# Parallel Computing of Kernel Density Estimates with MPI

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Parallel Computing of Kernel Density Estimates with MPI Szymon Lukasik Department of Automatic Control, Cracow University of Technology, ul. Warszawska 24, Cracow, Poland Abstract. Kernel density estimation is nowadays a very popular tool for nonparametric probabilistic density estimation. One of its most important disadvantages is computational complexity of calculations needed, especially for data-based bandwidth selection and adaptation of bandwidth coefficient. The article presents parallel methods which can significantly improve calculation time. Results of using reference implementation based on Message Passing Interface standard in multicomputer environment are included as well as a discussion on effectiveness of parallelization. Key words: kernel density estimation, plug-in method, least squares cross-validation, adaptive bandwidth, parallel algorithms, MPI 1 Introduction Nonparametric methods find increasing number of applications in data mining problems. One of its main tools is kernel density estimation (KDE) introduced by Rosenblatt in 1956 [1] and Parzen in 1962 [2]. It has been successfully used in various applications like image processing [3], medical monitoring [4] and market analysis [5]. Theoretical and practical aspects of the estimation itself are covered in detail in numerous publications, e.g. popular monographs [6] and [7]. For n-dimensional probabilistic variable X with sample x i of length m, kernel K and bandwidth h, the kernel density estimation evaluated for x is defined as a function: ˆf(x) = 1 mh n m ( ) x xi K h i=1. (1) It can be seen that computation of KDE is of complexity O(nm). Thus, long samples and large number of points p for which kernel density estimates are calculated can seriously influence the estimation time. The evaluation of density estimates can be made even more resource exhausting when one wishes to use bandwidth variation as suggested by Abramson [8]. Computational complexity of additional calculations is O(nm 2 ) in this case.

2 2 S. Lukasik Methods of data-based optimal bandwidth calculation have also high computational demands. Second order plug-in method [9], which involves estimating second derivative of density function from given sample, is of O(nm 2 ) complexity. Also least squares cross-validation method (LSCV) [10, 11], where selecting optimal bandwidth is based on minimizing objective function g(h), has the same polynomial time complexity. Few approximation techniques have been proposed to deal with the problem of time-consuming calculations of kernel density estimates. The first of them, proposed by Silverman [12], uses fast Fourier transform (FFT). The other one applies Fast Gauss Transform (FGT) as suggested by Elgammal [13]. An alternative to those methods could use parallel processing for obtaining density function estimates. The pioneer paper in this subject is due to Racine [14]. It proves the usability of parallel computations for kernel density estimation but covers in detail only the estimation itself. Parallelization is done by dividing set of points where estimator is to be evaluated. Each processor obtains the density function estimation for approximately p c points (where c denotes number of CPUs involved). The aim of this paper is to verify how parallel processing can be applied for kernel estimation, bandwidth selection and adaptation. All presented algorithms have been implemented and tested in a multicomputer environment using MPI (Message Passing Interface) [16]. A possibility of parallelization at the sample level, by distributing the sample and calculating approximately m c sums in (1) separately on each of the c CPUs for every evaluated point x, is also discussed. 2 Parallelization methods Following subsections will briefly present routines for obtaining kernel density estimates using parallel processing. All algorithms will be included in the form of pseudo-code with group operations treated as collective ones. In the presented code listings subsequent notation was used: proc rank is current processor number (including 0 as a root/master processor), proc no - overall number of processors involved c, sample[k] - kth sample element, sample length - sample length m, x eval[k] - kth evaluation point, f[k] - the estimator value for x eval[k] and ev points - the overall number of points p where estimator is to be evaluated. 2.1 Kernel Density Estimation Parallelization of estimation process can be achieved either by dividing set of evaluation points or sample data. Both of suggested parallelization schemes were presented using code attached below: Parallel KDE at evaluation level Broadcast(sample); shift:=proc_rank*ev_points/proc_no;

3 Parallel Computing of KDE with MPI 3 /* evaluation of KDE for x[k+shift] using all sample elements */ for k:=1 to ev_points/proc_no do f[k+shift]:=compute_kde(x[k+shift],sample,1,sample_length); Gather_at_root(f); return f; Parallel KDE at sample level Scatter(sample); shift:=proc_rank*sample_length/proc_no + 1; /* evaluation of KDE for x[k] using sample starting from element sample[shift] to element indexed by shift+sample_length/proc_no */ for k:=1 to ev_points do f[k]:=compute_kde(x[k],sample,shift,shift+sample_length/proc_no); Aggregate_at_root(f); return f; In the first case (presented already in [14]) whole sample should be distributed among processors taking part in calculations. In the end evaluated kernel estimator values should be gathered at the master machine. The alternative is to implement parallel model at the sample level - each CPU calculates all estimator values but considering only the part of a sample. Results are globally aggregated at the master machine. In this version of the algorithm there is no need to broadcast all sample points. 2.2 Bandwidth Selection Using Plug-in Method Let us consider commonly used two-stage direct plug-in method of Sheather- Jones [7]. Proposed parallel algorithm for plug-in bandwidth selection with parallelization at the sample level is introduced below: Parallel plug-in bandwidth selection Broadcast(sample); shift:=proc_rank*sample_length/proc_no + 1; /* estimation of plug-in psi functional of order i using sample starting from element sample[shift] of length sample_length/proc_no */ for i:=6 and 4 do psi[i]:=compute_sjf(i,sample,shift,shift+sample_length/proc_no); Aggregate_at_all(psi[i]); h=select_bandwidth_at_root(); return h; 2.3 Bandwidth Selection Using Least Squares Cross-Validation Method The problem of minimizing score function g(h) can be approached using direct evaluation of the function in selected range with a required step or by applying some optimization technique. Underlying evaluation of the score function can be

