Improving Barnes-Hut t-SNE Algorithm in Modern GPU Architectures with Random Forest KNN and Simulated Wide-Warp

2021 ◽  
Vol 17 (4) ◽  
pp. 1-26
Author(s):  
Bruno Henrique Meyer ◽  
Aurora Trinidad Ramirez Pozo ◽  
Wagner M. Nunan Zola
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Large Data ◽  
Multidimensional Data ◽  
Original Algorithm ◽  
Acceleration Techniques ◽  
Data Points ◽  
Gpu Architectures ◽  
Simulation Problem ◽  
Efficient Memory

The t-Distributed Stochastic Neighbor Embedding (t-SNE) is a widely used technique for dimensionality reduction but is limited by its scalability when applied to large datasets. Recently, BH-tSNE was proposed; this is a successful approximation that transforms a step of the original algorithm into an N-Body simulation problem that can be solved by a modified Barnes-Hut algorithm. However, this improvement still has limitations to process large data volumes (millions of records). Late studies, such as t-SNE-CUDA, have used GPUs to implement highly parallel BH-tSNE. In this research we have developed a new GPU BH-tSNE implementation that produces the embedding of multidimensional data points into three-dimensional space. We examine scalability issues in two of the most expensive steps of GPU BH-tSNE by using efficient memory access strategies , recent acceleration techniques , and a new approach to compute the KNN graph structure used in BH-tSNE with GPU. Our design allows up to 460% faster execution when compared to the t-SNE-CUDA implementation. Although our SIMD acceleration techniques were used in a modern GPU setup, we have also verified a potential for applications in the context of multi-core processors.

SCATTERING THEORY FOR ZAKHAROV EQUATIONS IN THREE-DIMENSIONAL SPACE WITH LARGE DATA

2004 ◽  
Vol 06 (06) ◽  
pp. 881-899 ◽  
Author(s):  
AKIHIRO SHIMOMURA
Keyword(s):  
Scattering Theory ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Large Data ◽  
Zakharov Equation ◽  
Unique Existence ◽  
Wave Operators ◽  
The Fourier Transform ◽  
The Given ◽  
Three Dimensional Space

We study the scattering theory for the Zakharov equation in three-dimensional space. We show the unique existence of the solution for this equation which tends to the given free profile with no restriction on the size of the scattered states and on the support of the Fourier transform of them. This yields the existence of the pseudo wave operators.

Wavelet Compression of Three-Dimensional Time-Lapse Biological Image Data

2005 ◽  
Vol 11 (1) ◽  
pp. 9-17 ◽  
Author(s):  
H. Narfi Stefansson ◽  
Kevin W. Eliceiri ◽  
Charles F. Thomas ◽  
Amos Ron ◽  
Ron DeVore ◽  
...  
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Image Data ◽  
Large Data ◽  
Time Lapse ◽  
Large Data Sets ◽  
Multidimensional Data ◽  
Data Sets ◽  
Optical Sectioning ◽  
Dynamic Events

The use of multifocal-plane, time-lapse recordings of living specimens has allowed investigators to visualize dynamic events both within ensembles of cells and individual cells. Recordings of such four-dimensional (4D) data from digital optical sectioning microscopy produce very large data sets. We describe a wavelet-based data compression algorithm that capitalizes on the inherent redunancies within multidimensional data to achieve higher compression levels than can be obtained from single images. The algorithm will permit remote users to roam through large 4D data sets using communication channels of modest bandwidth at high speed. This will allow animation to be used as a powerful aid to visualizing dynamic changes in three-dimensional structures.

