In [14]:
import matplotlib.pyplot as plt
plt.figure(figsize=(1, 1))
plt.imshow(img, cmap="Greys")
plt.xticks([])
plt.yticks([])
Out[14]:
([], [])
ls
train-images-idx3-ubyte.gz week_2.ipynb train-labels-idx1-ubyte.gz week_2_prep.ipynb
pwd
'/Users/bb/Documents/GitHub/MTH548/preps/week_2'
import gzip
with gzip.open("train-images-idx3-ubyte.gz", 'rb') as foo:
f = foo.read()
f[:20]
b'\x00\x00\x08\x03\x00\x00\xea`\x00\x00\x00\x1c\x00\x00\x00\x1c\x00\x00\x00\x00'
f[6]
234
ord("`")
96
for x in f[:20]:
print(x)
0 0 8 3 0 0 234 96 0 0 0 28 0 0 0 28 0 0 0 0
import numpy as np
images = np.array([b for b in f[16:]]).reshape(-1, 28*28)
images
array([[0, 0, 0, ..., 0, 0, 0],
[0, 0, 0, ..., 0, 0, 0],
[0, 0, 0, ..., 0, 0, 0],
...,
[0, 0, 0, ..., 0, 0, 0],
[0, 0, 0, ..., 0, 0, 0],
[0, 0, 0, ..., 0, 0, 0]])
images.shape
(60000, 784)
img = images[90].reshape(28, 28)
img
array([[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 25, 214, 225, 90, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 7, 145, 212, 253, 253, 60, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 106, 253, 253, 246, 188, 23, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
45, 164, 254, 253, 223, 108, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24,
236, 253, 252, 124, 28, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 217,
253, 218, 116, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 158, 175, 225,
253, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 217, 241, 248,
114, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 21, 201, 253, 253, 114,
3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 107, 253, 253, 213, 19,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 170, 254, 254, 169, 0,
0, 0, 0, 0, 2, 13, 100, 133, 89, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 18, 210, 253, 253, 100, 0,
0, 0, 19, 76, 116, 253, 253, 253, 176, 4, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 41, 222, 253, 208, 18, 0,
0, 93, 209, 232, 217, 224, 253, 253, 241, 31, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 157, 253, 253, 229, 32, 0,
154, 250, 246, 36, 0, 49, 253, 253, 168, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 128, 253, 253, 253, 195, 125,
247, 166, 69, 0, 0, 37, 236, 253, 168, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 37, 253, 253, 253, 253, 253,
135, 32, 0, 7, 130, 73, 202, 253, 133, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 7, 185, 253, 253, 253, 253,
64, 0, 10, 210, 253, 253, 253, 153, 9, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 66, 253, 253, 253, 253,
238, 218, 221, 253, 253, 235, 156, 37, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 5, 111, 228, 253, 253,
253, 253, 254, 253, 168, 19, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 110, 178,
253, 253, 249, 63, 5, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0]])
with np.printoptions(linewidth=5*28):
print(img)
[[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 25 214 225 90 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 145 212 253 253 60 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 106 253 253 246 188 23 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 45 164 254 253 223 108 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 24 236 253 252 124 28 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 100 217 253 218 116 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 158 175 225 253 92 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 24 217 241 248 114 2 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 21 201 253 253 114 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 107 253 253 213 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 170 254 254 169 0 0 0 0 0 2 13 100 133 89 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 18 210 253 253 100 0 0 0 19 76 116 253 253 253 176 4 0 0 0 0 0] [ 0 0 0 0 0 0 0 41 222 253 208 18 0 0 93 209 232 217 224 253 253 241 31 0 0 0 0 0] [ 0 0 0 0 0 0 0 157 253 253 229 32 0 154 250 246 36 0 49 253 253 168 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 128 253 253 253 195 125 247 166 69 0 0 37 236 253 168 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 37 253 253 253 253 253 135 32 0 7 130 73 202 253 133 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 7 185 253 253 253 253 64 0 10 210 253 253 253 153 9 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 66 253 253 253 253 238 218 221 253 253 235 156 37 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 5 111 228 253 253 253 253 254 253 168 19 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 9 110 178 253 253 249 63 5 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]]
import matplotlib.pyplot as plt
plt.figure(figsize=(1, 1))
plt.imshow(img, cmap="Greys")
plt.xticks([])
plt.yticks([])
([], [])
