Package cepp. R topics documented: December 22, 2014

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1 Package cepp December 22, 2014 Type Package Title Context Driven Exploratory Projection Pursuit Version 1.0 Date Author Mohit Dayal Maintainer Mohit Dayal Functions and Data to support context epp. Depends R (>= 2.10), trust, randtoolbox Suggests tourr License GPL-3 Repository CRAN Date/Publication :00:21 NeedsCompilation no R topics documented: cepp-package ALPHA bases Colon evaluator geodesic Olive oil measurements penorms pp Index 11 1

2 2 ALPHA cepp-package Context Driven Exploratory Projection Pursuit. Functions and Data for Context-driven Exploratory Projection Pursuit. Package: cepp Type: Package Version: 1.0 Date: License: GPL - 3 Mohit Dayal Maintainer: Mohit Dayal <mohitdayal2000@gmail.com> ALPHA Global variables These variables need to be initialized for some of the methods to work. METHOD ALPHA These global variables are automatically initialized when the package is loaded. The variables METHOD and ALPHA are used by the basis_nearby function and are useful only if you want to optimize the index via simulated annealing. ALPHA can be set to any number in (0,1), with smaller values implying a more localized search. By default set to The METHOD variable controls how a new basis is created from an old one and can be set to either one of the strings "linear" or "geodesic". You should set it to geodesic if your index is rotationally invariant. Default value is geodesic.

3 bases 3 References E.K. Lee, D. Cook, S. Klinke, and T. Lumley. Projection pursuit for exploratory supervised classification. Journal of Computational and Graphical Statistics, 14(4): , 2005 bases Create random bases Generate bases. basis_random(n, d = 2) basis_nearby(current, alpha = ALPHA, method = METHOD) Arguments n d current alpha method The number of rows. The number of columns. The current matrix. How "far" should the new matrix be? How should be new matrix be found? One of linear or geodesic. basis_random returns a new orthonormal matrix of specified dimensions. basis_nearby generates a new orthonormal matrix, hybridizes it with the current matrix and returns it. A matrix of specified dimensions. Taken from the tourr package See Also ALPHA, METHOD

4 4 Colon Colon Gene expression data from Alon et al. (1999) Gene expression data (2000 genes for 62 samples) from the microarray experiments of Colon tissue samples of Alon et al. (1999). data(colon) This data set contains 62 samples with 2000 genes: 40 tumor tissues, coded 2 and 22 normal tissues, coded 1. A list with the following elements: X Y gene.names a (62 x 2000) matrix giving the expression levels of 2000 genes for the 62 Colon tissue samples. Each row corresponds to a patient, each column to a gene. a numeric vector of length 62 giving the type of tissue sample (tumor or normal). a vector containing the names of the 2000 genes for the gene expression matrix X. Source The data are described in Alon et al. (1999) and can be freely downloaded from princeton.edu/oncology/affydata/index.html. References Alon, U. and Barkai, N. and Notterman, D.A. and Gish, K. and Ybarra, S. and Mack, D. and Levine, A.J. (1999). Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays, Proc. Natl. Acad. Sci. USA,96(12), Examples # how many samples and how many genes? data(colon) dim(colon$x) norm <- Colon$X[Colon$Y == 1,] tumor <- Colon$X[Colon$Y == 2,] gene1 <- pp.2(r=2,n=50,oth=tumor,data=norm) F1 <- basis_random(2000) t1 <- caller(start=f1,index=gene1,n=rep(3,5),bases=5)

5 evaluator 5 evaluator Functions to evaluate spatial quantiles These are objective functions whose minimization yields the spatial quantiles. evaluator.2(samp) evaluator.3(samp) Arguments samp The data for which quantiles are required. Either function returns another function suitable for passing to an optimizer like nlm or trust. A function that should be passed to an optimizer. Mohit Dayal References P. Chaudhuri. On a geometric notion of quantiles for multivariate data. Journal of the American Statistical Association, 91(434): , Examples x <- rnorm(500) dim(x) <- c(250,2) ev <- evaluator.2(x) ##The Spatial Median trust(ev,parinit=c(median(x[1,]),median(x[2,])),u=c(0,0),rinit=0.5,rmax=2e5) ##Quantile for vector (0.2,0.3) trust(ev,parinit=c(median(x[1,]),median(x[2,])),u=c(0.2,0.3),rinit=0.5,rmax=2e5)

6 6 geodesic geodesic Functions for geodesic search These functions are for a geodesic search. search_geodesic(current, alpha = 1, index, max.tries = 5, n = 5) caller(start,index,n,bases) Arguments current, start The starting projection. alpha index max.tries n bases Maximum distance to travel (currently ignored). The projection index. Maximum number of failed attempts before giving up. Number of random steps to take to find best direction. Can be a vector for caller. Total number of bases to find. The function search_geodesic finds only one basis at a time. The caller is a wrapper function that calls search_geodesic bases number of times. search_geodesic returns the basis found. caller returns a list of bases. The list may be shorter than specified if no better bases can be found. The function has been copied as is from the tourr package.

