Multivalue classifier from PRML chapter4

classifier.py

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from pandas import Series, DataFrame
from numpy.random import randint, randn, rand, multivariate_normal

K = 3    # Number of classes (2 or 3)
N = 50   # Number of training data
HR = 200 # Heatmap resolution

def classify(x1, x2, W_t):
    ys = np.dot(W_t, np.array([1,x1,x2]))
    cls = np.argmax(ys) + 1
    yval = ys[cls - 1]
    markers = [0.5, 1.0]
    delta = 0.01
    for p in markers:
        if np.abs(yval - p) < delta:
            return 0
    return cls

def prep_data():
    mean1 = [-2, 2]
    mean2 = [0, 0]
    mean3 = [2, -2]
    cov = [[1.0,0.8], [0.8,1.0]]

    df1 = DataFrame(multivariate_normal(mean1, cov, N), columns=['x1','x2'])
    df2 = DataFrame(multivariate_normal(mean2, cov, N), columns=['x1','x2'])
    df3 = DataFrame(multivariate_normal(mean3, cov, N), columns=['x1','x2'])
    df1['x0'] = df2['x0'] = df3['x0'] = 1
    (df1['cls'], df2['cls'], df3['cls']) = (1, 2, 3)

    if K == 2:
        df = pd.concat([df1,df2], ignore_index=True)
    if K == 3:
        df = pd.concat([df1,df2,df3], ignore_index=True)

    return df


def solve(df):
    X = df[['x0','x1','x2']]
    T = DataFrame(np.zeros(shape=(len(df),K)), columns=range(1,K+1))
    for index, point in df.iterrows():
        c = point.cls
        T.ix[index,c] = 1

    temp = np.linalg.inv(np.dot(X.T, X))
    W = np.dot(np.dot(temp, X.T), T)
    
    return W.T
    

if __name__ == "__main__":
    fig = plt.figure()
    ax = fig.add_subplot(111)

    df = prep_data()
    W_t = solve(df)

    X = Y = np.linspace(-6,6,HR)
    field = DataFrame(np.zeros(shape=(len(X),len(Y))))
    for x, xval in enumerate(X):
        for y, yval in enumerate(Y):
            field.ix[y,x] = classify(xval,yval,W_t)

    xim = ax.imshow(field.values, extent=(-6,6,6,-6), vmin=0, vmax=3,
                    alpha=0.2)

    cls1 = df[df['cls']==1][['x1','x2']]
    cls2 = df[df['cls']==2][['x1','x2']]
    cls3 = df[df['cls']==3][['x1','x2']]
    ax.scatter(cls1.x1, cls1.x2, color='blue', marker='x')
    ax.scatter(cls2.x1, cls2.x2, color='orange', marker='o')
    ax.scatter(cls3.x1, cls3.x2, color='red', marker='+')

    ax.set_xlim(-6,6)
    ax.set_ylim(-6,6)

    fig.show()