cal = A.sum(axis=0)\npercentage = A \/ cal\nprint(percentage)<\/code><\/pre>\n\n\n\u6211\u4eec\u7ecf\u8fc7\u7b2c\u4e00\u6b65\u8ba1\u7b97\uff0c\u83b7\u53d6\u4e86\u4e00\u4e2a\uff081\uff0c4\uff09\u7684cal\u77e9\u9635\uff0c\u800cA\u662f\u4e00\u4e2a\uff083\uff0c4\uff09\u7684\u77e9\u9635\uff0c\u8fd9\u65f6\u5019\u6211\u4eec\u5982\u679c\u6267\u884c\u7b2c\u4e8c\u884c\u64cd\u4f5c\uff0cpython\u4f1a\u81ea\u52a8\u5c06cal\u4ece\uff081\uff0c4\uff09\u6269\u5c55\u5230\uff083\uff0c4\uff09\u7136\u540e\u548cA\u8ba1\u7b97\uff0c\u6700\u7ec8\u8fbe\u5230\u6211\u4eec\u60f3\u8981\u7684\u8ba1\u7b97\u7ed3\u679c\u3002<\/p>\n\n\n
\u540c\u7406\uff0c\u5bf9\u4e8e\u4e00\u4e2a \uff08m, n\uff09\u7684\u77e9\u9635\u52a0\u4e0a\uff081, n\uff09\u7684\u77e9\u9635\uff0c\u53ef\u4ee5\u76f4\u63a5\u76f8\u52a0\uff0cpython\u4f1a\u81ea\u52a8\u6269\u5c55\u81f3\uff08m,n\uff09\u7136\u540e\u518d\u76f8\u52a0 \u3002<\/p>\n\n\n
\u6d4b\u9a8c<\/h2>\n\n\n
1. \u795e\u7ecf\u5143\u8282\u70b9\u8ba1\u7b97\u4ec0\u4e48\uff1f <\/strong><\/p>\n\n\n- \u795e\u7ecf\u5143\u8282\u70b9\u5148\u8ba1\u7b97\u6fc0\u6d3b\u51fd\u6570\uff0c\u518d\u8ba1\u7b97\u7ebf\u6027\u51fd\u6570(z = Wx + b)<\/li>
- \u795e\u7ecf\u5143\u8282\u70b9\u5148\u8ba1\u7b97\u7ebf\u6027\u51fd\u6570\uff08z = Wx + b\uff09\uff0c\u518d\u8ba1\u7b97\u6fc0\u6d3b\u3002<\/li>
- \u795e\u7ecf\u5143\u8282\u70b9\u8ba1\u7b97\u51fd\u6570g\uff0c\u51fd\u6570g\u8ba1\u7b97(Wx + b)\u3002<\/li>
- \u5728 \u5c06\u8f93\u51fa\u5e94\u7528\u4e8e\u6fc0\u6d3b\u51fd\u6570\u4e4b\u524d\uff0c\u795e\u7ecf\u5143\u8282\u70b9\u8ba1\u7b97\u6240\u6709\u7279\u5f81\u7684\u5e73\u5747\u503c<\/li><\/ol>\n\n\n
\uff082\uff09<\/p>\n\n\n
2.\u4e0b\u9762\u54ea\u4e00\u4e2a\u662fLogistic\u635f\u5931\uff1f <\/strong><\/p>\n\n\n![\"\"](\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-42.png\")
<\/figure><\/div>\n\n\n3. \u5047\u8bbeimg\u662f\u4e00\u4e2a\uff0832,32,3\uff09\u6570\u7ec4\uff0c\u5177\u67093\u4e2a\u989c\u8272\u901a\u9053\uff1a\u7ea2\u8272\u3001\u7eff\u8272\u548c\u84dd\u8272\u768432×32\u50cf\u7d20\u7684\u56fe\u50cf\u3002 \u5982\u4f55\u5c06\u5176\u91cd\u65b0\u8f6c\u6362\u4e3a\u5217\u5411\u91cf\uff1f <\/strong><\/p>\n\n\nx = img.reshape(32*32*3,1)<\/code><\/pre>\n\n\n4. \u4e0b\u9762\u7684\u8fd9\u4e24\u4e2a\u968f\u673a\u6570\u7ec4\u201ca\u201d\u548c\u201cb\u201d, \u8bf7\u95ee\u6570\u7ec4<\/strong>c<\/strong><\/code>\u7684\u7ef4\u5ea6\u662f\u591a\u5c11\uff1f <\/strong><\/p>\n\n\na = np.random.randn(2, 3) # a.shape = (2, 3)\nb = np.random.randn(2, 1) # b.shape = (2, 1)\nc = a + b<\/code><\/pre>\n\n\n(2,3)<\/p>\n\n\n
