From 1de33808dc09ec1b9827f47f9229c917306d165f Mon Sep 17 00:00:00 2001
From: Patrik <N3uroSt4t@users.noreply.github.com>
Date: Tue, 1 Dec 2015 14:17:20 +0100
Subject: [PATCH] Create README.md

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+
+[<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/banner.png" alt="Visit QuantNet">](http://quantlet.de/index.php?p=info)
+
+## [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/qloqo.png" alt="Visit QuantNet">](http://quantlet.de/) **SMSsvmspiral** [<img src="https://github.com/QuantLet/Styleguide-and-Validation-procedure/blob/master/pictures/QN2.png" width="60" alt="Visit QuantNet 2.0">](http://quantlet.de/d3/ia)
+
+
+```yaml
+Name of Quantlet: SMSsvmspiral
+
+Published in: Multivariate Statistics: Exercises and Solutions
+
+Description: 'plots the area of two different groups via svm classification using anipotropic Gaussian kernel for artificial spiral data'
+
+Keywords: 'support vector machines, svm, classification, kde, kernel density estimation, anisotropic kernel, kernel'
+
+See also: 'SMScartdiag, SMScartsq, SMSdisfbank2, SMSeppbank, SMSsimpdbank, SMSsimpdsimu, SMSsir2cars, SMSsir2simu, SMSsircars, SMSsirsimu, SMSsircars, SMSsirsimu, SMSsiruscomp, SMSsvmbankrupt, SMSsvmorange, SMSsvmspiral'
+
+Author: Wolfgang Härdle, Dedy Dwi Prastyo, Awdesch Melzer
+
+Example: '2-dim plot of a svm classification for spiral data using anisotropic Gaussian kernel.'
+```
+
+
+![Picture1](SMSsvmspiral01_r.png)
+![Picture1](SMSsvmspiral02_r.png)
+![Picture1](SMSsvmspiral03_r.png)
+![Picture1](SMSsvmspiral04_r.png)
+
+
+```R
+# clear history, close windows
+rm(list=ls(all=TRUE))
+graphics.off()
+
+
+# install and load packages
+libraries = c("kernlab","tseries","quadprog","zoo")
+lapply(libraries, function(x) if (!(x %in% installed.packages())) {
+    install.packages(x)})
+lapply(libraries, library, quietly = TRUE, character.only = TRUE)  
+
+set.seed(1)
+# Generating spiral data
+
+tetha = seq(length=100, from=0, to=3)
+
+a     = 1
+b     = 0.5 	 # b is near to zero, spiral approaches a circle
+
+r     = a*exp(b*tetha)
+
+# X(+1) members of first group, centering in (c1p,c2p)
+
+c1p   = 0
+c2p   = 0
+
+X1p   = c1p + r*cos(tetha*pi)
+X2p   = c2p + r*sin(tetha*pi)
+
+# X(-1) members of second group, centering in (c1n,c2n)
+
+c1n   = 1
+c2n   = 0
+
+X1n   = 1 - (c1n + r*cos(tetha*pi))
+X2n   = - (c2n + r*sin(tetha*pi))
+
+# Agregating data
+
+X1    = c(X1p, X1n)
+X2    = c(X2p, X2n)
+
+# generating indicator variable
+
+yp    = array(1:100, dim=c(100,1))
+yn    = array(1:100, dim=c(100,1))
+
+
+for (i in 1:100){ 
+	yp[i] = 1
+	yn[i] = -1
+}
+
+Y     = c(yp,yn)
+
+# Generating noise, N(0,0.01)
+
+e     = rnorm(200, mean = 0, sd = 0.1)
+
+X1    = X1 + e
+X2    = X2 + e
+
+Spiral.noise = cbind(X2, X1)
+
+# --------------------------------------------------------------------------
+
+
+# Main program for SVM classification plot
+# read simulated data
+  
+sgm = c(0.2,8,0.2,8)   
+C = c(0.1,0.1,8,8)
+
+for (i in 1:4){
+ 
+  SpiralModel = ksvm(Spiral.noise, Y, type="C-svc", kernel="rbfdot", kpar=list(sigma=sgm[i]), C=C[i], prob.model=TRUE, cross=4)
+  str = paste("s=",sprintf("%0.1f",sgm[i]),", c=",sprintf("%0.1f",C[i]),"                          ",sep="")
+  plot(SpiralModel, data=Spiral.noise,cex=0.7,cex.main=1.5)
+  title(sub=str)
+  print(SpiralModel)
+}
+
+
+
+```