LAB 06.02 - NMF face search

!wget --no-cache -O init.py -q https://raw.githubusercontent.com/fagonzalezo/ai4eng-unal/main/content/init.py
import init; init.init(force_download=False); init.get_weblink()

from local.lib.rlxmoocapi import submit, session
session.LoginSequence(endpoint=init.endpoint, course_id=init.course_id, lab_id="L06.02", varname="student");

Dataset

we will use the faces dataset

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from IPython.display import Image
%matplotlib inline

import numpy as np
faces = np.load("local/data/faces.npy")
faces.shape

(535, 361)

def plot_faces(faces):
    assert len(faces)<=30, "can only plot at most 30 faces"
    plt.figure(figsize=(15,2))
    for i in range(len(faces)):
        plt.subplot(2,15,i+1)
        plt.imshow(faces[i].reshape(19,19), cmap=plt.cm.Greys_r)
        plt.xticks([]); plt.yticks([])

plot_faces(np.random.permutation(faces)[:30])

Task 1: Distance function for a vector

complete the following function so that given a vector \(v \in \mathbb{R}^n\) and a numpy array \(X \in \mathbb{R}^{m\times n}\) (whose rows are vectors of the same size as \(v\)) returns a new array \(\in \mathbb{R}^m\) with the Euclidean distance between \(v\) and each vector in \(X\).

Recall that the Euclidean distance between vectors \(z=[z_0,...z_{n-1}]\) and \(w=[w_0,...,w_{n-1}]\) is given by

\[\text{distance}(z,w) = \sqrt{\sum_{i=0}^{n-1} (z_i-w_i)^2}\]

hint: use np.linalg.norm to compute a distance between two vectors

challenge: solve it using one line of code.

note: your function must return a 1D numpy array of dimension \(m\), not a list.

for instance, for the following values of \(v\) and \(X\)

X = array([[9, 5, 1, 3, 8, 3, 3, 3, 9, 2],
           [9, 7, 0, 7, 9, 1, 4, 7, 3, 6],
           [8, 0, 0, 5, 0, 5, 5, 1, 1, 5],
           [8, 2, 9, 5, 6, 0, 8, 7, 2, 8],
           [0, 6, 3, 0, 6, 6, 1, 2, 8, 0]])
              
v = np.array([9, 7, 0, 7, 9, 1, 4, 7, 3, 6])

you should get the following result

array([ 9.74679434,  0.        , 13.89244399, 11.91637529, 16.40121947])

def distances(v, X):
    result = .... # your code here
    return result

check manually your code

X = np.random.randint(10, size=(5,10))
v = X[1]

print ("X=\n", X)
print ("\nv=", v)
distances(v, X)

submit your code

student.submit_task(globals(), task_id="task_01");

Task 2: Positions of closest vectors

complete the following function so that given \(v\) and \(X\) as previously, returns the positions of the \(n\) closest vectors to \(v\) in \(X\).

hint: use the np.argsort function

challenge: solve it using one line of code

for the example \(v\) and \(X\) above you should get the following outputs

>> closest(v, X, 2)
array([1, 0])

>> closest(v, X, 3)
array([1, 0, 3])

def closest(v, X, n):
    assert n<len(X), "n must at most the number of vectors in X"
    result = .... # your code here
    return result

check manually your code

X = np.random.randint(10, size=(5,10))
v = X[1]

print ("X=\n", X)
print ("\nv=", v,"\n\n")
print (closest(v, X, 2))
print (closest(v, X, 3))

observe now how we can use your functions to search for faces similar to any other face

plt.figure(figsize=(1,1))
fi = 314 # np.random.randint(len(faces)) # 314 
face = faces[fi]
plt.imshow(faces[fi].reshape(19,19), cmap=plt.cm.Greys_r)
print ("TARGET FACE")

TARGET FACE

plot_faces(faces[closest(face, faces, 30)])
print ("SIMILAR FACES")

SIMILAR FACES

But they do not look so similar, this is because we are doing comparison pixel by pixel. We will fix this in the next task

submit your code

student.submit_task(globals(), task_id="task_02");

Task 3: Use NMF to find similar faces

Make the comparison in the faces space resulting from transforming them using NMF. For this you have to:

• create an instance of NMF with n_components=30, init="random", random_state=0

• fit the instance with \(X\)

• transform \(X\)

• transform \(v\)

• return the positions of closest \(n\) vectors in the transformed \(X\) to the transformed \(v\)

For the target face above, you should get the following

from IPython.display import Image
Image(filename='local/imgs/similar-images2.png')

def find_similar(v,X,n):
    from sklearn.decomposition import NMF
    
    nmf = NMF(n_components=30, init="random", random_state=0)
    nmf... ## your code here. call the 'fit' method
    Xt = ... # use nmf to transform X
    vt = ... # use nmf to transform v .. you will have to use reshape like this v.reshape(1,-1)
    
    result = ... # your code here
    
    return result

check manually your answer

plot_faces(faces[find_similar(face, faces, 30)])

submit your code

student.submit_task(globals(), task_id="task_03");