5. \u4e0b\u9762\u7684\u8fd9\u4e24\u4e2a\u968f\u673a\u6570\u7ec4\u201ca\u201d\u548c\u201cb\u201d ,\u8bf7\u95ee\u6570\u7ec4\u201c<\/strong>c<\/strong><\/code>\u201d\u7684\u7ef4\u5ea6\u662f\u591a\u5c11\uff1f <\/strong><\/p>\n\n\na = np.random.randn(4, 3) # a.shape = (4, 3)\nb = np.random.randn(3, 2) # b.shape = (3, 2)\nc = a * b<\/code><\/pre>\n\n\n\u65e0\u6cd5\u8ba1\u7b97\u3002\u56e0\u4e3aa\u3001b\u4e24\u4e2a\u77e9\u9635\u7ef4\u5ea6\u4e0d\u540c\u3002.<\/p>\n\n\n
6. \u5047\u8bbe\u4f60\u7684\u6bcf\u4e00\u4e2a\u5b9e\u4f8b\u6709n_x\u4e2a\u8f93\u5165\u7279\u5f81\uff0c\u60f3\u4e00\u4e0b\u5728X=[x^(1), x^(2)\u2026x^(m)]\u4e2d\uff0cX\u7684\u7ef4\u5ea6\u662f\u591a\u5c11\uff1f <\/strong><\/p>\n\n\n\uff08n_x\uff0cm\uff09\u3002\u5c06\u8f93\u5165\u7279\u5f81\u8f6c\u5316\u4e3a\u5217\u5411\u91cf\uff0c\u7136\u540e\u53e0\u52a0m\u4e2a\u3002<\/p>\n\n\n
7. \u770b\u4e00\u4e0b\u4e0b\u9762\u7684\u8fd9\u4e24\u4e2a\u968f\u673a\u6570\u7ec4\u201ca\u201d\u548c\u201cb\u201d \u8bf7\u95eec\u7684\u7ef4\u5ea6\u662f\u591a\u5c11\uff1f <\/strong><\/p>\n\n\na = np.random.randn(12288, 150) # a.shape = (12288, 150)\nb = np.random.randn(150, 45) # b.shape = (150, 45)\nc = np.dot(a, b)<\/code><\/pre>\n\n\n\uff0812288\uff0c45\uff09\u3002dot\u662f\u77e9\u9635\u70b9\u4e58\uff08\u77e9\u9635\u4e58\u6cd5\uff09\u3002<\/p>\n\n\n
8. \u770b\u4e00\u4e0b\u4e0b\u9762\u7684\u8fd9\u4e2a\u4ee3\u7801\u7247\u6bb5\uff0c \u8bf7\u95ee\u8981\u600e\u4e48\u628a\u5b83\u4eec\u5411\u91cf\u5316\uff1f <\/strong><\/p>\n\n\n# a.shape = (3,4)\n# b.shape = (4,1)\nfor i in range(3):\n for j in range(4):\n c[i][j] = a[i][j] + b[j]<\/code><\/pre>\n\n\nc = a + b.T<\/code><\/pre>\n\n\n9. \u4e0b\u9762\u7684\u4ee3\u7801 \u8bf7\u95eec\u7684\u7ef4\u5ea6\u4f1a\u662f\u591a\u5c11\uff1f <\/strong><\/p>\n\n\na = np.random.randn(3, 3)\nb = np.random.randn(3, 1)\nc = a * b<\/code><\/pre>\n\n\n\uff083\uff0c3\uff09\u3002\u7531\u4e8e\u5e7f\u64ad\u673a\u5236\uff0cb\u4f1a\u88ab\u6269\u5c55\u6210\uff083\uff0c3\uff09\u7136\u540e\u6267\u884c\u77e9\u9635\u5143\u7d20\u76f8\u4e58\u3002<\/p>\n\n\n
\u7f16\u7a0b\u4f5c\u4e1a<\/h2>\n\n\n
\u6211\u4eec\u5728\u8fd9\u4e00\u8282\u8981\u505a\u7684\u5c31\u662f\u5199\u4e00\u4e2a\u80fd\u591f\u8bc6\u522b\u732b\u7684\u795e\u7ecf\u7f51\u7edc\uff0c\u5176\u5b9e\u8bf4\u662f\u795e\u7ecf\u7f51\u7edc\uff0c\u672c\u8d28\u4e0a\u5c31\u662f\u4e00\u4e2a\u903b\u8f91\u56de\u5f52\u52a0\u4e0a\u4e00\u4e2a\u53c2\u6570b\uff0c\u672c\u8d28\u4e0a\u90fd\u662f\u4e00\u4e2aax+b\u7684\u4e8c\u5206\u7c7b\u95ee\u9898\u3002<\/p>\n\n\n
