining. The aim of this study was to find the most optimum value similarity. Jaccard similarity method used similarity, cosine similarity and a combination of Jaccard similarity and cosine similarity. By combining the two similarity is expected to increase the value of the similarity of the two titles. While the document is used only in the form of a title document of practical work in the Department of Informatics Engineering University of Ahmad Dahlan. All these articles have been through the process of preprocessing beforehand. And the method used is the method of document clustering with Shared Nearest Neighbor (SNN). Results from this study is the cosine similarity method gives the best value of proximity or similarity compared to Jaccard similarity and a combination of bot

A novel double-hybrid learning method for modal frequency-based damage assessment of bridge structures under different environmental variation patterns

Monitoring of modal frequencies under an unsupervised learning framework is a practical strategy for damage assessment of civil structures, especially bridges. However, the key challenge is related to high sensitivity of modal frequencies to environmental and/or operational changes that may lead to economic and safety losses. The other challenge pertains to different environmental and/or operational variation patterns in modal frequencies due to differences in structural types, materials, and applications, measurement periods in terms of short and/or long monitoring programs, geographical locations of structures, weather conditions, and influences of single or multiple environmental and/or operational factors, which may cause barriers to employing stateof-the-art unsupervised learning approaches. To cope with these issues, this paper proposes a novel double-hybrid learning technique in an unsupervised manner. It contains two stages of data partitioning and anomaly detection, both of which comprise two hybrid algorithms. For the first stage, an improved hybrid clustering method based on a coupling of shared nearest neighbor searching and density peaks clustering is proposed to prepare local information for anomaly detection with the focus on mitigating environmental and/or operational effects. For the second stage, this paper proposes an innovative non-parametric hybrid anomaly detector based on local outlier factor. In both stages, the number of nearest neighbors is the key hyperparameter that is automatically determined by leveraging a self-adaptive neighbor searching algorithm. Modal frequencies of two full-scale bridges are utilized to validate the proposed technique with several comparisons. Results indicate that this technique is able to successfully eliminate different environmental and/or operational variations and correctly detect damage

Data clustering using a model granular magnet

We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an interaction between neighboring points, whose strength is a decreasing function of the distance between the neighbors. This magnetic system exhibits three phases. At very low temperatures it is completely ordered; all spins are aligned. At very high temperatures the system does not exhibit any ordering and in an intermediate regime clusters of relatively strongly coupled spins become ordered, whereas different clusters remain uncorrelated. This intermediate phase is identified by a jump in the order parameters. The spin-spin correlation function is used to partition the spins and the corresponding data points into clusters. We demonstrate on three synthetic and three real data sets how the method works. Detailed comparison to the performance of other techniques clearly indicates the relative success of our method.Comment: 46 pages, postscript, 15 ps figures include

Sketch-based subspace clustering of hyperspectral images

Sparse subspace clustering (SSC) techniques provide the state-of-the-art in clustering of hyperspectral images (HSIs). However, their computational complexity hinders their applicability to large-scale HSIs. In this paper, we propose a large-scale SSC-based method, which can effectively process large HSIs while also achieving improved clustering accuracy compared to the current SSC methods. We build our approach based on an emerging concept of sketched subspace clustering, which was to our knowledge not explored at all in hyperspectral imaging yet. Moreover, there are only scarce results on any large-scale SSC approaches for HSI. We show that a direct application of sketched SSC does not provide a satisfactory performance on HSIs but it does provide an excellent basis for an effective and elegant method that we build by extending this approach with a spatial prior and deriving the corresponding solver. In particular, a random matrix constructed by the Johnson-Lindenstrauss transform is first used to sketch the self-representation dictionary as a compact dictionary, which significantly reduces the number of sparse coefficients to be solved, thereby reducing the overall complexity. In order to alleviate the effect of noise and within-class spectral variations of HSIs, we employ a total variation constraint on the coefficient matrix, which accounts for the spatial dependencies among the neighbouring pixels. We derive an efficient solver for the resulting optimization problem, and we theoretically prove its convergence property under mild conditions. The experimental results on real HSIs show a notable improvement in comparison with the traditional SSC-based methods and the state-of-the-art methods for clustering of large-scale images

Bringing UMAP Closer to the Speed of Light with GPU Acceleration

The Uniform Manifold Approximation and Projection (UMAP) algorithm has become widely popular for its ease of use, quality of results, and support for exploratory, unsupervised, supervised, and semi-supervised learning. While many algorithms can be ported to a GPU in a simple and direct fashion, such efforts have resulted in inefficient and inaccurate versions of UMAP. We show a number of techniques that can be used to make a faster and more faithful GPU version of UMAP, and obtain speedups of up to 100x in practice. Many of these design choices/lessons are general purpose and may inform the conversion of other graph and manifold learning algorithms to use GPUs. Our implementation has been made publicly available as part of the open source RAPIDS cuML library (https://github.com/rapidsai/cuml)