吴恩达471机器学习入门课程2第1周——手写数字识别（0和1）_吴恩达手写数字识别

使用神经网络来识别手写数字 0 和 1。

问题描述

在这个练习中，您将使用神经网络来识别手写数字“0”和“1”。这是一个二元分类任务。
自动手写数字识别在今天被广泛使用——从识别邮件信封上的邮政编码到识别银行支票上写的金额。
在未来的任务中，您将扩展此网络以识别所有10个数字（0-9）。

这个练习将向您展示如何使用您所学的方法来完成这个分类任务。

1.导入模块

import numpy as np
import tensorflow as tf
from tensorflow.python import keras
from keras.models import Sequential
from keras.layers import Dense
import matplotlib.pyplot as plt
from autils import *
%matplotlib inline

import logging
logging.getLogger("tensorflow").setLevel(logging.ERROR)
tf.autograph.set_verbosity(0)
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2. 数据集

您将从加载此任务的数据集开始。

• 下面显示的load_data()函数将数据加载到变量X和y中。
• 该数据集包含1000个手写数字1的训练示例，仅限于0和1。
  • 每个训练示例都是数字的20像素x 20像素灰度图像。
    • 每个像素由浮点数表示，表示该位置的灰度强度。
    • 20x20像素网格被“展开”为400维向量。
    • 每个训练示例成为我们的数据矩阵X中的一行。
    • 这给了我们一个1000 x 400的矩阵X，其中每一行都是手写数字图像的训练示例。
  • 训练集的第二部分是一个1000 x 1的向量y，它包含训练集的标签。
    • 如果图像是数字0，则y = 0，如果图像是数字1，则y = 1。

x,y = load_data()
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2.1 数据可视化

import warnings
warnings.simplefilter(action='ignore', category=FutureWarning)


m, n = x.shape

fig, axes = plt.subplots(8,8, figsize=(8,8))
fig.tight_layout(pad=0.1)

for i,ax in enumerate(axes.flat):
    random_index = np.random.randint(1000)
    X_random_reshaped = x[random_index].reshape((20,20)).T
    ax.imshow(X_random_reshaped, cmap='gray')
    ax.set_title(f"id:{random_index},{y[random_index,0]}")
    ax.set_axis_off()
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3 模型展示

您将在本作业中使用的神经网络如下图所示。

• 三个全连接层，激活函数为sigmoid
  • 回想一下，我们的输入是数字图像的像素值。
  • 由于图像的大小为 $20\times 20$，这给了我们 $400$ 的输入
• 这些参数的维度大小适用于神经网络，第 1 层神经元为 25个 ，第 2 层神经元为 15个，第 3 层输出层为 1 个神经元。
  • 回想一下，这些参数的尺寸确定如下：
    • 如果网络在一层中有 $s_{in}$ 单位，在下一层中有 $s_{out}$ 单位，则
      • $W$▁的维数为▁$s_{in}▁\times ▁s_{out}$。
      • $b$ 将是一个包含 $s_{out}$ 元素的向量
  • 因此,W和b的形状是
    • layer1：W1的形状是（400，25），b1的形状是（25，）
    • layer2：W2的形状是（25，15），b2的形状是：（15，）
    • layer3: W3 的形状是 (15, 1) b3 的形状是: (1,)

Note: 偏置向量b可以表示为一维（n）或二维（n，1）数组。Tensorflow使用一维表示，本实验室将保持该约定。

下面，使用Keras顺序模型和具有sigmoid激活的密集层来构建上述网络。

tf.random.set_seed(1234)
model = Sequential(
    [
        tf.keras.Input(shape=(400,)),
        Dense(25,activation="sigmoid",name="layer1"),
        Dense(15,activation="sigmoid",name="layer2"),
        Dense(1,activation="sigmoid",name="layer3")
    ]
)
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model.summary()
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Model: "sequential"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 layer1 (Dense)              (None, 25)                10025     
                                                                 