\u8fd9\u5757\u8bf4\u660e\u7684\u6bd4\u8f83\u5c11\uff0c\u56e0\u4e3a\u603b\u4f53\u4e0a\u548c\u903b\u8f91\u56de\u5f52\u86ee\u50cf\u7684\uff0c\u5c31\u662f\u5dee\u4e86\u4e2a\u6743\u91cdb\u3002<\/p>\n\n\n
\u9996\u5148\u5bfc\u5305\uff1a<\/p>\n\n\n
import numpy as np\nimport matplotlib.pyplot as plt\nimport h5py\nfrom lr_utils import load_dataset<\/code><\/pre>\n\n\n\u7136\u540e\u6211\u4eec\u521d\u59cb\u5316\u6570\u636e<\/p>\n\n\n
train_set_x_orig , train_set_y , test_set_x_orig , test_set_y , classes = load_dataset()<\/code><\/pre>\n\n\n\u6211\u4eec\u67e5\u770b\u4e00\u4e0b\u56fe\u7247\u6570\u636e\u5e76\u7b80\u5355\u67e5\u770b\u4e00\u4e0b\u6570\u636e\uff1a<\/p>\n\n\n
# \u67e5\u770b\u4e00\u4e0b\u56fe\u7247
plt.imshow(train_set_x_pic[0])
plt.show()
print('\u8bad\u7ec3\u96c6\u5927\u5c0f:', train_set_x_pic.shape[0])
print('\u6d4b\u8bd5\u96c6\u5927\u5c0f:', test_set_x_pic.shape[0])
print('\u56fe\u7247\u7684\u5927\u5c0f:', train_set_x_pic.shape[1:])<\/pre>\n\n\n\u8f93\u51fa\u5982\u4e0b\uff1a<\/p>\n\n\n
![\"\"](\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-44.png\")
<\/figure><\/div>\n\n\n![\"\"](\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-45.png\")
<\/figure><\/div>\n\n\n\u7136\u540e\u505a\u4e00\u4e9b\u7b80\u5355\u7684\u6570\u636e\u9884\u5904\u7406\uff0c\u6bd4\u5982\u5c06\u6240\u6709\u7684\u56fe\u7247RGB\u6570\u636e\u7ec4\u6210\u6210\u4e00\u7ef4\u7684\u5e76\u8fdb\u884c\u6807\u51c6\u5316\u3002<\/p>\n\n\n
train_set_x_flatten = train_set_x_pic.reshape(train_set_x_pic.shape[0], -1).T
test_set_x_flatten = test_set_x_pic.reshape(test_set_x_pic.shape[0], -1).T
# \u6807\u51c6\u5316RGB\u989c\u8272\uff0c\u56e0\u6b64\u539f\u503c\u8303\u56f4\u8f83\u5927\uff0c\u6807\u51c6\u5316\u52300~1\u4e4b\u95f4
train_set_x = train_set_x_flatten \/ 255
test_set_x = test_set_x_flatten \/ 255<\/pre>\n\n\n\u7136\u540e\u5c31\u662f\u51e0\u4e2a\u9700\u8981\u7528\u5230\u7684\u65b9\u6cd5\uff0c<\/p>\n\n\n
\u9996\u5148\u662f\u6fc0\u6d3b\u51fd\u6570sigmoid\u51fd\u6570<\/p>\n\n\n
def sigmoid(z):
\"\"\"
<\/em> sigmoid<\/em>\u51fd\u6570
<\/em> <\/em>:param<\/em><\/strong> z:
<\/em> <\/em>:return<\/em><\/strong>:
<\/em> \"\"\"
<\/em> <\/em>return 1 \/ (1 + np.exp(-z))<\/pre>\n\n\n\u7136\u540e\u662f\u524d\u5411\u4f20\u64ad\u548c\u53cd\u9988\u7684\u65b9\u6cd5<\/p>\n\n\n
def propagate(w, b, X, Y):
\"\"\"
<\/em> <\/em>\u524d\u540e\u4f20\u64ad\u4ee5\u53ca\u6210\u672c\u8ba1\u7b97
<\/em> <\/em>:param<\/em><\/strong> w:
<\/em> <\/em>:param<\/em><\/strong> b:
<\/em> <\/em>:param<\/em><\/strong> X:
<\/em> <\/em>:param<\/em><\/strong> Y:
<\/em> <\/em>:return<\/em><\/strong>:
<\/em> \"\"\"
<\/em> <\/em>n = X.shape[1]