4 4 S. Lukasik easily parallelized at the sample level. Due to lack of space, only the algorithm of direct parallel minimization of g(h) will be presented here. Experimental results were obtained using golden section rule [15]. Parallel LSCV bandwidth selection Broadcast(sample); shift:=proc_rank*sample_length/proc_no + 1; g_min:=infinity, h_min:=0; for h:=h_start to h_stop do /* calculation of g(h) using sample starting from element sample[shift] of length sample_length/proc_no */ g:=compute_g(h,sample,shift,shift+sample_length/proc_no); Aggregate_at_root(g); if g<g_min then g_min:=g, h_min:=h; return h_min; 2.4 Adaptive Bandwidth In order to reduce computational burden of bandwidth modifying coefficients calculation using Abramson method [8] parallel processing can be applied as presented below: Parallel bandwidth adaptation Broadcast(sample); shift:=proc_rank*sample_length/proc_no; /* first obtain unmodified estimates for sample points taking into consideration all sample elements */ for k:=1 to sample_length/proc_no do f[k+shift]:=compute_kde(sample[k+shift],sample,1,sample_length); Gather_at_all(f); /* then calculate geometric mean of estimates using sample_length/proc_no KDE values starting from f[1+shift] */ mean=compute_mean(f,1+shift,1+shift+sample_length/proc_no); Product_at_all(mean); /* obtain modifying coefficients */ for k:=1 to sample_length/proc_no do s[k+shift]:=(f[k+shift]/mean)^(-0.5); Gather_at_all(s); return s; Modifying coefficients s i can be easily incorporated into variable bandwidth parallel kernel density estimation (with h i = h s i ) similarly as it was presented in Section Experimental Results Reference implementation of proposed parallel algorithms was prepared to examine their efficiency. As a measure of parallelization performance following

5 Parallel Computing of KDE with MPI 5 efficiency function was chosen: E(c) = T (c) 1 %. (2) T (1) c where: T (c), T (1) are computation times for c CPUs and one CPU accordingly. Presented results were obtained for multiple execution of algorithms in Ethernet standard computer network of 6 Pentium R 4 machines with MPICH-2 library used as a parallelization tool. The estimation was performed with radial normal kernel function for randomly generated one-dimensional samples. Some sample lengths correspond to those considered in [14], the others were chosen to create broader view on an average parallel estimation execution time (given in seconds). Due to space limitations only selected results were presented - full set can be obtained from author s web site (http://www.pk.edu.pl/~szymonl). 3.1 Parallel Kernel Density Estimation First, the performance of two proposed parallelization schemes were tested for varying sample size and number of evaluation points. During the testing procedure m = p was assumed (like in [14]). Obtained results (presented in Fig. 1) include, for reference, computation times for sequential (c = 1) version of the KDE. T(c) [s] Sequential KDE, c=1 Parallel KDE (evaluation level), c=2,...,6 Parallel KDE (sample level), c=2,...,6 m=p E(c) [%] Fig. 1. Execution times and efficiency of parallel kernel density estimation methods It can be seen that results for small sample lengths are not encouraging, taking into consideration both calculation time and efficiency. The overhead, which include times of communication, synchronization and input/output operations, has a significant influence on effectiveness of multicomputer parallel

6 6 S. Lukasik system. Nevertheless, increasing problem size leads to speed-up which close to linear. Parallelization at the evaluation level in most cases performs better than the scheme with distribution of sample elements. The time cost of global aggregation (using MPI Reduce) in the multicomputer environment dominates the gain achieved by distributing smaller amount of data at the first phase of estimation. The proposed parallelization scheme can be applied successfully when m p, though. The difference between performances of the presented methods is under these assumptions neglectable. For instance, if m = 50000, p = 5000 and c = 3 algorithm using parallelization at the sample level is only 0.3 s slower (which is a fraction of s processing time for c = 1). 3.2 Parallel Bandwidth Selectors Observing high computational complexity of data-based bandwidth selectors leads to preliminary conclusion, that parallel processing in the case of both plug-in and LSCV methods will give significant improvement in calculation time. Results of test performed for variable sample lengths presented in Fig. 2 confirm it. When ruling out cases where too many CPUs were assigned to a very small task, relatively high parallelization effectiveness can be also noticed. Advantage of using parallel processing is in case of least squares cross validation more considerable - it is a direct effect of substantial computational demands raised by this method. T plugin (c) [s] Sequential plug-in, c=1 Sequential LSCV, c=1 Parallel plug-in, c=2,...,6 Parallel LSCV, c=2,..., T LSCV (c) [s] m E(c) [%] Fig. 2. Execution times and efficiency of parallel plug-in method and parallel least squares cross-validation