The Curve-Mesh Concept in Reconstructing Smooth Surface From Noisy Data

1990 ◽  
Author(s):  
P. D. Kaklis
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Test Function ◽  
Statistical Framework ◽  
Continuous Surface ◽  
Data Points ◽  
Constrained Minimization Problem ◽  
Numerical Performance ◽  
Newton Raphson ◽  
Three Dimensional Space

Abstract This paper is concerned with the problem of filtering the noise encountered in the measurements taken from a smooth (GC2-continuous) surface in the three-dimensional space. For this purpose, the data points are firstly considered to belong to a three-dimensional entity which is drastically simpler than a surface, namely the noisy curvature-continuous quadrilateral curve-mesh connecting the data points. The curve-mesh concept, apparently introduced by Hosaka (1969), is then combined with the concept of fairing in a statistical framework introduced by Reinsen (1967; 1971), yielding a constrained minimization problem for the fairing curve-mesh. After establishing that this problem has a unique solution in an appropriate Hilbert space, a convergent Newton-Raphson-type algorithm for constructing it in a cubic-spline subspace is presented in detail. Finally, the numerical performance of this algorithm in the context of a Monte-Carlo experimentation with the so-called Franke’s principal test function (1979,1980,1982) is discussed.

Representative reduction of crystallographic orientation data

2013 ◽  
Vol 46 (4) ◽  
pp. 960-971 ◽  
Author(s):  
Katja Jöchen ◽  
Thomas Böhlke
Keyword(s):  
Crystallographic Orientation ◽  
Electron Backscatter Diffraction ◽  
Three Dimensional ◽  
Large Data ◽  
Data Sets ◽  
Data Set ◽  
Orientation Data ◽  
Clustering Technique ◽  
Orientation Space ◽  
Data Points

Experimental techniques [e.g.electron backscatter diffraction (EBSD)] yield detailed crystallographic information on the grain scale. In both two- and three-dimensional applications of EBSD, large data sets in the range of 105–109single-crystal orientations are obtained. With regard to the precise but efficient micromechanical computation of the polycrystalline material response, small representative sets of crystallographic orientation data are required. This paper describes two methods to systematically reduce experimentally measured orientation data. Inspired by the work of Gao, Przybyla & Adams [Metall. Mater. Trans. A(2006),37, 2379–2387], who used a tessellation of the orientation space in order to compute correlation functions, one method in this work uses a similar procedure to partition the orientation space into boxes, but with the aim of extracting the mean orientation of the data points of each box. The second method to reduce crystallographic texture data is based on a clustering technique. It is shown that, in terms of representativity of the reduced data, both methods deliver equally good results. While the clustering technique is computationally more costly, it works particularly well when the measured data set shows pronounced clusters in the orientation space. The quality of the results and the performance of the tessellation method are independent of the examined data set.

Assessing Circularity in Three Dimensions1

2000 ◽  
Vol 123 (1) ◽  
pp. 128-134 ◽  
Author(s):  
Shuo-Yan Chou ◽  
Shih-Wei Lin ◽  
Chien-Hong Chen
Keyword(s):  
Cross Section ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Coordinate Measuring Machines ◽  
Single Plane ◽  
Research Designs ◽  
Data Points ◽  
Three Dimensional Space ◽  
Assessment Results

This research resolves an inconsistency problem that arises from assessing circularity of workpiece measured by coordinate measuring machines (CMMs). Although the notion of circularity is employed to constrain two-dimensional circular features, in practice the measured points are obtained in a three-dimensional space and are in general not in the same plane, let alone being in a “perpendicular” cross-section. All of the algorithms currently used for assessing circularity deal with data in a single plane that is perpendicular to the axis of a cylindrical feature from which the circular feature is extracted. This discrepancy causes the assessed circularity significantly departing from the actual circularity and resulting in rejection of in-tolerance parts. This research designs a compensation procedure for deriving two-dimensional data from three-dimensional biased measured points. The circularity is assessed based on the compensated two-dimensional data points. The assessment results with the compensation are compared with those without compensation. A program containing a variety of implementations of form fitting algorithms is developed and used to illustrate the improvement on the accuracy of assessment.