# \u8ba1\u7b97\u4ee3\u4ef7
A = sigmoid(np.dot(w.T, X) + b)
cost = np.mean(-Y * np.log(A) - (1 - Y) * np.log(1 - A))
# \u53cd\u5411\u4f20\u64ad
dw = (1 \/ n) * (X @ (A - Y).T)
db = (1 \/ n) * np.sum(A - Y)
return dw, db, cost<\/pre>\n\n\n\u7136\u540e\u662f\u8c03\u7528n\u6b21\u4f20\u64ad\u4ee5\u83b7\u53d6\u4e00\u4e2a\u6bd4\u8f83\u597d\u7684\u7ed3\u679c\uff1a<\/p>\n\n\n
def optimize(w, b, X, Y, iterations_times, learning_rate, print_cost=False):
\"\"\"
<\/em> <\/em>\u8fd0\u884c\u68af\u5ea6\u4e0b\u964d\u6765\u4f18\u5316<\/em>w<\/em>\u548c<\/em>b
<\/em> <\/em>:param<\/em><\/strong> w:
<\/em> <\/em>:param<\/em><\/strong> b:
<\/em> <\/em>:param<\/em><\/strong> X:
<\/em> <\/em>:param<\/em><\/strong> Y:
<\/em> <\/em>:param<\/em><\/strong> iterations_times:
<\/em> <\/em>:param<\/em><\/strong> learning_rate:
<\/em> <\/em>:param<\/em><\/strong> print_cost:
<\/em> <\/em>:return<\/em><\/strong>:
<\/em> \"\"\"
<\/em> <\/em>costs = []
for i in range(iterations_times):
wb, db, cost = propagate(w, b, X, Y)
w = w - learning_rate * wb
b = b - learning_rate * db
# \u8bb0\u5f55\u6210\u672c
if i % 100 == 0:
costs.append(cost)
if print_cost and i % 100 == 0:
print('\u8fed\u4ee3\u6b21\u6570\uff1a%i\uff0c\u8bef\u5dee\u503c\uff1a%f' % (i, cost))
return w, b, costs<\/pre>\n\n\n\u9884\u6d4b\u51fd\u6570\uff1a<\/p>\n\n\n
def predict(w, b, X):
\"\"\"
<\/em> <\/em>\u9884\u6d4b
<\/em> <\/em>:param<\/em><\/strong> w:
<\/em> <\/em>:param<\/em><\/strong> b:
<\/em> <\/em>:param<\/em><\/strong> X:
<\/em> <\/em>:return<\/em><\/strong>:
<\/em> \"\"\"
<\/em> <\/em>n = X.shape[1]
Y_prediction = np.zeros((1, n))
A = sigmoid((w.T @ X) + b)
for i in range(A.shape[1]):
Y_prediction[0, i] = 1 if A[0, i] > 0.5 else 0
return Y_prediction<\/pre>\n\n\n\u5c06\u6240\u6709\u7684\u65b9\u6cd5\u6574\u5408\u8d77\u6765\uff0c\u65b9\u4fbf\u8c03\u7528\uff1a<\/p>\n\n\n
def model(X_train, Y_train, X_test, Y_test, num_iterations=2000, learning_rate=0.01, print_cost=True):
\"\"\"
<\/em> <\/em>\u603b\u4f53\u6a21\u578b
<\/em> <\/em>:param<\/em><\/strong> X_train:
<\/em> <\/em>:param<\/em><\/strong> Y_train:
<\/em> <\/em>:param<\/em><\/strong> X_test:
<\/em> <\/em>:param<\/em><\/strong> Y_test:
<\/em> <\/em>:param<\/em><\/strong> num_iterations:
<\/em> <\/em>:param<\/em><\/strong> learning_rate:
<\/em> <\/em>:param<\/em><\/strong> print_cost:
<\/em> <\/em>:return<\/em><\/strong>:
<\/em> \"\"\"
<\/em> <\/em>w, b = init_weight(X_train.shape[0])
wb, db, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)
Y_prediction_test = predict(wb, db, X_test)