 layer2 (Dense)              (None, 15)                390       
                                                                 
 layer3 (Dense)              (None, 1)                 16        
                                                                 
=================================================================
Total params: 10,431
Trainable params: 10,431
Non-trainable params: 0
_________________________________________________________________
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w1,b1 = model.get_layer('layer1').get_weights()
w2,b2 = model.get_layer('layer2').get_weights()
w3,b3 = model.get_layer('layer3').get_weights()
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model.compile(
    loss=tf.keras.losses.BinaryCrossentropy(),
    optimizer= tf.keras.optimizers.Adam(learning_rate=0.001)
)
model.fit(
    x,y,
    epochs=20
)
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Epoch 1/20
32/32 [==============================] - 1s 2ms/step - loss: 0.6223
Epoch 2/20
32/32 [==============================] - 0s 2ms/step - loss: 0.4593
Epoch 3/20
32/32 [==============================] - 0s 2ms/step - loss: 0.3129
Epoch 4/20
32/32 [==============================] - 0s 2ms/step - loss: 0.2148
Epoch 5/20
32/32 [==============================] - 0s 2ms/step - loss: 0.1557
Epoch 6/20
32/32 [==============================] - 0s 2ms/step - loss: 0.1193
Epoch 7/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0956
Epoch 8/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0787
Epoch 9/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0665
Epoch 10/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0571
Epoch 11/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0499
Epoch 12/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0440
Epoch 13/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0394
Epoch 14/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0355
Epoch 15/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0323
Epoch 16/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0297
Epoch 17/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0274
Epoch 18/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0255
Epoch 19/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0238
Epoch 20/20
32/32 [==============================] - 0s 2ms/step - loss: 0.0224





<keras.callbacks.History at 0x17a7a949ca0>
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输入的是1000/time400数据，也就是说每个数据是400个像素点的灰度值。那预测也是输出400个像素点的灰度值

