Numerical Computing with Python

Curse of dimensionality with 1D, 2D, and 3D example

A quick analysis has been done to see how distance 60 random points are expanding with the increase in dimensionality. Initially, random points are drawn for one-dimension:

# 1-Dimension Plot 
>>> import numpy as np 
>>> import pandas as pd 
>>> import matplotlib.pyplot as plt 
 
>>> one_d_data = np.random.rand(60,1) 
>>> one_d_data_df = pd.DataFrame(one_d_data) 
>>> one_d_data_df.columns = ["1D_Data"] 
>>> one_d_data_df["height"] = 1 
 
>>> plt.figure() 
>>> plt.scatter(one_d_data_df['1D_Data'],one_d_data_df["height"]) 
>>> plt.yticks([]) 
>>> plt.xlabel("1-D points") 
>>> plt.show()

If we observe the following graph, all 60 data points are very nearby in one-dimension:

Here we are repeating the same ...