print('\u8bad\u7ec3\u96c6\u51c6\u786e\u7387:', (1 - (np.mean(np.abs(Y_prediction_test - Y_test)))) * 100, '%')
return wb, db, costs<\/pre>\n\n\n\u6700\u540e\u6211\u4eec\u6765\u8c03\u7528\u4e00\u4e0b\u770b\u770b<\/p>\n\n\n
d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations=2000, learning_rate=0.005, print_cost=True)
<\/pre>\n\n\n\u53ef\u4ee5\u770b\u5230\u8f93\u51fa\u5982\u4e0b\uff1a<\/p>\n\n\n
![\"\"](\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-46.png\")
<\/figure><\/div>\n\n\n\u5b8c\u6574\u4ee3\u7801\uff1a<\/p>\n\n\n
# -*- coding:utf-8 -*-
import numpy as np
import matplotlib.pyplot as plt
import h5py
from course_1_week_2.lr_utils import load_dataset
# \u8bad\u7ec3\u96c6\u56fe\u7247\uff0c \u8bad\u7ec3\u96c6\u6807\u7b7e\uff0c \u6d4b\u8bd5\u96c6\u56fe\u7247\uff0c\u6d4b\u8bd5\u96c6\u6807\u7b7e\uff0c\u5206\u7c7b\u6807\u7b7e\u6587\u672c\u63cf\u8ff0
train_set_x_pic, train_set_y, test_set_x_pic, test_set_y, classes = load_dataset()
# \u67e5\u770b\u4e00\u4e0b\u56fe\u7247
plt.imshow(train_set_x_pic[0])
plt.show()
print('\u8bad\u7ec3\u96c6\u5927\u5c0f:', train_set_x_pic.shape[0])
print('\u6d4b\u8bd5\u96c6\u5927\u5c0f:', test_set_x_pic.shape[0])
print('\u56fe\u7247\u7684\u5927\u5c0f:', train_set_x_pic.shape[1:])
train_set_x_flatten = train_set_x_pic.reshape(train_set_x_pic.shape[0], -1).T
test_set_x_flatten = test_set_x_pic.reshape(test_set_x_pic.shape[0], -1).T
# \u6807\u51c6\u5316RGB\u989c\u8272\uff0c\u56e0\u6b64\u539f\u503c\u8303\u56f4\u8f83\u5927\uff0c\u6807\u51c6\u5316\u52300~1\u4e4b\u95f4
train_set_x = train_set_x_flatten \/ 255
test_set_x = test_set_x_flatten \/ 255
def sigmoid(z):
\"\"\"
<\/em> sigmoid<\/em>\u51fd\u6570
<\/em> <\/em>:param<\/em><\/strong> z:
<\/em> <\/em>:return<\/em><\/strong>:
<\/em> \"\"\"
<\/em> <\/em>return 1 \/ (1 + np.exp(-z))
def init_weight(dim):
\"\"\"
<\/em> <\/em>\u521d\u59cb\u5316\u7ef4\u5ea6
<\/em> <\/em>:param<\/em><\/strong> dim:
<\/em> <\/em>:return<\/em><\/strong>:
<\/em> \"\"\"
<\/em> <\/em>w = np.zeros((dim, 1))
b = 0
return w, b
def propagate(w, b, X, Y):
\"\"\"
<\/em> <\/em>\u524d\u540e\u4f20\u64ad\u4ee5\u53ca\u6210\u672c\u8ba1\u7b97
<\/em> <\/em>:param<\/em><\/strong> w:
<\/em> <\/em>:param<\/em><\/strong> b:
<\/em> <\/em>:param<\/em><\/strong> X:
<\/em> <\/em>:param<\/em><\/strong> Y:
<\/em> <\/em>
![\"\"](\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-43.png\")
<\/figure><\/div>\n\n\n![\"\"](\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-40.png\")
<\/figure>\n\n\n![\"\"](\"\/wp-content\/uploads\/2020\/01\/\u56fe\u7247-41.png\")
<\/figure><\/div>\n\n\n