プログラミングのない世界 (4)#
手書き文字認識#
from sklearn import datasets
digits = datasets.load_digits()
digits.images.shape
(1797, 8, 8)
digits.images[3]
array([[ 0., 0., 7., 15., 13., 1., 0., 0.],
[ 0., 8., 13., 6., 15., 4., 0., 0.],
[ 0., 2., 1., 13., 13., 0., 0., 0.],
[ 0., 0., 2., 15., 11., 1., 0., 0.],
[ 0., 0., 0., 1., 12., 12., 1., 0.],
[ 0., 0., 0., 0., 1., 10., 8., 0.],
[ 0., 0., 8., 4., 5., 14., 9., 0.],
[ 0., 0., 7., 13., 13., 9., 0., 0.]])
fig = plt.figure()
ax = fig.add_subplot()
ax.imshow(digits.images[3], cmap=plt.cm.gray_r)
plt.show()
_, axes = plt.subplots(nrows=1, ncols=10, figsize=(10, 3))
for ax, image, label in zip(axes, digits.images, digits.target):
ax.set_axis_off()
ax.imshow(image, cmap=plt.cm.gray_r, interpolation="nearest")
#ax.set_title("Training: %i" % label)
より大きなデータセットを使う
from sklearn.datasets import fetch_openml
X, y = fetch_openml("mnist_784", version=1, return_X_y=True, as_frame=False)
X.shape, y.shape
((70000, 784), (70000,))
np.sqrt(784)
28.0
X[3].reshape((28,28))
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, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 124, 253, 255, 63, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 96, 244, 251, 253, 62, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 127, 251, 251, 253, 62, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 68, 236, 251, 211, 31, 8, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 60, 228, 251, 251, 94, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 155, 253, 253, 189, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 20, 253, 251, 235, 66, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
32, 205, 253, 251, 126, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
104, 251, 253, 184, 15, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80,
240, 251, 193, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 253,
253, 253, 159, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 251,
251, 251, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 221, 251,
251, 172, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 234, 251, 251,
196, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 253, 251, 251,
89, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 159, 255, 253, 253,
31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 48, 228, 253, 247, 140,
8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 64, 251, 253, 220, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 64, 251, 253, 220, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 24, 193, 253, 220, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0]])
fig = plt.figure()
ax = fig.add_subplot()
ax.imshow(X[9].reshape((28,28)), cmap=plt.cm.gray_r)
plt.show()
y[9]
'4'
X = X / 255.0
X[3].reshape((28,28))
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訓練 (train) 用と評価 (test) 用のデータセットに分割する:
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0, test_size=0.7)
list(map(np.shape,(X_train,X_test,y_train,y_test)))
[(21000, 784), (49000, 784), (21000,), (49000,)]
mlp = MLPClassifier(
hidden_layer_sizes=(40,),
max_iter=8,
alpha=1e-4,
solver="sgd",
verbose=10,
random_state=1,
learning_rate_init=0.2,
)
import warnings
from sklearn.exceptions import ConvergenceWarning
with warnings.catch_warnings():
warnings.filterwarnings("ignore", category=ConvergenceWarning, module="sklearn")
mlp.fit(X_train, y_train)
Iteration 1, loss = 0.44139186
Iteration 2, loss = 0.19174891
Iteration 3, loss = 0.13983521
Iteration 4, loss = 0.11378556
Iteration 5, loss = 0.09443967
Iteration 6, loss = 0.07846529
Iteration 7, loss = 0.06506307
Iteration 8, loss = 0.05534985
print("Training set score: %f" % mlp.score(X_train, y_train))
print("Test set score: %f" % mlp.score(X_test, y_test))
Training set score: 0.986429
Test set score: 0.953061
mlp.predict([X_test[9]]), y_test[9]
(array(['7'], dtype='<U1'), '7')
fig = plt.figure()
ax = fig.add_subplot()
ax.imshow(X_test[9].reshape((28,28)), cmap=plt.cm.gray_r)
plt.show()
機械学習の結果、各層には次に可視化するような重みが掛かるようになっている:
mlp.coefs_[0].shape
(784, 40)
fig, axes = plt.subplots(5, 8, figsize=(14,14))
# use global min / max to ensure all weights are shown on the same scale
vmin, vmax = mlp.coefs_[0].min(), mlp.coefs_[0].max()
for coef, ax in zip(mlp.coefs_[0].T, axes.ravel()):
ax.matshow(coef.reshape(28, 28), cmap=plt.cm.gray, vmin=0.5 * vmin, vmax=0.5 * vmax)
ax.set_xticks(())
ax.set_yticks(())
ax.set_aspect('equal')
plt.tight_layout()
#plt.subplots_adjust(hspace=None)
plt.show()
