Data file used in the example: https://file.io/86F7M1iYqVUt
Question
Using the multivariate data in the file fld1.xlsx:
(a) determine the discriminant line found by Fishers Linear Discriminant.
(b) Plot both the data and the discriminant line on a scatter plot
(c) Using this line, determine the class of each of the data points in the dataset, assuming that the
threshold is 0 (i.e. positive values are in one class and negative values in the other).
(d) Determine what percentage of data points are incorrectly classified.
NOTE: The first 2 columns in fld1.xlsx are data columns. The third column is the class to which each data
point belongs.
Python Implementation
import pandas as pd
import numpy as np
import matplotlib.pyplot
fld1 = pd.read_excel("fld1.xlsx", header=None)
fld1_np = pd.DataFrame.to_numpy(fld1)
output_arr = fld1_np[:,2]
fld1_np_1 = pd.DataFrame.to_numpy(fld1.head(300))
fld1_np_0 = pd.DataFrame.to_numpy(fld1.tail(200))
fld1_class_1 = fld1_np_1[:, :2]
fld1_class_0 = fld1_np_0[:, :2]
data_X = np.concatenate((fld1_class_1,fld1_class_0))
matplotlib.pyplot.figure()
matplotlib.pyplot.scatter(fld1_class_1[:,0], fld1_class_1[:,1], c = 'r', marker = '.')
matplotlib.pyplot.scatter(fld1_class_0[:,0], fld1_class_0[:,1], c = 'b', marker = '.')
class1_mean = np.mean(fld1_class_1,axis = 0)
class0_mean = np.mean(fld1_class_0,axis = 0)
class1_mc = fld1_class_1 - class1_mean
class0_mc = fld1_class_0 - class0_mean
class1_cov = np.dot(class1_mc.T, class1_mc)
class0_cov = np.dot(class0_mc.T, class0_mc)
Sw = class1_cov + class0_cov
w = np.dot(np.linalg.inv(Sw),(class1_mean - class0_mean))
print("Fisher's Linear Discriminant point is: \n",w)
print(w[0])
print(w[1])
matplotlib.pyplot.axline((0,0),w,c='black',linestyle='--')
thresh = 0
slope_1 = -w[0]/w[1]
y_intercept = thresh/w[1]
print("y-intercept is ", y_intercept)
matplotlib.pyplot.axline((0,y_intercept),slope = slope_1,c='green',linestyle='--')
prediction = (np.sign(np.dot(w,data_X.T) + thresh) + 1)/2
error = np.sum(abs(prediction - output_arr))
print("\nnumber of errors = ",error)
print("\npercentage of errors = ",(error/500)*100,"%")
matplotlib.pyplot.show()
