It has been shown the Andrews curves are able to preserve means, distance (up to a constant) and variances. Which means that Andrews curves that are represented by functions close together suggest that the corresponding data points will also be close together. Now, we will demonstrate the effectiveness of the Andrew curves on the iris dataset (which we already used here). Let's create a function to compute the values of the functions give a single sample:
import numpy as np def andrew_curve4(x,theta): # iris has 4 four dimensions base_functions = [lambda x : x/np.sqrt(2.), lambda x : x*np.sin(theta), lambda x : x*np.cos(theta), lambda x : x*np.sin(2.*theta)] curve = np.zeros(len(theta)) for f in base_functions: curve = curve + f(x) return curveAt this point we can load the dataset and plot the curves for a subset of samples:
samples = np.loadtxt('iris.csv', usecols=[0,1,2,3], delimiter=',') #samples = samples - np.mean(samples) #samples = samples / np.std(samples) classes = np.loadtxt('iris.csv', usecols=, delimiter=',',dtype=np.str) theta = np.linspace(-np.pi,np.pi,100) import pylab as pl for s in samples[:20]: # setosa pl.plot(theta, andrew_curve4(s,theta), 'r') for s in samples[50:70]: # versicolor pl.plot(theta, andrew_curve4(s,theta), 'b') for s in samples[100:120]: # virginica pl.plot(theta, andrew_curve4(s,theta), 'g') pl.xlim(-np.pi,np.pi) pl.show()
In the plot above, the each color used represents a class and we can easily note that the lines that represent samples from the same class have similar curves.