with gzip.open("train-labels-idx1-ubyte.gz", 'rb') as foo:
f = foo.read()
f[:20]
b'\x00\x00\x08\x01\x00\x00\xea`\x05\x00\x04\x01\t\x02\x01\x03\x01\x04\x03\x05'
labels = np.array([b for b in f[8:]])
labels[:10]
array([5, 0, 4, 1, 9, 2, 1, 3, 1, 4])
labels[90]
6
N = 46689
img = images[N].reshape(28, 28)
label = labels[N]
plt.figure(figsize=(1, 1))
plt.imshow(img, cmap="Greys")
plt.xticks([])
plt.yticks([])
plt.title(label);
Distances:
Create blobs with sklearn:
from sklearn.datasets import make_blobs
X, y = make_blobs(
n_samples = 10,
n_features = 2,
centers = 4,
cluster_std = 1,
random_state = 1
)
X, y
(array([[ -7.23731039, -9.03108652],
[ -8.86394306, -5.05323981],
[ -7.37541495, -1.94406175],
[ -5.37320505, -2.58629112],
[ 0.08525186, 3.64528297],
[-10.32012971, -4.3374029 ],
[ -0.79415228, 2.10495117],
[ -7.02266844, -7.57041289],
[ -1.34052081, 4.15711949],
[ -8.53560457, -6.01348926]]),
array([2, 1, 3, 3, 0, 1, 0, 2, 0, 1]))
X, y = make_blobs(
n_samples = 200,
n_features = 2,
centers = 4,
cluster_std = 1,
random_state = 1
)
plt.figure(figsize=(6, 6))
plt.scatter(X[:, 0], X[:, 1], c=y, s=60, cmap="seismic")
<matplotlib.collections.PathCollection at 0x7febd2b6b700>
plt.style.available
['Solarize_Light2', '_classic_test_patch', '_mpl-gallery', '_mpl-gallery-nogrid', 'bmh', 'classic', 'dark_background', 'fast', 'fivethirtyeight', 'ggplot', 'grayscale', 'seaborn', 'seaborn-bright', 'seaborn-colorblind', 'seaborn-dark', 'seaborn-dark-palette', 'seaborn-darkgrid', 'seaborn-deep', 'seaborn-muted', 'seaborn-notebook', 'seaborn-paper', 'seaborn-pastel', 'seaborn-poster', 'seaborn-talk', 'seaborn-ticks', 'seaborn-white', 'seaborn-whitegrid', 'tableau-colorblind10']
X, y = make_blobs(
n_samples = 200,
n_features = 2,
centers = 5,
cluster_std = 1,
random_state = 1
)
plt.style.use('ggplot')
plt.figure(figsize=(6, 6))
plt.scatter(X[:, 0], X[:, 1], c=y, s=60, cmap="viridis")
<matplotlib.collections.PathCollection at 0x7febd3196a30>
%config InlineBackend.figure_format = 'retina'
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap, Normalize
def plot_clusters(X, y, p=None, p_label=None, neighbors=None):
"""
Plots nearest neighbors of a given point.
X:
A 2-dimensional numpy array with coordinates
of points in clusters
y:
A 1-dimensional numpy array with labels of points
p:
An array with coordinates of the point whose
neighbors will be plotted.
p_label:
The predicted label of the point p.
neighbors:
A list of row numbers of X which are the nearest
neighbors of the point p.
"""
# build a custom colormap
col_list = ['dodgerblue', 'limegreen', 'red', 'orange', 'fuchsia']
colors = ListedColormap(col_list)
norm = Normalize(0, len(col_list))
plt.figure(figsize=(8, 8))
with plt.style.context('seaborn'):
scatter = plt.scatter(X[:, 0],
X[:, 1],
c=y,
s=90,
cmap=colors,
norm=norm,
label=y)
if p is not None:
p_col = "k" if p_label is None else colors(norm(p_label))
plt.plot(p[0], p[1], marker="*", mfc=p_col, mec="k", ms=30, mew=2)
if neighbors is not None:
plt.scatter(X[neighbors, 0],
X[neighbors, 1],
edgecolors='black',
linewidth=3,
facecolors="None",
s=300)
plt.legend(*scatter.legend_elements(),
markerscale=1.5,
prop={
"size": 12,
"weight": "normal"
})
plt.show()
plot_clusters(X, y, p=[0, 0], p_label=2, neighbors=[1, 10, 17, 100])
from sklearn.datasets import make_blobs
X, y = make_blobs(n_samples=200,
n_features=2,
centers=3,
center_box=(0, 10),
cluster_std=1,
random_state=10
)
p = [7, 4]
p_label = 2
neighbors = [103, 109, 24, 164, 131, 82, 122, 7, 21, 80]
plot_clusters(X, y, p, p_label, neighbors)
images
array([[0, 0, 0, ..., 0, 0, 0],
[0, 0, 0, ..., 0, 0, 0],
[0, 0, 0, ..., 0, 0, 0],
...,
[0, 0, 0, ..., 0, 0, 0],
[0, 0, 0, ..., 0, 0, 0],
[0, 0, 0, ..., 0, 0, 0]])
labels
array([5, 0, 4, ..., 5, 6, 8])
rng = np.random.default_rng(2)
reorder = rng.permutation(len(images))
reorder
array([58490, 29928, 51871, ..., 29028, 840, 22721])
images = images[reorder]
labels = labels[reorder]
train_num = 10000
test_num = 1000
train_images = images[:train_num]
train_labels = labels[:train_num]
test_images = images[train_num: train_num + test_num]
test_labels = labels[train_num: train_num + test_num]
c = rng.integers(0, 100, (10, 10))
c
array([[48, 56, 0, 22, 40, 81, 41, 98, 86, 24],
[80, 71, 36, 15, 43, 71, 92, 52, 26, 45],
[23, 27, 87, 15, 70, 34, 56, 58, 59, 91],
[ 2, 25, 0, 94, 17, 70, 70, 38, 96, 96],
[80, 77, 36, 11, 72, 35, 0, 4, 59, 87],
[39, 74, 59, 49, 70, 97, 49, 79, 14, 61],
[67, 15, 6, 16, 97, 94, 92, 15, 60, 37],
[32, 79, 55, 88, 78, 3, 75, 14, 14, 32],
[16, 50, 52, 95, 27, 68, 43, 51, 21, 0],
[12, 48, 65, 34, 35, 61, 61, 96, 95, 5]])
import seaborn as sns
plt.figure(figsize=(10, 8))
sns.heatmap(c,
annot=True,
annot_kws = {"fontsize": 16},
cbar=True,
linewidth=2,
square=True,
cmap="Blues_r"
)
plt.xlabel("Predictions")
plt.ylabel("Actual labels")
plt.show()
