#Loading Modules

import numpy as np

import mlpy

import matplotlib.pyplot as plt # required for plotting

#Loading Dataset

iris = np.loadtxt('iris.csv', delimiter=',')

x, y = iris[:, :4], iris[:, 4].astype(np.int) # x: (observations x attributes) matrix, y: classes (1: setosa, 2: versicolor, 3: virginica)

x.shape

y.shape

#Dimensionality reduction by Principal Component Analysis (PCA)

pca = mlpy.PCA() # new PCA instance

pca.learn(x) # learn from data

z = pca.transform(x, k=2) # embed x into the k=2 dimensional subspace

z.shape

#Plot the principal components:

plt.set_cmap(plt.cm.Paired)

fig1 = plt.figure(1)

title = plt.title("PCA on iris dataset")

plot = plt.scatter(z[:, 0], z[:, 1], c=y)

labx = plt.xlabel("First component")

laby = plt.ylabel("Second component")

plt.show()

#Learning by Kernel Support Vector Machines (SVMs) on principal components:

linear_svm = mlpy.LibSvm(kernel_type='linear') # new linear SVM instance

linear_svm.learn(z, y) # learn from principal components

#For plotting purposes, we build the grid where we will compute the predictions (zgrid):

xmin, xmax = z[:,0].min()-0.1, z[:,0].max()+0.1

ymin, ymax = z[:,1].min()-0.1, z[:,1].max()+0.1

xx, yy = np.meshgrid(np.arange(xmin, xmax, 0.01), np.arange(ymin, ymax, 0.01))

zgrid = np.c_[xx.ravel(), yy.ravel()]

#Now we perform the predictions on the grid. The pred() method returns the prediction for each point in zgrid:

yp = linear_svm.pred(zgrid)

#Plot the predictions:

plt.set_cmap(plt.cm.Paired)

fig2 = plt.figure(2)

title = plt.title("SVM (linear kernel) on principal components")

plot1 = plt.pcolormesh(xx, yy, yp.reshape(xx.shape))

plot2 = plt.scatter(z[:, 0], z[:, 1], c=y)

labx = plt.xlabel("First component")

laby = plt.ylabel("Second component")

limx = plt.xlim(xmin, xmax)

limy = plt.ylim(ymin, ymax)

plt.show()