7 Parallel Computing of KDE with MPI Parallel Bandwidth Adaptation Finally parallelized routine for bandwidth adaptation was under investigation. The test was conducted with m = p. Considered scheme of algorithm involved also parallelizing the density estimation itself at evaluation level. Results of the test are enclosed in Fig Sequential KDE with bandwidth adaptation, c=1 Parallel KDE with bandwidth adaptation, c=2,...,6 95 T(c) [s] E(c) [%] 0 m=p 80 Fig. 3. Execution times and efficiency of parallel KDE with bandwidth adaptation In contrast to parallel kernel estimation with fixed bandwidth, performing parallel bandwidth adaptation can be judged as highly effective, even when relatively small sample is under consideration. The obtained speed-up of computation, with increasing CPUs number, is in this case close to linear. 4 Conclusion The article positively verifies the possibility of applying parallel algorithms for speeding up time-consuming process of kernel density estimation. Beneficial effects of parallelization, already proved for KDE [14] itself, were also confirmed for popular data dependent bandwidth selectors and bandwidth adaptation. Moreover, for fixed sample size, gain of using parallel calculation is in those cases more significant. The option of using the alternative parallelization scheme for kernel density estimation - at the sample level - was also under consideration. Empirical studies proved that the proposed method is, in general case, not as effective as parallel evaluation of density estimates. As in every parallel processing application it is important to note, that proper care has to be taken of granularity of calculation if one wishes to obtain effective use of engaged resources. Parallel bandwidth selectors and bandwidth adaptation

8 8 S. Lukasik involve substantial number of collective operations executed between calculation cycles so it would be also advisable to use load-balancing in order to eliminate overhead generated by MPI tasks synchronization routine (MPI Barrier). Acknowledgments. I would like to thank Prof. Zbigniew Kokosiński for his support and comments on an earlier version of this paper. I m also grateful for valuable suggestions of anonymous reviewers. References 1. Rosenblatt, M.: Remarks on Some Nonparametric Estimates of a Density Function. Annals of Mathematical Statistics 27 (1956) Parzen, E.: On Estimation of a Probability Density Function and Mode. Annals of Mathematical Statistics 33 (1962) Mittal, A., Paragios, N.: Motion-Based Background Subtraction Using Adaptive Kernel Density Estimation. IEEE Computer Society Conference on Computer Vision and Pattern Recognition 2 (2004) Cerrito, P.B., Barnes, G.R.: The Use of Kernel Density Estimators to Monitor Protocol Compliance. Proceedings of the Twenty-Fifth Annual SAS R Users Group International Conference SUGI25 (2000) paper no Donthu N., Rust, R.T.: Estimating Geographic Customers Densities using Kernel Density Estimation. Marketing Science 8 (1989) Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, London (1986) 7. Wand, M.P., Jones, M.C.: Kernel Smoothing. Chapman and Hall, London (1995) 8. Abramson, I.: On Bandwidth Variation in Kernel Estimates - a Square Root Law. The Annals of Statistics 10 (1982) Sheather, S.J., Jones, M.C.: A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation. Journal of the Royal Statistical Society. Series B. Methodological 53/3 (1991) Rudemo, M.: Empirical Choice of Histograms and Kernel Density Estimators. Scandinavian Journal of Statistics 9 (1982) Bowman, A.W.: An Alternative Method of Cross-Validation for the Smoothing of Density Estimates. Biometrika 71 (1984) Silverman, B.W.: Algorithm AS 176: Kernel Density Estimation Using the Fast Fourier Transform. Applied Statistics 31/1 (1982) Elgammal, A., Duraiswami, R., Davis, L.S.: Efficient Kernel Density Estimation Using the Fast Gauss Transform with Applications to Color Modeling and Tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 25/11 (2003) Racine, J.: Parallel distributed kernel estimation. Computational Statistics and Data Analysis 40/2 (2002) Gill, P.E., Murray, W., Wright, M.H.: Practical Optimization. Academic Press, London (1981) 16. Snir, M., Otto, S., Huss-Lederman, S., Walker, D., Dongarra J.: MPI: The Complete Reference. The MIT Press, Cambridge (1996)

### A Performance Study of Load Balancing Strategies for Approximate String Matching on an MPI Heterogeneous System Environment

A Performance Study of Load Balancing Strategies for Approximate String Matching on an MPI Heterogeneous System Environment Panagiotis D. Michailidis and Konstantinos G. Margaritis Parallel and Distributed

### Introduction to Kernel Smoothing

Introduction to Kernel Smoothing Density 0.000 0.002 0.004 0.006 700 800 900 1000 1100 1200 1300 Wilcoxon score M. P. Wand & M. C. Jones Kernel Smoothing Monographs on Statistics and Applied Probability

### A Complete Gradient Clustering Algorithm for Features Analysis of X-ray Images

A Complete Gradient Clustering Algorithm for Features Analysis of X-ray Images Małgorzata Charytanowicz, Jerzy Niewczas, Piotr A. Kowalski, Piotr Kulczycki, Szymon Łukasik, and Sławomir Żak Abstract Methods

### Kernel density estimation with adaptive varying window size

Pattern Recognition Letters 23 (2002) 64 648 www.elsevier.com/locate/patrec Kernel density estimation with adaptive varying window size Vladimir Katkovnik a, Ilya Shmulevich b, * a Kwangju Institute of

### Least Squares Estimation

Least Squares Estimation SARA A VAN DE GEER Volume 2, pp 1041 1045 in Encyclopedia of Statistics in Behavioral Science ISBN-13: 978-0-470-86080-9 ISBN-10: 0-470-86080-4 Editors Brian S Everitt & David

### LOAD BALANCING FOR MULTIPLE PARALLEL JOBS

European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2000 Barcelona, 11-14 September 2000 ECCOMAS LOAD BALANCING FOR MULTIPLE PARALLEL JOBS A. Ecer, Y. P. Chien, H.U Akay

