Andrew's Curves for high dimensional multi-variate data

andrew-curves.py

#!/usr/bin/env
# -*- coding: utf-8 -*-

from math import ceil, sqrt, pi

import pylab
import numpy as np
import pandas as pd
from sklearn import datasets

# -------------------------------------------------

def andrews_curves(M, m=100):
    # validating samples data
    if not isinstance(M, np.ndarray):
        raise ValueError('Unsupported format for samples.')

    # validating data dimensions
    if not 1 <= len(M.shape) <= 2:
        raise ValueError("Only data vectors (1D) and collections of data vectors (2D) arrays supported")

    # getting data vectors
    X = np.reshape(M, (1, -1)) if len(M.shape) == 1 else M.copy()

    # getting the rows and the amount
    rows, n = X.shape

    # andrew curve dimension (a.k.a, amount theta angles)
    t = np.linspace(-pi, pi, m)

    # matrix Amxn:
    # m: range of values for angle 'theta'
    # n: amount of components for the Fourier function
    A = np.empty((m, n))

    # setting first column of A
    A[:, 0] = [1.0 / sqrt(2.0)] * m

    # filling columns of A
    for i in range(1, n):
        # computing the scaling coefficient for angle 'theta'
        c = ceil(i / 2)

        # computing i-th column of matrix A
        col = np.sin(c * t) if i % 2 == 1 else np.cos(c * t)

        # setting column in matrix A
        A[:, i] = col[:]

    # computing Andrew's Curves for provided data
    andrew_curves = np.dot(A, X.T).T

    # returning the Andrew's Curves (raveling if needed)
    return np.ravel(andrew_curves) if andrew_curves.shape[0] == 1 else andrew_curves

# -------------------------------------------------

# loading iris data set
iris = datasets.load_iris()
X = iris.data
Y = iris.target

# building data frame with Andrew's Curves of iris samples
df = pd.DataFrame(andrews_curves(X))
df['class'] = Y

# plotting the 3 classes
ax = df[df['class'] == 0].iloc[:, :-1].T.plot(color='b', legend=None)
df[df['class'] == 1].iloc[:, :-1].T.plot(ax=ax, color='g', legend=None)
df[df['class'] == 2].iloc[:, :-1].T.plot(ax=ax, color='r', legend=None)

# showing plot
pylab.show()