11. 数据集准备
现在是时候尝试应用我们的模型来解决一个简单的分类问题。为了检测模型是否能够顺利训练，下面我们将生成一个含有两个类的点集（如下图所示，两个类别的点分别用不同颜色表示），然后尝试训练模型来对这些点进行分类（二元分类问题）。
# number of samples in the data set N_SAMPLES = 1000 # ratio between training and test sets TEST_SIZE = 0.1
# we will use sklearn.make_moons() to generate the dataset: # - n_samples: 生成样本数量 # - noise: 高斯噪声 # - random_state: 生成随机种子，给定一个int型数据，能够保证每次生成数据相同 X, y = make_moons(n_samples = N_SAMPLES, noise=0.2, random_state=100) # split the dataset into training set (90%) & test set (10%) # - test_size: 如果是浮点数，则应该在0.0和1.0之间，表示要测试集占总数据集的比例；如果是int类型，表示测试集的绝对数量。 # - random_state: 随机数生成器使用的种子 X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=TEST_SIZE, random_state=42)
下面我们来观察一下刚刚生成好的数据集。
shape of X: (1000, 2) X = [[ 2.24907069e-05 1.07275825e+00] [-5.59037377e-02 4.25241282e-01] [ 2.40944879e-02 4.08065802e-01] ... [ 1.75841594e+00 -5.77404262e-01] [ 1.26710180e+00 -4.42980152e-01] [-1.75927072e-01 5.83509936e-01]] shape of X: (900, 2)
# check the information in Y print("shape of Y: ", y.shape) # (1000,) print("number of zeros in Y: ", np.sum(y==0)) # 500 print("number of ones in Y: ", np.sum(y==1)) # 500 print("Y = ", y)
shape of Y: (1000,) number of zeros in Y: 500 number of ones in Y: 500 Y = [0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1]
# the function making up the graph of a dataset def make_plot(X, y, plot_name, file_name=None, XX=None, YY=None, preds=None, dark=False): if (dark): plt.style.use('dark_background') else: sns.set_style("whitegrid") plt.figure(figsize=(16,12)) axes = plt.gca() axes.set(xlabel="$X_1$", ylabel="$X_2$") plt.title(plot_name, fontsize=30) plt.subplots_adjust(left=0.20) plt.subplots_adjust(right=0.80) if(XX is not None and YY is not None and preds is not None): plt.contourf(XX, YY, preds.reshape(XX.shape), 25, alpha = 1, cmap=cm.Spectral) plt.contour(XX, YY, preds.reshape(XX.shape), levels=[.5], cmap="Greys", vmin=0, vmax=.6) plt.scatter(X[:, 0], X[:, 1], c=y.ravel(), s=40, cmap=plt.cm.Spectral, edgecolors='black') if(file_name): plt.savefig(file_name) plt.close()
make_plot(X, y, "Dataset")
请同学们依次尝试将 sklearn.make_moons() 函数中 noise 取 0, 0.2, 0.4, 0.8, 1.0 等不同值，查看并截图保存对应的数据集图像和训练结果，分析其趋势，及出现这样趋势的原因。
然后，请同学们将 sklearn.make_moons() 中 noise 固定为 0.8，将sklearn.model_selection.train_test_split() 函数中的 TEST_SIZE 改为 0.98，观察和原先 noise 为 0.2、TEST_SIZE 为 0.1 的情况相比，训练集上的准确度和测试集上的准确度都分别发生了什么变化？出现这样变化的原因是什么？
调整 make_moons() 函数中的 noise 和 train_test_split() 函数中的 TEST_SIZE，改变数据集中点的分布。 将 sklearn.make_moons() 中 noise 固定为 0.8，将sklearn.model_selection.train_test_split() 函数中的 TEST_SIZE 改为 0.98，观察和原先 noise 为 0.2、TEST_SIZE 为 0.1 的情况相比，训练过程折线图表示如图所示，测试结果如图所示。
结论：当测试集占总数据量10%，noise等于0.2时，训练速度较慢，但是Acc和Cost曲线比较平滑，且测试效果和模型最终在训练集上得到的效果相差不大，即可以学习出一种较好的模型。而当测试集占总数据量98%，noise等于0.8时，训练速度较快，但是Acc曲线出现毛刺，且测试效果和模型最终在训练集上得到的效果很大，即出现过拟合现象。分析可知，当训练集占比过小，模型只能学习到很少的知识，无法得到好的模型。
12. 模型训练及测试
下面我们来调用 train 函数对模型进行训练。
# let's train the neural network params_values = train(X=np.transpose(X_train), Y=np.transpose(y_train.reshape((y_train.shape[0], 1))), nn_architecture=NN_ARCHITECTURE, epochs=10000, learning_rate=0.01)
Iteration: 00000 - cost: 0.69365 - accuracy: 0.50444 X.shape: (2, 900) Y_hat.shape: (1, 900) Y.shape: (1, 900) Iteration: 00050 - cost: 0.69349 - accuracy: 0.50444 Iteration: 00100 - cost: 0.69334 - accuracy: 0.50444 Iteration: 00150 - cost: 0.69319 - accuracy: 0.50444 Iteration: 00200 - cost: 0.69307 - accuracy: 0.50444 Iteration: 00250 - cost: 0.69295 - accuracy: 0.50444 Iteration: 00300 - cost: 0.69284 - accuracy: 0.50444 Iteration: 00350 - cost: 0.69272 - accuracy: 0.50444 Iteration: 00400 - cost: 0.69260 - accuracy: 0.50444 Iteration: 00450 - cost: 0.69249 - accuracy: 0.50444 Iteration: 00500 - cost: 0.69238 - accuracy: 0.50444 Iteration: 00550 - cost: 0.69228 - accuracy: 0.50444 Iteration: 00600 - cost: 0.69217 - accuracy: 0.50444 Iteration: 00650 - cost: 0.69206 - accuracy: 0.50444 Iteration: 00700 - cost: 0.69194 - accuracy: 0.50444 Iteration: 00750 - cost: 0.69182 - accuracy: 0.50444 Iteration: 00800 - cost: 0.69170 - accuracy: 0.50444 Iteration: 00850 - cost: 0.69156 - accuracy: 0.50444 Iteration: 00900 - 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调用一次 full_forward_propagation()，在测试集上评估训练好的模型。
# prediction Y_test_hat, _ = full_forward_propagation(np.transpose(X_test), params_values, NN_ARCHITECTURE)
# accuracy achieved on the test set acc_test = get_accuracy_value(Y_test_hat, np.transpose(y_test.reshape((y_test.shape[0], 1)))) print("Test set accuracy: {:.2f}".format(acc_test))
Test set accuracy: 0.98