### Automated Learning and Data Visualization

1 Automated Learning and Data Visualization William S. Cleveland Department of Statistics Department of Computer Science Purdue University Methods of Statistics, Machine Learning, and Data Mining 2 Mathematical

### A Practical Performance Comparison of Parallel Sorting Algorithms on Homogeneous Network of Workstations

A Practical Performance Comparison of Parallel Sorting Algorithms on Homogeneous Network of Workstations Haroon Rashid and Kalim Qureshi* COMSATS Institute of Information Technology, Abbottabad, Pakistan

### Parametric versus Semi/nonparametric Regression Models

Parametric versus Semi/nonparametric Regression Models Hamdy F. F. Mahmoud Virginia Polytechnic Institute and State University Department of Statistics LISA short course series- July 23, 2014 Hamdy Mahmoud

### Parallel Processing over Mobile Ad Hoc Networks of Handheld Machines

Parallel Processing over Mobile Ad Hoc Networks of Handheld Machines Michael J Jipping Department of Computer Science Hope College Holland, MI 49423 jipping@cs.hope.edu Gary Lewandowski Department of Mathematics

### Bandwidth Selection for Nonparametric Distribution Estimation

Bandwidth Selection for Nonparametric Distribution Estimation Bruce E. Hansen University of Wisconsin www.ssc.wisc.edu/~bhansen May 2004 Abstract The mean-square efficiency of cumulative distribution function

### PARALLEL PROGRAMMING

PARALLEL PROGRAMMING TECHNIQUES AND APPLICATIONS USING NETWORKED WORKSTATIONS AND PARALLEL COMPUTERS 2nd Edition BARRY WILKINSON University of North Carolina at Charlotte Western Carolina University MICHAEL

### Complete Gradient Clustering Algorithm for Features Analysis of X-ray Images

Complete Gradient Clustering Algorithm for Features Analysis of X-ray Images Małgorzata Charytanowicz, Jerzy Niewczas, Piotr Kulczycki, Piotr A. Kowalski, Szymon Łukasik, and Sławomir Żak Abstract Methods

### Measuring MPI Send and Receive Overhead and Application Availability in High Performance Network Interfaces

Measuring MPI Send and Receive Overhead and Application Availability in High Performance Network Interfaces Douglas Doerfler and Ron Brightwell Center for Computation, Computers, Information and Math Sandia

### Load Balancing on a Non-dedicated Heterogeneous Network of Workstations

Load Balancing on a Non-dedicated Heterogeneous Network of Workstations Dr. Maurice Eggen Nathan Franklin Department of Computer Science Trinity University San Antonio, Texas 78212 Dr. Roger Eggen Department

### GRAPHICS PROCESSING UNITS IN ACCELERATION OF BANDWIDTH SELECTION FOR KERNEL DENSITY ESTIMATION

Int. J. Appl. Math. Comput. Sci., 2013, Vol. 23, No. 4, 869 885 DOI: 10.2478/amcs-2013-0065 GRAPHICS PROCESSING UNITS IN ACCELERATION OF BANDWIDTH SELECTION FOR KERNEL DENSITY ESTIMATION WITOLD ANDRZEJEWSKI,

### FPGA area allocation for parallel C applications

1 FPGA area allocation for parallel C applications Vlad-Mihai Sima, Elena Moscu Panainte, Koen Bertels Computer Engineering Faculty of Electrical Engineering, Mathematics and Computer Science Delft University

### Predict the Popularity of YouTube Videos Using Early View Data

000 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050

### Support Vector Machines with Clustering for Training with Very Large Datasets

Support Vector Machines with Clustering for Training with Very Large Datasets Theodoros Evgeniou Technology Management INSEAD Bd de Constance, Fontainebleau 77300, France theodoros.evgeniou@insead.fr Massimiliano

### Spatio-Temporal Nonparametric Background Modeling and Subtraction

Spatio-Temporal Nonparametric Background Modeling and Subtraction Raviteja Vemulapalli and R. Aravind Department of Electrical engineering Indian Institute of Technology, Madras Background subtraction

### ACCELERATING SELECT WHERE AND SELECT JOIN QUERIES ON A GPU

Computer Science 14 (2) 2013 http://dx.doi.org/10.7494/csci.2013.14.2.243 Marcin Pietroń Pawe l Russek Kazimierz Wiatr ACCELERATING SELECT WHERE AND SELECT JOIN QUERIES ON A GPU Abstract This paper presents

### Building an Inexpensive Parallel Computer

Res. Lett. Inf. Math. Sci., (2000) 1, 113-118 Available online at http://www.massey.ac.nz/~wwiims/rlims/ Building an Inexpensive Parallel Computer Lutz Grosz and Andre Barczak I.I.M.S., Massey University

### Parallel Simulated Annealing Algorithm for Graph Coloring Problem

Parallel Simulated Annealing Algorithm for Graph Coloring Problem Szymon Łukasik 1, Zbigniew Kokosiński 2, and Grzegorz Świętoń 2 1 Systems Research Institute, Polish Academy of Sciences, ul. Newelska

### Parallel Ray Tracing using MPI: A Dynamic Load-balancing Approach

Parallel Ray Tracing using MPI: A Dynamic Load-balancing Approach S. M. Ashraful Kadir 1 and Tazrian Khan 2 1 Scientific Computing, Royal Institute of Technology (KTH), Stockholm, Sweden smakadir@csc.kth.se,

