Showing papers by "Jerome H. Friedman published in 1974"

A Projection Pursuit Algorithm for Exploratory Data Analysis

Abstract: An algorithm for the analysis of multivariate data is presented and is discussed in terms of specific examples. The algorithm seeks to find one-and two-dimensional linear projections of multivariate data that are relatively highly revealing.

Measurement of multivariate scaling and factorization in exclusive multiparticle production

Abstract: Several new model independent techniques for the analysis of multidimensional data are presented and applied to exclusive multiparticle production. For the reaction pp-+pprr'n+~c-~from 12 to 28 GeV/c, an algorithm that directly compares two multidimensional point distributions is used to show that the shape of d120/d($?)12 is energy independent while d60/dx6 (x=p,,/pmax) varies dramatically with beam energy. A multidimensional test for independence is used to show that the multivariate differential cross-section approximately factors into its cylindrical momentum components, d180/d(a18 r d%/dp;, ' d60/d(p12+ * d60/d$. The shape of d60/dcp6 i 6 also shown to be compatible with that predicted solely by kinematics. (Submitted to The Physical Review) *Work supported by the U.S. Atomic Energy Commission. Multiparticle production presents a difficult problem in data analysis due to the large number of independent observables necessary to completely describe the data. Excluding spin information, an n-particle final state requires jn-4 independent measurables for a complete description. The normalized multivariate differential cross section can be thought of as a probability density function in the chosen measurables, x x 1 2 ' l ‘X3n-4’ defined over their physically allowed values. Each event can be represented as a point in the multidimensional space . whose coordinates are the measurables of the event. This point contains all the information in the event and, thus, the collection or swarm of experimental points in this space contains all the information from the experiment. The purpose of data analysis is to infer the properties of the unknown probability density function (p.d.f.) from the experimental point sample in the multidimensional space. For exclusive experiments where all 3n-4 independent observables are measured, this p.d.f. is directly related to the transition matrix element squared for the reaction. This report describes the results of applying several newly developed nonparametric (model independent) techniques for investigating the properties of multidimensional point swarms 1,2 to the reaction pp+pp~+~+~r-lrfrom from 12 to 28 GeV/c.3 An algorithm that directly compares the shapes of two multidimensional point distributions is used to study the energy dependence of the multivariate differential cross-section, while a multivariate independence test is used to study its factorization properties.