prediction = np.zeros(x.shape[0])
yhat = np.zeros(x.shape[0])
for i in range(x.shape[0]):
    prediction[i] = model.predict(x[i].reshape(1,400))
    if prediction[i] >0.5:
        yhat[i] = 1
    else:
        yhat[i] = 0
    print(f"num:{i},prediction:{prediction[i]},yhat:{yhat[i]}")
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1/1 [==============================] - 0s 30ms/step
num:0,prediction:0.017245078459382057,yhat:0.0
1/1 [==============================] - 0s 31ms/step
num:1,prediction:0.017561491578817368,yhat:0.0
1/1 [==============================] - 0s 36ms/step
num:2,prediction:0.018371105194091797,yhat:0.0
1/1 [==============================] - 0s 28ms/step
num:3,prediction:0.016776276752352715,yhat:0.0
1/1 [==============================] - 0s 33ms/step
num:4,prediction:0.016123982146382332,yhat:0.0
1/1 [==============================] - 0s 35ms/step
num:5,prediction:0.01637193374335766,yhat:0.0
1/1 [==============================] - 0s 30ms/step
num:6,prediction:0.016457650810480118,yhat:0.0
1/1 [==============================] - 0s 29ms/step
num:7,prediction:0.022780779749155045,yhat:0.0
1/1 [==============================] - 0s 30ms/step
num:8,prediction:0.01629982516169548,yhat:0.0
1/1 [==============================] - 0s 29ms/step
num:9,prediction:0.01717321388423443,yhat:0.0
1/1 [==============================] - 0s 32ms/step
num:10,prediction:0.016451770439743996,yhat:0.0
1/1 [==============================] - 0s 36ms/step
num:11,prediction:0.0167677141726017,yhat:0.0
1/1 [==============================] - 0s 30ms/step
num:12,prediction:0.016313461586833,yhat:0.0
1/1 [==============================] - 0s 29ms/step
num:13,prediction:0.01943032070994377,yhat:0.0
1/1 [==============================] - 0s 32ms/step
num:14,prediction:0.01611424796283245,yhat:0.0
1/1 [==============================] - 0s 33ms/step
num:15,prediction:0.01825297810137272,yhat:0.0
1/1 [==============================] - 0s 37ms/step
num:16,prediction:0.016284190118312836,yhat:0.0
1/1 [==============================] - 0s 29ms/step
num:17,prediction:0.016130782663822174,yhat:0.0
1/1 [==============================] - 0s 35ms/step
num:18,prediction:0.01709396205842495,yhat:0.0
1/1 [==============================] - 0s 29ms/step
num:19,prediction:0.016696887090802193,yhat:0.0
1/1 [==============================] - 0s 31ms/step
num:20,prediction:0.01634596846997738,yhat:0.0
1/1 [==============================] - 0s 28ms/step
num:21,prediction:0.01664787344634533,yhat:0.0
1/1 [==============================] - 0s 35ms/step
num:22,prediction:0.016392642632126808,yhat:0.0
1/1 [==============================] - 0s 30ms/step
num:23,prediction:0.02348409779369831,yhat:0.0
1/1 [==============================] - 0s 34ms/step
num:24,prediction:0.017231397330760956,yhat:0.0
1/1 [==============================] - 0s 30ms/step
num:25,prediction:0.016674473881721497,yhat:0.0
1/1 [==============================] - 0s 32ms/step
num:26,prediction:0.022125374525785446,yhat:0.0
1/1 [==============================] - 0s 36ms/step
num:27,prediction:0.017969287931919098,yhat:0.0
1/1 [==============================] - 0s 33ms/step
num:28,prediction:0.02634265273809433,yhat:0.0
1/1 [==============================] - 0s 31ms/step
num:29,prediction:0.016846399754285812,yhat:0.0
1/1 [==============================] - 0s 31ms/step
num:30,prediction:0.031125672161579132,yhat:0.0
1/1 [==============================] - 0s 30ms/step
num:31,prediction:0.016067367047071457,yhat:0.0
1/1 [==============================] - 0s 29ms/step
num:32,prediction:0.016007831320166588,yhat:0.0
1/1 [==============================] - 0s 34ms/step
num:33,prediction:0.016938723623752594,yhat:0.0
1/1 [==============================] - 0s 42ms/step
num:34,prediction:0.01603429950773716,yhat:0.0
1/1 [==============================] - 0s 37ms/step
num:35,prediction:0.016739122569561005,yhat:0.0
1/1 [==============================] - 0s 29ms/step
num:36,prediction:0.016892068088054657,yhat:0.0
1/1 [==============================] - 0s 41ms/step
num:37,prediction:0.016361510381102562,yhat:0.0
1/1 [==============================] - 0s 34ms/step
num:38,prediction:0.016079727560281754,yhat:0.0
1/1 [==============================] - 0s 36ms/step
num:39,prediction:0.01598520390689373,yhat:0.0
1/1 [==============================] - 0s 41ms/step
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1/1 [==============================] - 0s 43ms/step
num:41,prediction:0.01620468869805336,yhat:0.0
1/1 [==============================] - 0s 37ms/step
num:42,prediction:0.016878359019756317,yhat:0.0
1/1 [==============================] - 0s 30ms/step
num:43,prediction:0.017137937247753143,yhat:0.0
1/1 [==============================] - 0s 32ms/step
num:44,prediction:0.016577575355768204,yhat:0.0
1/1 [==============================] - 0s 33ms/step
num:45,prediction:0.01610025390982628,yhat:0.0
1/1 [==============================] - 0s 31ms/step
num:46,prediction:0.016063405200839043,yhat:0.0
1/1 [==============================] - 0s 34ms/step
num:47,prediction:0.016535844653844833,yhat:0.0
1/1 [==============================] - 0s 31ms/step
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1/1 [==============================] - 0s 31ms/step
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1/1 [==============================] - 0s 29ms/step
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1/1 [==============================] - 0s 31ms/step
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1/1 [==============================] - 0s 34ms/step
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1/1 [==============================] - 0s 28ms/step
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1/1 [==============================] - 0s 30ms/step
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1/1 [==============================] - 0s 33ms/step
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1/1 [==============================] - 0s 31ms/step
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1/1 [==============================] - 0s 32ms/step
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1/1 [==============================] - 0s 30ms/step
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1/1 [==============================] - 0s 31ms/step
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1/1 [==============================] - 0s 31ms/step
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1/1 [==============================] - 0s 33ms/step
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1/1 [==============================] - 0s 28ms/step
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1/1 [==============================] - 0s 34ms/step
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1/1 [==============================] - 0s 35ms/step
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1/1 [==============================] - 0s 36ms/step
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1/1 [==============================] - 0s 40ms/step
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1/1 [==============================] - 0s 32ms/step
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1/1 [==============================] - 0s 35ms/step
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1/1 [==============================] - 0s 29ms/step
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1/1 [==============================] - 0s 30ms/step
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1/1 [==============================] - 0s 36ms/step
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1/1 [==============================] - 0s 31ms/step
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1/1 [==============================] - 0s 32ms/step
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1/1 [==============================] - 0s 29ms/step
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1/1 [==============================] - 0s 46ms/step
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1/1 [==============================] - 0s 36ms/step
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1/1 [==============================] - 0s 34ms/step
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1/1 [==============================] - 0s 31ms/step
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1/1 [==============================] - 0s 31ms/step
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1/1 [==============================] - 0s 36ms/step
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1/1 [==============================] - 0s 31ms/step
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1/1 [==============================] - 0s 37ms/step
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1/1 [==============================] - 0s 33ms/step
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1/1 [==============================] - 0s 29ms/step
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1/1 [==============================] - 0s 50ms/step
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1/1 [==============================] - 0s 36ms/step
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1/1 [==============================] - 0s 33ms/step
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1/1 [==============================] - 0s 40ms/step
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与之前做对比

import warnings
warnings.simplefilter(action='ignore', category=FutureWarning)

m, n = x.shape

fig, axes = plt.subplots(8,8, figsize=(8,8))
fig.tight_layout(pad=0.1,rect=[0, 0.03, 1, 0.92]) #[left, bottom, right, top]

for i,ax in enumerate(axes.flat):
    random_index = np.random.randint(m)
    X_random_reshaped = x[random_index].reshape((20,20)).T
    ax.imshow(X_random_reshaped, cmap='gray')
    ax.set_title(f"{y[random_index,0]},{yhat[random_index].astype(int)}")
    ax.set_axis_off()
fig.suptitle("Label, yhat", fontsize=16)
plt.show()
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​

​