### A Load Balancing Technique for Some Coarse-Grained Multicomputer Algorithms

A Load Balancing Technique for Some Coarse-Grained Multicomputer Algorithms Thierry Garcia and David Semé LaRIA Université de Picardie Jules Verne, CURI, 5, rue du Moulin Neuf 80000 Amiens, France, E-mail:

### Overlapping Data Transfer With Application Execution on Clusters

Overlapping Data Transfer With Application Execution on Clusters Karen L. Reid and Michael Stumm reid@cs.toronto.edu stumm@eecg.toronto.edu Department of Computer Science Department of Electrical and Computer

### A Flexible Cluster Infrastructure for Systems Research and Software Development

Award Number: CNS-551555 Title: CRI: Acquisition of an InfiniBand Cluster with SMP Nodes Institution: Florida State University PIs: Xin Yuan, Robert van Engelen, Kartik Gopalan A Flexible Cluster Infrastructure

### Multilevel Load Balancing in NUMA Computers

FACULDADE DE INFORMÁTICA PUCRS - Brazil http://www.pucrs.br/inf/pos/ Multilevel Load Balancing in NUMA Computers M. Corrêa, R. Chanin, A. Sales, R. Scheer, A. Zorzo Technical Report Series Number 049 July,

### Maximizing Productivity through Parallel and Distributed Computing

Maximizing Productivity through Parallel and Distributed Computing Philip Chan Software Technology Department College of Computer Studies De La Salle University 2401 Taft Avenue, Manila, Philippines pc@ccs.dlsu.edu.ph

### MOSIX: High performance Linux farm

MOSIX: High performance Linux farm Paolo Mastroserio [mastroserio@na.infn.it] Francesco Maria Taurino [taurino@na.infn.it] Gennaro Tortone [tortone@na.infn.it] Napoli Index overview on Linux farm farm

### Local outlier detection in data forensics: data mining approach to flag unusual schools

Local outlier detection in data forensics: data mining approach to flag unusual schools Mayuko Simon Data Recognition Corporation Paper presented at the 2012 Conference on Statistical Detection of Potential

### Syntax Menu Description Options Remarks and examples Stored results Methods and formulas References Also see. Description

Title stata.com lpoly Kernel-weighted local polynomial smoothing Syntax Menu Description Options Remarks and examples Stored results Methods and formulas References Also see Syntax lpoly yvar xvar [ if

### Why High-Order Polynomials Should Not be Used in Regression Discontinuity Designs

Why High-Order Polynomials Should Not be Used in Regression Discontinuity Designs Andrew Gelman Guido Imbens 2 Aug 2014 Abstract It is common in regression discontinuity analysis to control for high order

### GMP implementation on CUDA - A Backward Compatible Design With Performance Tuning

1 GMP implementation on CUDA - A Backward Compatible Design With Performance Tuning Hao Jun Liu, Chu Tong Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto haojun.liu@utoronto.ca,

### Numerical Summarization of Data OPRE 6301

Numerical Summarization of Data OPRE 6301 Motivation... In the previous session, we used graphical techniques to describe data. For example: While this histogram provides useful insight, other interesting

### Parallel Scalable Algorithms- Performance Parameters

www.bsc.es Parallel Scalable Algorithms- Performance Parameters Vassil Alexandrov, ICREA - Barcelona Supercomputing Center, Spain Overview Sources of Overhead in Parallel Programs Performance Metrics for

### Studying Auto Insurance Data

Studying Auto Insurance Data Ashutosh Nandeshwar February 23, 2010 1 Introduction To study auto insurance data using traditional and non-traditional tools, I downloaded a well-studied data from http://www.statsci.org/data/general/motorins.

### Subspace Analysis and Optimization for AAM Based Face Alignment

Subspace Analysis and Optimization for AAM Based Face Alignment Ming Zhao Chun Chen College of Computer Science Zhejiang University Hangzhou, 310027, P.R.China zhaoming1999@zju.edu.cn Stan Z. Li Microsoft

### How Bandwidth Selection Algorithms Impact Exploratory Data Analysis Using Kernel Density Estimation. Jared K. Harpole

How Bandwidth Selection Algorithms Impact Exploratory Data Analysis Using Kernel Density Estimation By Jared K. Harpole Submitted to the Department of Psychology and the Graduate Faculty of the University

### CHARACTERISTICS IN FLIGHT DATA ESTIMATION WITH LOGISTIC REGRESSION AND SUPPORT VECTOR MACHINES

CHARACTERISTICS IN FLIGHT DATA ESTIMATION WITH LOGISTIC REGRESSION AND SUPPORT VECTOR MACHINES Claus Gwiggner, Ecole Polytechnique, LIX, Palaiseau, France Gert Lanckriet, University of Berkeley, EECS,

### ON THE EXISTENCE AND LIMIT BEHAVIOR OF THE OPTIMAL BANDWIDTH FOR KERNEL DENSITY ESTIMATION

Statistica Sinica 17(27), 289-3 ON THE EXISTENCE AND LIMIT BEHAVIOR OF THE OPTIMAL BANDWIDTH FOR KERNEL DENSITY ESTIMATION J. E. Chacón, J. Montanero, A. G. Nogales and P. Pérez Universidad de Extremadura

### International Journal of Information Technology, Modeling and Computing (IJITMC) Vol.1, No.3,August 2013

FACTORING CRYPTOSYSTEM MODULI WHEN THE CO-FACTORS DIFFERENCE IS BOUNDED Omar Akchiche 1 and Omar Khadir 2 1,2 Laboratory of Mathematics, Cryptography and Mechanics, Fstm, University of Hassan II Mohammedia-Casablanca,

