# version code 7927bee20c8d+
# Please fill out this stencil and submit using the provided submission script.
import time # for timing
from mnist_loader import load_data
import power_svd
from matutil import *
import random
from Orthogonalization_problems.py import orthonormalize
## 1: () Squared Distance
def sq_dist(u, v):
'''
Input:
- u, v: two Vecs with the same domain
Output:
- the square of the Euclidean distance between u and v
Example:
>>> u = list2vec([1, 2])
>>> v = list2vec([2, 3])
>>> sq_dist(u, v)
2
'''
pass
## 2: () Nearest Neighbor
def nn(u, veclist):
'''
Input:
- u: a Vec
- veclist: a list of Vecs
Output:
- The index of the vector in veclist nearest to u
Example:
>>> from vecutil import list2vec
>>> nn(list2vec([1,2]), [list2vec(l) for l in [[2,5],[1,3],[1.5,2]]])
2
'''
pass
## 3: () Nearest Neighbor Label
def nn_label(u, veclist, labels):
'''
Input:
- u: a Vec
- veclist: a list of Vecs
- labels: a list of labels, one for each Vec in veclist
Output:
- the label of the vector in veclist nearest to u
Example:
>>> from vecutil import list2vec
>>> u = list2vec([1,2])
>>> veclist = [list2vec(l) for l in [[2,5],[1,3],[1.5,2]]]
>>> labels = [0, 1, 0]
>>> nn_label(u, veclist, labels)
0
'''
pass
## 4: () Error Rate
def error_rate(guessed_labels, correct_labels):
'''
Input:
- guessed_labels: a list of guessed labels
- correct_labels: a list of true labels
Output:
- the fraction of guessed labels that are not equal to the corresponding correct label
Example:
>>> error_rate([0, 1, 0, 1, 1], [0, 1, 2, 3, 4])
0.6
'''
pass
#Load training and testing data
images, labels = load_data()
train_images = images[:3000]
train_labels = labels[:3000]
test_images = images[3000:3100]
test_labels = labels[3000:3100]
## 5: () Predictions from Nearest Neighbor on Image Vectors
guessed_labels_raw = ...
## 6: () Error Rate for Nearest Neighbor on Image Vectors
raw_nn_error_rate = ...
## 7: (Task 11.6.2) Procedure to Find Centroid
def find_centroid(veclist):
'''
Input:
- veclist: a list of Vecs
Output:
- a Vec, the centroid of veclist
Example:
>>> from vecutil import list2vec
>>> vs = [list2vec(l) for l in [[1,2,3],[2,3,4],[9,10,11]]]
>>> find_centroid(vs)
Vec({0, 1, 2},{0: 4.0, 1: 5.0, 2: 6.0})
'''
pass
## 8: () Centroid of Training Images
centroid = ...
## 9: () Centered Training Images
centered_train_images = ...
## 10: () Centered Test Images
centered_test_images = ...
## 11: () Right Singular Vectors
right_singular_vs = ...
## 12: () 10 Principal Components
M10 = ...
## 13: () Predictions from Nearest Neighbor on 10 Principal Components
# From your Python interaction, copy the list of labels that nearest neighbor assigns
# to the 100 test images; paste the list here.
guessed_labels_10 = ...
## 14: () Error Rate for Nearest Neighbor on 10 Principal Components
# In your Python interaction, find the error rate of nearest neighbor, and enter it here.
svd10_nn_error_rate = ...
## 15: () 20 Principal Components
M20 = ...
## 16: () Predictions from Nearest Neighbor on 20 Principal Components
# From your Python interaction, copy the list of labels that nearest neighbor assigns
# to the 100 test images; paste the list here.
guessed_labels_20 = ...
## 17: () Error Rate for Nearest Neighbor on 20 Principal Components
# In your Python interaction, find the error rate of nearest neighbor, and enter it here.
svd20_nn_error_rate = ...