Distances and Angles between Images¶

# PACKAGE: DO NOT EDIT THIS CELL
import numpy as np
import scipy

import matplotlib as mpl
import matplotlib.pyplot as plt
import sklearn
from ipywidgets import interact
from load_data import load_mnist

# Plot figures so that they can be shown in the notebook
%matplotlib inline
%config InlineBackend.figure_format = 'svg'

from load_data import load_mnist
MNIST = load_mnist('./')
images = MNIST['data'].astype(np.double)
labels = MNIST['target'].astype(np.int)

# GRADED FUNCTION: DO NOT EDIT THIS LINE

def distance(x0, x1):
    """Compute distance between two vectors x0, x1 using the dot product.
    
    Args:
    x0, x1: ndarray of shape (D,) to compute distance between. 
    
    Returns:
    the distance between the x0 and x1.
    """
    # YOUR CODE HERE
    ### Uncomment and modify the code below
    distance = np.dot(x1-x0,x1-x0)**(0.5) # <-- EDIT THIS to compute the distance between x0 and x1
    return distance

# Some sanity checks, you may want to have more interesting test cases to test your implementation
a = np.array([1, 0])
b = np.array([0, 1])
np.testing.assert_allclose(distance(a, b), np.sqrt(2), rtol=1e-7)

a = np.array([1, 0])
b = np.array([1., np.sqrt(3)])
np.testing.assert_allclose(distance(a, b), np.sqrt(3), rtol=1e-7)

# Some hidden tests below
### ...

# GRADED FUNCTION: DO NOT EDIT THIS LINE

def angle(x0, x1):
    """Compute the angle between two vectors x0, x1 using the dot product.
    
    Args:
    x0, x1: ndarray of shape (D,) to compute the angle between. 
    
    Returns:
    the angle between the x0 and x1.
    """
    # YOUR CODE HERE
    ### Uncomment and modify the code below
    angle = np.arccos((np.dot(x0,x1)/(np.dot(x0,x0)*np.dot(x1,x1))**(0.5))) # <-- EDIT THIS to compute angle between x0 and x1
    return angle

# Some sanity checks, you may want to have more interesting test cases to test your implementation
a = np.array([1, 0])
b = np.array([0, 1])
np.testing.assert_allclose(angle(a,b) / (np.pi * 2) * 360., 90)

a = np.array([1, 0])
b = np.array([1., np.sqrt(3)])
np.testing.assert_allclose(angle(a,b) / (np.pi * 2) * 360., 60., rtol=1e-4)

# Some hidden tests below

def plot_vector(v, w):
    """Plot two 2D vectors."""
    fig = plt.figure(figsize=(4,4))
    ax = fig.gca()
    plt.xlim([-2, 2])
    plt.ylim([-2, 2])
    plt.grid()
    ax.arrow(0, 0, v[0], v[1], head_width=0.05, head_length=0.1, 
             length_includes_head=True, linewidth=2, color='r');
    ax.arrow(0, 0, w[0], w[1], head_width=0.05, head_length=0.1, 
             length_includes_head=True, linewidth=2, color='r');

# Tests symmetry
random = np.random.RandomState(42)
x = random.randn(3)
y = random.randn(3)
for _ in range(10):
    np.testing.assert_allclose(distance(x,y), distance(y,x))
    np.testing.assert_allclose(angle(x,y), angle(y,x), rtol=1e-4)

distances = []
for i in range(len(images[:500])):
    for j in range(len(images[:500])):
        distances.append(distance(images[i], images[j]))

# GRADED FUNCTION: DO NOT EDIT THIS LINE

def most_similar_image():
    """Find the index of the digit, among all MNIST digits (excluding the first),
       that is the closest to the first image in the dataset, your answer should be a single integer
    """
    # YOUR CODE HERE
    idx = 1
    return idx

### Some hidden tests below

mean_images = {}
for n in np.unique(labels):
    mean_images[n] = np.mean(images[labels==n], axis=0)

MD = np.zeros((10, 10))
AG = np.zeros((10, 10))
for i in mean_images.keys():
    for j in mean_images.keys():
        MD[i, j] = distance(mean_images[i], mean_images[j])
        AG[i, j] = angle(mean_images[i].ravel(), mean_images[j].ravel())