### A Simultaneous Solution for General Linear Equations on a Ring or Hierarchical Cluster

Acta Technica Jaurinensis Vol. 3. No. 1. 010 A Simultaneous Solution for General Linear Equations on a Ring or Hierarchical Cluster G. Molnárka, N. Varjasi Széchenyi István University Győr, Hungary, H-906

### The Impact of Big Data on Classic Machine Learning Algorithms. Thomas Jensen, Senior Business Analyst @ Expedia

The Impact of Big Data on Classic Machine Learning Algorithms Thomas Jensen, Senior Business Analyst @ Expedia Who am I? Senior Business Analyst @ Expedia Working within the competitive intelligence unit

### STATISTICAL DATA ANALYSIS COURSE VIA THE MATLAB WEB SERVER

STATISTICAL DATA ANALYSIS COURSE VIA THE MATLAB WEB SERVER Ale š LINKA Dept. of Textile Materials, TU Liberec Hálkova 6, 461 17 Liberec, Czech Republic e-mail: ales.linka@vslib.cz Petr VOLF Dept. of Applied

### D-optimal plans in observational studies

D-optimal plans in observational studies Constanze Pumplün Stefan Rüping Katharina Morik Claus Weihs October 11, 2005 Abstract This paper investigates the use of Design of Experiments in observational

### Studio 4. software for machine vision engineers. intuitive powerful adaptable. Adaptive Vision 4 1

Studio 4 intuitive powerful adaptable software for machine vision engineers Introduction Adaptive Vision Studio Adaptive Vision Studio software is the most powerful graphical environment for machine vision

### A Hybrid Load Balancing Policy underlying Cloud Computing Environment

A Hybrid Load Balancing Policy underlying Cloud Computing Environment S.C. WANG, S.C. TSENG, S.S. WANG*, K.Q. YAN* Chaoyang University of Technology 168, Jifeng E. Rd., Wufeng District, Taichung 41349

### A simple and fast algorithm for computing exponentials of power series

A simple and fast algorithm for computing exponentials of power series Alin Bostan Algorithms Project, INRIA Paris-Rocquencourt 7815 Le Chesnay Cedex France and Éric Schost ORCCA and Computer Science Department,

### Robert Collins CSE598G. More on Mean-shift. R.Collins, CSE, PSU CSE598G Spring 2006

More on Mean-shift R.Collins, CSE, PSU Spring 2006 Recall: Kernel Density Estimation Given a set of data samples x i ; i=1...n Convolve with a kernel function H to generate a smooth function f(x) Equivalent

### Mean-Shift Tracking with Random Sampling

1 Mean-Shift Tracking with Random Sampling Alex Po Leung, Shaogang Gong Department of Computer Science Queen Mary, University of London, London, E1 4NS Abstract In this work, boosting the efficiency of

### Runtime and Implementation of Factoring Algorithms: A Comparison

Runtime and Implementation of Factoring Algorithms: A Comparison Justin Moore CSC290 Cryptology December 20, 2003 Abstract Factoring composite numbers is not an easy task. It is classified as a hard algorithm,

### Proposal and Development of a Reconfigurable Parallel Job Scheduling Algorithm

Proposal and Development of a Reconfigurable Parallel Job Scheduling Algorithm Luís Fabrício Wanderley Góes, Carlos Augusto Paiva da Silva Martins Graduate Program in Electrical Engineering PUC Minas {lfwgoes,capsm}@pucminas.br

### An Overview of Knowledge Discovery Database and Data mining Techniques

An Overview of Knowledge Discovery Database and Data mining Techniques Priyadharsini.C 1, Dr. Antony Selvadoss Thanamani 2 M.Phil, Department of Computer Science, NGM College, Pollachi, Coimbatore, Tamilnadu,

### Implementation of a Buffer Memory in Minicomputers

Using the cache memory structure as applied to a 12-bit minicomputer (PDP-8/E), and the 100-ns processor constructed of H and S series TTL gates, the resultant performance is 5 to 10 times the conventional

### An Ecient Dynamic Load Balancing using the Dimension Exchange. Ju-wook Jang. of balancing load among processors, most of the realworld

An Ecient Dynamic Load Balancing using the Dimension Exchange Method for Balancing of Quantized Loads on Hypercube Multiprocessors * Hwakyung Rim Dept. of Computer Science Seoul Korea 11-74 ackyung@arqlab1.sogang.ac.kr

### A new binary floating-point division algorithm and its software implementation on the ST231 processor

19th IEEE Symposium on Computer Arithmetic (ARITH 19) Portland, Oregon, USA, June 8-10, 2009 A new binary floating-point division algorithm and its software implementation on the ST231 processor Claude-Pierre

### Solution of Linear Systems

Chapter 3 Solution of Linear Systems In this chapter we study algorithms for possibly the most commonly occurring problem in scientific computing, the solution of linear systems of equations. We start

### Applications to Data Smoothing and Image Processing I

Applications to Data Smoothing and Image Processing I MA 348 Kurt Bryan Signals and Images Let t denote time and consider a signal a(t) on some time interval, say t. We ll assume that the signal a(t) is

### AMSCO S Ann Xavier Gantert

AMSCO S Integrated ALGEBRA 1 Ann Xavier Gantert AMSCO SCHOOL PUBLICATIONS, INC. 315 HUDSON STREET, NEW YORK, N.Y. 10013 Dedication This book is dedicated to Edward Keenan who left a profound influence