Three Dimensional structure and organization of diploid chromosomes by optical section microscopy

1987 ◽  
Vol 45 ◽  
pp. 633-635
Author(s):  
David A. Agard ◽  
Yasushi Hiraoka ◽  
John W. Sedat
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Developmental State ◽  
Mitotic Cell ◽  
Biological Properties ◽  
Dimensional Structure ◽  
Specific Gene ◽  
Three Dimensional Structure ◽  
Complementary Techniques ◽  
Dynamic Structures

In an effort to understand the complex relationship between structure and biological function within the nucleus, we have embarked on a program to examine the three-dimensional structure and organization of Drosophila melanogaster embryonic chromosomes. Our overall goal is to determine how DNA and proteins are organized into complex and highly dynamic structures (chromosomes) and how these chromosomes are arranged in three dimensional space within the cell nucleus. Futher, we hope to be able to correlate structual data with such fundamental biological properties as stage in the mitotic cell cycle, developmental state and transcription at specific gene loci.Towards this end, we have been developing methodologies for the three-dimensional analysis of non-crystalline biological specimens using optical and electron microscopy. We feel that the combination of these two complementary techniques allows an unprecedented look at the structural organization of cellular components ranging in size from 100A to 100 microns.

Automated 3-D cell population analysis in thick tissue sections using laser-scanning confocal-microscopy data

1993 ◽  
Vol 51 ◽  
pp. 562-563
Author(s):  
Hakan Ancin
Keyword(s):  
Laser Scanning ◽  
Population Analysis ◽  
Three Dimensional ◽  
Large Data ◽  
Laser Scanning Confocal Microscopy ◽  
Tissue Slices ◽  
Scanning Confocal Microscopy ◽  
Tissue Sections ◽  
Spatially Adaptive ◽  
Microscopy Data

This paper presents methods for performing detailed quantitative automated three dimensional (3-D) analysis of cell populations in thick tissue sections while preserving the relative 3-D locations of cells. Specifically, the method disambiguates overlapping clusters of cells, and accurately measures the volume, 3-D location, and shape parameters for each cell. Finally, the entire population of cells is analyzed to detect patterns and groupings with respect to various combinations of cell properties. All of the above is accomplished with zero subjective bias.In this method, a laser-scanning confocal light microscope (LSCM) is used to collect optical sections through the entire thickness (100 - 500μm) of fluorescently-labelled tissue slices. The acquired stack of optical slices is first subjected to axial deblurring using the expectation maximization (EM) algorithm. The resulting isotropic 3-D image is segmented using a spatially-adaptive Poisson based image segmentation algorithm with region-dependent smoothing parameters. Extracting the voxels that were labelled as "foreground" into an active voxel data structure results in a large data reduction.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Flavin radicals, conformational sampling and robust design principles in interprotein electron transfer: the trimethylamine dehydrogenase-electron-transferring flavoprotein complex

2004 ◽  
Vol 71 ◽  
pp. 1-14
Author(s):  
David Leys ◽  
Jaswir Basran ◽  
François Talfournier ◽  
Kamaldeep K. Chohan ◽  
Andrew W. Munro ◽  
...  
Keyword(s):  
Electron Transfer ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Kinetic Studies ◽  
Molecular Assembly ◽  
Conformational Sampling ◽  
Trimethylamine Dehydrogenase ◽  
Key Residues ◽  
Electron Transferring Flavoprotein ◽  
Electron Transfer Complex

TMADH (trimethylamine dehydrogenase) is a complex iron-sulphur flavoprotein that forms a soluble electron-transfer complex with ETF (electron-transferring flavoprotein). The mechanism of electron transfer between TMADH and ETF has been studied using stopped-flow kinetic and mutagenesis methods, and more recently by X-ray crystallography. Potentiometric methods have also been used to identify key residues involved in the stabilization of the flavin radical semiquinone species in ETF. These studies have demonstrated a key role for 'conformational sampling' in the electron-transfer complex, facilitated by two-site contact of ETF with TMADH. Exploration of three-dimensional space in the complex allows the FAD of ETF to find conformations compatible with enhanced electronic coupling with the 4Fe-4S centre of TMADH. This mechanism of electron transfer provides for a more robust and accessible design principle for interprotein electron transfer compared with simpler models that invoke the collision of redox partners followed by electron transfer. The structure of the TMADH-ETF complex confirms the role of key residues in electron transfer and molecular assembly, originally suggested from detailed kinetic studies in wild-type and mutant complexes, and from molecular modelling.

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