1 矩阵、向量
在之前我们都是将每个元素做运算，这样做看着费时费力，现在我们从万物皆向量的角度重新看待这个问题，用向量的运算去表示线性函数。
现在我们使用代码来实现以上过程：
之前的代码：
import numpy as np import dataset import plot_utils m = 100 xs, ys = dataset.get_beans(m) print(xs) print(ys) plot_utils.show_scatter(xs, ys) w1 = 0.1 w2 = 0.2 b = 0.1 ## [[a,b][c,d]] ## x1s[a,c] ## x2s[b,d] ## 逗号，区分的是维度，冒号：区分的是索引，省略号… 用来代替全索引长度 # 在所有的行上，把第0列切割下来形成一个新的数组 x1s = xs[:, 0] x2s = xs[:, 1] # 前端传播 def forward_propgation(x1s, x2s): z = w1 * x1s + w2 * x2s + b a = 1 / (1 + np.exp(-z)) return a plot_utils.show_scatter_surface(xs, ys, forward_propgation) for _ in range(500): for i in range(m): x = xs[i] ## 豆豆特征 y = ys[i] ## 豆豆是否有毒 x1 = x[0] x2 = x[1] a = forward_propgation(x1, x2) e = (y - a) ** 2 deda = -2 * (y - a) dadz = a * (1 - a) dzdw1 = x1 dzdw2 = x2 dzdb = 1 dedw1 = deda * dadz * dzdw1 dedw2 = deda * dadz * dzdw2 dedb = deda * dadz * dzdb alpha = 0.01 w1 = w1 - alpha * dedw1 w2 = w2 - alpha * dedw2 b = b - alpha * dedb plot_utils.show_scatter_surface(xs, ys, forward_propgation)
使用向量矩阵后的代码：
import numpy as np import dataset import plot_utils m = 100 X, Y = dataset.get_beans(m) print(X) print(Y) plot_utils.show_scatter(X, Y) # w1 = 0.1 # w2 = 0.2 W = np.array([0.1, 0.1]) # b = 0.1 B = np.array([0.1]) # 前端传播 def forward_propgation(X): # z = w1 * x1s + w2 * x2s + b # ndarray的dot函数：点乘运算 # ndarray的T属性：转置运算 Z = X.dot(W.T) + B # a = 1 / (1 + np.exp(-z)) A = 1 / (1 + np.exp(-Z)) return A plot_utils.show_scatter_surface(X, Y, forward_propgation) for _ in range(500): for i in range(m): Xi = X[i] ## 豆豆特征 Yi = Y[i] ## 豆豆是否有毒 A = forward_propgation(Xi) E = (Yi - A) ** 2 dEdA = -2 * (Yi - A) dAdZ = A * (1 - A) dZdW = Xi dZdB = 1 dEdW = dEdA * dAdZ * dZdW dEdB = dEdA * dAdZ * dZdB alpha = 0.01 W = W - alpha * dEdW B = B - alpha * dEdB plot_utils.show_scatter_surface(X, Y, forward_propgation)
2 Keras
诚如你所见，你恰好发现了 Keras。Keras 是一个用 Python 编写的高级神经网络 API，它能够以 TensorFlow, CNTK, 或者 Theano 作为后端运行。Keras 的开发重点是支持快速的实验。能够以最小的时延把你的想法转换为实验结果，是做好研究的关键。
🔗参考链接：Keras官网
环境准备：
安装Tensorflow和Keras：
pip install keras -i https://pypi.mirrors.ustc.edu.cn/simple/ pip install tensorflow -i https://pypi.mirrors.ustc.edu.cn/simple/ 12
如果遇到ddl缺失问题，我们只需要去微软的官网下载一个Visual C++软件包：参考链接
3 代码实现
我们对上述过程代码实现：
豆豆数据集模拟：dataset.py
import numpy as np def get_beans(counts): xs = np.random.rand(counts,2)*2 ys = np.zeros(counts) for i in range(counts): x = xs[i] if (x[0]-0.5*x[1]-0.1)>0: ys[i] = 1 return xs,ys def get_beans1(counts): xs = np.random.rand(counts) xs = np.sort(xs) ys = np.zeros(counts) for i in range(counts): x = xs[i] yi = 0.7*x+(0.5-np.random.rand())/50+0.5 if yi > 0.8: ys[i] = 1 else: ys[i] = 0 return xs,ys def get_beans2(counts): xs = np.random.rand(counts)*2 xs = np.sort(xs) ys = np.zeros(counts) for i in range(counts): x = xs[i] yi = 0.7*x+(0.5-np.random.rand())/50+0.5 if yi > 0.8 and yi < 1.4: ys[i] = 1 return xs,ys def get_beans3(counts): xs = np.random.rand(counts)*2 xs = np.sort(xs) ys = np.zeros(counts) for i in range(counts): x = xs[i] yi = 0.7*x+(0.5-np.random.rand())/50+0.5 if yi > 0.8 and yi < 1.4: ys[i] = 1 if yi > 1.6 and yi < 1.8: ys[i] = 1 return xs,ys def get_beans4(counts): xs = np.random.rand(counts,2)*2 ys = np.zeros(counts) for i in range(counts): x = xs[i] if (np.power(x[0]-1,2)+np.power(x[1]-0.3,2))<0.5: ys[i] = 1 return xs,ys
绘图工具：plot_utils.py
import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D import numpy as np from keras.models import Sequential#导入keras def show_scatter_curve(X,Y,pres): plt.scatter(X, Y) plt.plot(X, pres) plt.show() def show_scatter(X,Y): if X.ndim>1: show_3d_scatter(X,Y) else: plt.scatter(X, Y) plt.show() def show_3d_scatter(X,Y): x = X[:,0] z = X[:,1] fig = plt.figure() ax = Axes3D(fig) ax.scatter(x, z, Y) plt.show() def show_surface(x,z,forward_propgation): x = np.arange(np.min(x),np.max(x),0.1) z = np.arange(np.min(z),np.max(z),0.1) x,z = np.meshgrid(x,z) y = forward_propgation(X) fig = plt.figure() ax = Axes3D(fig) ax.plot_surface(x, z, y, cmap='rainbow') plt.show() def show_scatter_surface(X,Y,forward_propgation): if type(forward_propgation) == Sequential: show_scatter_surface_with_model(X,Y,forward_propgation) return x = X[:,0] z = X[:,1] y = Y fig = plt.figure() ax = Axes3D(fig) ax.scatter(x, z, y) x = np.arange(np.min(x),np.max(x),0.1) z = np.arange(np.min(z),np.max(z),0.1) x,z = np.meshgrid(x,z) X = np.column_stack((x[0],z[0])) for j in range(z.shape[0]): if j == 0: continue X = np.vstack((X,np.column_stack((x[0],z[j])))) r = forward_propgation(X) y = r[0] if type(r) == np.ndarray: y = r y = np.array([y]) y = y.reshape(x.shape[0],z.shape[1]) ax.plot_surface(x, z, y, cmap='rainbow') plt.show() def show_scatter_surface_with_model(X,Y,model): #model.predict(X) x = X[:,0] z = X[:,1] y = Y fig = plt.figure() ax = Axes3D(fig) ax.scatter(x, z, y) x = np.arange(np.min(x),np.max(x),0.1) z = np.arange(np.min(z),np.max(z),0.1) x,z = np.meshgrid(x,z) X = np.column_stack((x[0],z[0])) for j in range(z.shape[0]): if j == 0: continue X = np.vstack((X,np.column_stack((x[0],z[j])))) y = model.predict(X) # return # y = model.predcit(X) y = np.array([y]) y = y.reshape(x.shape[0],z.shape[1]) ax.plot_surface(x, z, y, cmap='rainbow') plt.show() def pre(X,Y,model): model.predict(X)
第一批豆豆：
import dataset import plot_utils from keras.models import Sequential from keras.layers import Dense m = 100 X, Y = dataset.get_beans1(m) plot_utils.show_scatter(X, Y) model = Sequential() # 当前层神经元的数量为1，激活函数类型：sigmoid，输入数据特征维度：1 model.add(Dense(units=1, activation='sigmoid', input_dim=1)) # loss（损失函数、代价函数）：mean_squared_error均方误差； # optimizer（优化器）：sgd（随机梯度下降算法）； # metrics（评估标准）：accuracy（准确度）； model.compile(loss='mean_squared_error', optimizer='sgd', metrics=['accuracy']) # epochs：回合数（全部样本完成一次训练）、batch_size：批数量（一次训练使用多少个样本） model.fit(X, Y, epochs=5000, batch_size=10) pres = model.predict(X) plot_utils.show_scatter_curve(X, Y, pres)
🚩训练结果：
🔨 第二批豆豆：
import dataset import plot_utils from keras.models import Sequential from keras.layers import Dense from keras.optimizers import SGD m = 100 X, Y = dataset.get_beans2(m) plot_utils.show_scatter(X, Y) model = Sequential() model.add(Dense(units=2, activation='sigmoid', input_dim=1)) model.add(Dense(units=1, activation='sigmoid')) # 调整学习率为0.05 model.compile(loss='mean_squared_error', optimizer=SGD(lr=0.05), metrics=['accuracy']) model.fit(X, Y, epochs=5000, batch_size=10) pres = model.predict(X) plot_utils.show_scatter_curve(X, Y, pres)
🚩训练结果：
🔨 第三批豆豆：
import dataset import plot_utils from keras.models import Sequential from keras.layers import Dense from keras.optimizers import SGD m = 100 X, Y = dataset.get_beans(m) plot_utils.show_scatter(X, Y) model = Sequential() # 当前层神经元的数量为1，激活函数类型：sigmoid，输入数据特征维度：2 model.add(Dense(units=1, activation='sigmoid', input_dim=2)) # loss（损失函数、代价函数）：mean_squared_error均方误差； # optimizer（优化器）：sgd（随机梯度下降算法）； # metrics（评估标准）：accuracy（准确度）； model.compile(loss='mean_squared_error', optimizer=SGD(lr=0.05), metrics=['accuracy']) # epochs：回合数（全部样本完成一次训练）、batch_size：批数量（一次训练使用多少个样本） model.fit(X, Y, epochs=5000, batch_size=10) pres = model.predict(X) plot_utils.show_scatter_surface(X, Y, model)
🚩豆豆毒性分布：
🚩训练结果：
🔨 第四批豆豆：
import dataset import plot_utils from keras.models import Sequential from keras.layers import Dense from keras.optimizers import SGD m = 100 X, Y = dataset.get_beans(m) plot_utils.show_scatter(X, Y) model = Sequential() # 当前层神经元的数量为2，激活函数类型：sigmoid，输入数据特征维度：2 model.add(Dense(units=2, activation='sigmoid', input_dim=2)) model.add(Dense(units=1, activation='sigmoid')) # loss（损失函数、代价函数）：mean_squared_error均方误差； # optimizer（优化器）：sgd（随机梯度下降算法）； # metrics（评估标准）：accuracy（准确度）； model.compile(loss='mean_squared_error', optimizer=SGD(lr=0.05), metrics=['accuracy']) # epochs：回合数（全部样本完成一次训练）、batch_size：批数量（一次训练使用多少个样本） model.fit(X, Y, epochs=5000, batch_size=10) pres = model.predict(X) plot_utils.show_scatter_surface(X, Y, model)
🚩训练结果：