### Challenges to Obtaining Good Parallel Processing Performance

Outline: Challenges to Obtaining Good Parallel Processing Performance Coverage: The Parallel Processing Challenge of Finding Enough Parallelism Amdahl s Law: o The parallel speedup of any program is limited

### Performance Visualization Tools. Performance Visualization Tools

Performance Visualization Tools 1 Performance Visualization Tools Lecture Outline : Following Topics will be discussed Characteristics of Performance Visualization technique Commercial and Public Domain

### Understanding the Benefits of IBM SPSS Statistics Server

IBM SPSS Statistics Server Understanding the Benefits of IBM SPSS Statistics Server Contents: 1 Introduction 2 Performance 101: Understanding the drivers of better performance 3 Why performance is faster

### e-issn: p-issn: X Page 67

International Journal of Computer & Communication Engineering Research (IJCCER) Volume 2 - Issue 2 March 2014 Performance Comparison of Gauss and Gauss-Jordan Yadanar Mon 1, Lai Lai Win Kyi 2 1,2 Information

### Cellular Computing on a Linux Cluster

Cellular Computing on a Linux Cluster Alexei Agueev, Bernd Däne, Wolfgang Fengler TU Ilmenau, Department of Computer Architecture Topics 1. Cellular Computing 2. The Experiment 3. Experimental Results

### Kernel Testing as an Alternative to χ 2 Analysis for Investigating the Distribution of Quantitative Traits

Kernel Testing as an Alternative to χ 2 Analysis for Investigating the Distribution of Quantitative Traits Jeffrey D. Hart, Anna Hale, J. Creighton Miller, Jr. Summary. Chi-square analysis is a popular

### 10.3 POWER METHOD FOR APPROXIMATING EIGENVALUES

55 CHAPTER NUMERICAL METHODS. POWER METHOD FOR APPROXIMATING EIGENVALUES In Chapter 7 we saw that the eigenvalues of an n n matrix A are obtained by solving its characteristic equation n c n n c n n...

### A Scalable Network Monitoring and Bandwidth Throttling System for Cloud Computing

A Scalable Network Monitoring and Bandwidth Throttling System for Cloud Computing N.F. Huysamen and A.E. Krzesinski Department of Mathematical Sciences University of Stellenbosch 7600 Stellenbosch, South

### RevoScaleR Speed and Scalability

EXECUTIVE WHITE PAPER RevoScaleR Speed and Scalability By Lee Edlefsen Ph.D., Chief Scientist, Revolution Analytics Abstract RevoScaleR, the Big Data predictive analytics library included with Revolution

### Concern Highlight: A Tool for Concern Exploration and Visualization

Concern Highlight: A Tool for Concern Exploration and Visualization Eugen C. Nistor André van der Hoek Department of Informatics School of Information and Computer Sciences University of California, Irvine

### On the Order of Search for Personal Identification with Biometric Images

On the Order of Search for Personal Identification with Biometric Images Kensuke Baba Library, Kyushu University 10-1, Hakozaki 6, Higashi-ku Fukuoka, 812-8581, Japan baba.kensuke.060@m.kyushu-u.ac.jp

### 2: Computer Performance

2: Computer Performance http://people.sc.fsu.edu/ jburkardt/presentations/ fdi 2008 lecture2.pdf... John Information Technology Department Virginia Tech... FDI Summer Track V: Parallel Programming 10-12

### PARALLEL ALGORITHMS FOR PREDICTIVE MODELLING

PARALLEL ALGORITHMS FOR PREDICTIVE MODELLING MARKUS HEGLAND Abstract. Parallel computing enables the analysis of very large data sets using large collections of flexible models with many variables. The

### Lizy Kurian John Electrical and Computer Engineering Department, The University of Texas as Austin

BUS ARCHITECTURES Lizy Kurian John Electrical and Computer Engineering Department, The University of Texas as Austin Keywords: Bus standards, PCI bus, ISA bus, Bus protocols, Serial Buses, USB, IEEE 1394

### The Effect of Process Topology and Load Balancing on Parallel Programming Models for SMP Clusters and Iterative Algorithms

The Effect of Process Topology and Load Balancing on Parallel Programming Models for SMP Clusters and Iterative Algorithms Nikolaos Drosinos and Nectarios Koziris National Technical University of Athens

### Part III. Lecture 3: Probability and Stochastic Processes. Stephen Kinsella (UL) EC4024 February 8, 2011 54 / 149

Part III Lecture 3: Probability and Stochastic Processes Stephen Kinsella (UL) EC4024 February 8, 2011 54 / 149 Today Basics of probability Empirical distributions Properties of probability distributions

### QF01/0407-1.0 الخطة الدراسية كلية العلوم وتكنولوجيا المعلومات- برنامج الماجستير/ الوصف المختصر

Algorithms analysis and design(0102721). The course introduces students to a variety of computer problems and methods of their solutions. It enables students to assess the complexity of problems and algorithms.