7 Olive oil measurements 7 Olive oil measurements Olive oil samples from Italy This data is from a paper by Forina, Armanino, Lanteri, Tiscornia (1983) Classification of Olive Oils from their Fatty Acid Composition, in Martens and Russwurm (ed) Food Research and Data Anlysis. We thank Prof. Michele Forina, University of Genova, Italy for making this dataset available. region Three super-classes of Italy: North, South and the island of Sardinia area Nine collection areas: three from North, four from South and 2 from Sardinia palmitic, palmitoleic, stearic, oleic, linoleic, linolenic, arachidic, eicosenoic fatty acids percent x 100 data(olive) Format A 572 x 10 numeric array Examples data(olive) head(olive) ##Permutation OlivesT <- as.matrix(olive[,-c(1:2)]) OlivesF <- OlivesT #You should set.seed here so as to "fix" the benchmark OlivesF[, palmitic ] <- OlivesF[sample(572,572), palmitic ] OlivesF[, palmitoleic ] <- OlivesF[sample(572,572), palmitoleic ] OlivesF[, stearic ] <- OlivesF[sample(572,572), stearic ] OlivesF[, oleic ] <- OlivesF[sample(572,572), oleic ] OlivesF[, linoleic ] <- OlivesF[sample(572,572), linoleic ] OlivesF[, linolenic ] <- OlivesF[sample(572,572), linolenic ] OlivesF[, arachidic ] <- OlivesF[sample(572,572), arachidic ] OlivesF[, eicosenoic ] <- OlivesF[sample(572,572), eicosenoic ] ## oil1 <- pp.2(r=2,n=50,oth=olivesf,data=olivest) ##In practice try at least >10 starting values F1 <- basis_random(8) ##Increase iterations to >2000 for useful results o1 <- optim(par=f1, fn=oil1,gr=basis_nearby,method= SANN,control=list(fnscale=-1,maxit=50,trace=6))

8 8 penorms penorms Parallelized functions for different norms These functions compute the L-1, L-2 and L-infinity norms for 2 and 3 dimensional vectors. These functions are parallelized, that is you can pass several vectors at once. penorm21(x, y) penorm2infi(x, y) penorm2(x, y) penorms2(x, y) penorm31(x, y, z) penorm3infi(x, y, z) penorm3(x, y, z) penorms3(x, y, z) Arguments x y z The vector of the first coordinates. The vector of the second coordinates. The vector of the third coordinates. The functions penorm21 and penorm31 return the L-1 norm for 2 and 3 dimensional vectors. The functions penorm2infi and penorm3infi return the L-infinity norm for 2 and 3 dimensional vectors. The functions penorm2 and penorm3 return the squared L-2 norms for 2 and 3 dimensional vectors. The functions penorms2 and penorms3 return the L-2 norms for 2 and 3 dimensional vectors. A vector of norms. Mohit Dayal Examples ##Compute the L-2 norm of vectors (1,3) and (2,5) ##penorms2(c(1,2),c(3,5))

9 pp 9 pp Creates the projection pursuit function. These functions encapsulate everything, that is, the data, the benchmark and the index parameters, needed to compute the projection index. pp.2(r = 1, n, data, oth,given_norm=penorms2) pp.3(r = 1, n, data, oth,given_norm=penorms3) Arguments r n data oth given_norm The radius multiplier. s between 0.5 and 3 seem to work well. Number of Monte-Carlo Evaluations to approximate the integral. s as low as 25 can be used. The data for which structure needs to be found. The benchmark dataset. Determines how the norm of the integrand is computed. By default, set to the L2 norm (penorms2 for 2-D projections and penorms3 for 3-D projections) You may set it any other norm function. Note that even ordered norms are rotationally invariant. pp.2 is for 2-D projection pursuit, while pp.3 is for 3-D projection pursuit. The actual index function, which takes a single matrix argument, and returns the index value for that projection. Mohit Dayal Examples ##Exploring structure in the RANDU data ##Or using the MINSTD generator randu <- as.matrix(randu) setseed(570) w <- congrurand(1200) dim(w) <- c(3,400)

10 10 pp w <- t(w) m <- geodesic a < ranif1 <- pp.2(r=1,n=50,data=randu,oth=w) set.seed(50) F1 <- basis_random(3) o1 <- optim(par=f1,fn=ranif1,gr=basis_nearby,method= SANN,control=list(fnscale=-1,maxit=200,trace=1)) plot(randu %*% o1$par) ##How accurate are the values? ranif1hi <- pp.2(r=1,n=500,data=randu,oth=w) ranif1hi(o1$par)

11 Index Topic datasets Colon, 4 Olive oil measurements, 7 Topic projection pursuit cepp-package, 2 ALPHA, 2, 3 bases, 3 basis_nearby (bases), 3 basis_random (bases), 3 caller (geodesic), 6 cepp (cepp-package), 2 cepp-package, 2 Colon, 4 evaluator, 5 geodesic, 6 METHOD, 3 METHOD (ALPHA), 2 olive (Olive oil measurements), 7 Olive oil measurements, 7 penorm2 (penorms), 8 penorm21 (penorms), 8 penorm2infi (penorms), 8 penorm3 (penorms), 8 penorm31 (penorms), 8 penorm3infi (penorms), 8 penorms, 8 penorms2 (penorms), 8 penorms3 (penorms), 8 pp, 9 search_geodesic (geodesic), 6 11