### Stochastic Doppler shift and encountered wave period distributions in Gaussian waves

Ocean Engineering 26 (1999) 507 518 Stochastic Doppler shift and encountered wave period distributions in Gaussian waves G. Lindgren a,*, I. Rychlik a, M. Prevosto b a Department of Mathematical Statistics,

### An Experimental Study of the Performance of Histogram Equalization for Image Enhancement

International Journal of Computer Sciences and Engineering Open Access Research Paper Volume-4, Special Issue-2, April 216 E-ISSN: 2347-2693 An Experimental Study of the Performance of Histogram Equalization

### Performance of Scientific Processing in Networks of Workstations: Matrix Multiplication Example

Performance of Scientific Processing in Networks of Workstations: Matrix Multiplication Example Fernando G. Tinetti Centro de Técnicas Analógico-Digitales (CeTAD) 1 Laboratorio de Investigación y Desarrollo

### A Fast Algorithm for Multilevel Thresholding

JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 17, 713-727 (2001) A Fast Algorithm for Multilevel Thresholding PING-SUNG LIAO, TSE-SHENG CHEN * AND PAU-CHOO CHUNG + Department of Electrical Engineering

### Cluster Computing at HRI

Cluster Computing at HRI J.S.Bagla Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019. E-mail: jasjeet@mri.ernet.in 1 Introduction and some local history High performance computing

### Parallel Algorithm for Dense Matrix Multiplication

Parallel Algorithm for Dense Matrix Multiplication CSE633 Parallel Algorithms Fall 2012 Ortega, Patricia Outline Problem definition Assumptions Implementation Test Results Future work Conclusions Problem

### Black-box Performance Models for Virtualized Web. Danilo Ardagna, Mara Tanelli, Marco Lovera, Li Zhang ardagna@elet.polimi.it

Black-box Performance Models for Virtualized Web Service Applications Danilo Ardagna, Mara Tanelli, Marco Lovera, Li Zhang ardagna@elet.polimi.it Reference scenario 2 Virtualization, proposed in early

### New Hash Function Construction for Textual and Geometric Data Retrieval

Latest Trends on Computers, Vol., pp.483-489, ISBN 978-96-474-3-4, ISSN 79-45, CSCC conference, Corfu, Greece, New Hash Function Construction for Textual and Geometric Data Retrieval Václav Skala, Jan

### Advanced Algebra 2. I. Equations and Inequalities

Advanced Algebra 2 I. Equations and Inequalities A. Real Numbers and Number Operations 6.A.5, 6.B.5, 7.C.5 1) Graph numbers on a number line 2) Order real numbers 3) Identify properties of real numbers

### Data Mining and Data Warehousing. Henryk Maciejewski. Data Mining Predictive modelling: regression

Data Mining and Data Warehousing Henryk Maciejewski Data Mining Predictive modelling: regression Algorithms for Predictive Modelling Contents Regression Classification Auxiliary topics: Estimation of prediction

### Data Science: An Action Plan for Expanding the Technical Areas of the Field of Statistics

Data Science: An Action Plan for Expanding the Technical Areas of the Field of Statistics William S. Cleveland Statistics Research, Bell Labs wsc@bell-labs.com Abstract An action plan to enlarge the technical

### Automatic online tuning for fast Gaussian summation

Automatic online tuning for fast Gaussian summation Vlad I. Morariu 1, Balaji V. Srinivasan 1, Vikas C. Raykar 2, Ramani Duraiswami 1, and Larry S. Davis 1 1 University of Maryland, College Park, MD 20742

### Operation Count; Numerical Linear Algebra

10 Operation Count; Numerical Linear Algebra 10.1 Introduction Many computations are limited simply by the sheer number of required additions, multiplications, or function evaluations. If floating-point

### PRIVACY-PRESERVING PUBLIC AUDITING FOR SECURE CLOUD STORAGE

PRIVACY-PRESERVING PUBLIC AUDITING FOR SECURE CLOUD STORAGE Abstract: Using Cloud Storage, users can remotely store their data and enjoy the on-demand high quality applications and services from a shared

### Package snpar. February 20, 2015

Package snpar February 20, 2015 Type Package Title Supplementary Non-parametric Statistics Methods Version 1.0 Date 2014-08-11 Author Debin Qiu Maintainer Debin Qiu contains several

### Communication Optimization and Auto Load Balancing in Parallel OSEM Algorithm for Fully 3-D SPECT Reconstruction

2005 IEEE Nuclear Science Symposium Conference Record M11-330 Communication Optimization and Auto Load Balancing in Parallel OSEM Algorithm for Fully 3-D SPECT Reconstruction Ma Tianyu, Zhou Rong, Jin

### Performance metrics for parallel systems

Performance metrics for parallel systems S.S. Kadam C-DAC, Pune sskadam@cdac.in C-DAC/SECG/2006 1 Purpose To determine best parallel algorithm Evaluate hardware platforms Examine the benefits from parallelism

### Moving Average Filters

CHAPTER 15 Moving Average Filters The moving average is the most common filter in DSP, mainly because it is the easiest digital filter to understand and use. In spite of its simplicity, the moving average

### Data Analysis. Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) SS Analysis of Experiments - Introduction

Data Analysis Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) Prof. Dr. Dr. h.c. Dieter Rombach Dr. Andreas Jedlitschka SS 2014 Analysis of Experiments - Introduction

### A Semi-parametric Approach for Decomposition of Absorption Spectra in the Presence of Unknown Components

A Semi-parametric Approach for Decomposition of Absorption Spectra in the Presence of Unknown Components Payman Sadegh 1,2, Henrik Aalborg Nielsen 1, and Henrik Madsen 1 Abstract Decomposition of absorption

### Scalable Data Analysis in R. Lee E. Edlefsen Chief Scientist UserR! 2011

Scalable Data Analysis in R Lee E. Edlefsen Chief Scientist UserR! 2011 1 Introduction Our ability to collect and store data has rapidly been outpacing our ability to analyze it We need scalable data analysis