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			581 строка
		
	
	
		
			23 KiB
		
	
	
	
		
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			581 строка
		
	
	
		
			23 KiB
		
	
	
	
		
			Markdown
		
	
# Отчет по лабораторной работе №1
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Пивоваров Я.В., Сидора Д.А., А-02-22
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## 1. В среде Google Colab создание нового блокнота.
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```
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import os
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os.chdir('/content/drive/MyDrive/Colab Notebooks')
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```
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* Импорт библиотек и модулей
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```
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from tensorflow import keras
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import matplotlib.pyplot as plt
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import numpy as np
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import sklearn
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```
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## 2. Загрузка и рассмотрение набора данных 
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```
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from keras.datasets import mnist
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(X_train, y_train), (X_test, y_test) = mnist.load_data()
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```
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## 3. Разбиение набора данных на обучающий и тестовый.
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```
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from sklearn.model_selection import train_test_split
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```
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* Объединение в один набор.
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```
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X = np.concatenate((X_train, X_test))
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y = np.concatenate((y_train, y_test))
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```
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* Разбиение по вариантам. (4 бригада -> k=4*4-1)
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```
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X_train, X_test, y_train, y_test = train_test_split(X, y,test_size = 10000,train_size = 60000, random_state = 15)
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```
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* Вывод размерностей.
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```
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print('Shape of X train:', X_train.shape)
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print('Shape of y train:', y_train.shape)
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```
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> Shape of X train: (60000, 28, 28)
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> Shape of y train: (60000,) 
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## 4. Вывод обучающих данных.
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* Выведем первые четыре элемента обучающих данных.
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```
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plt.figure(figsize=(10, 3))
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for i in range(4):
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    plt.subplot(1, 4, i + 1)
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    plt.imshow(X_train[i], cmap='gray')
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    plt.title(f'Label: {y_train[i]}')
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    plt.axis('off')
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plt.tight_layout()
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plt.show()
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```
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## 5. Предобработка данных.
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* Развернем каждое изображение в вектор.
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```
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num_pixels = X_train.shape[1] * X_train.shape[2]
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X_train = X_train.reshape(X_train.shape[0], num_pixels) / 255
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X_test = X_test.reshape(X_test.shape[0], num_pixels) / 255
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print('Shape of transformed X train:', X_train.shape)
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```
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> Shape of transformed X train: (60000, 784) 
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* Переведем метки в one-hot.
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```
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from keras.utils import to_categorical
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y_train = to_categorical(y_train)
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y_test = to_categorical(y_test)
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print('Shape of transformed y train:', y_train.shape)
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num_classes = y_train.shape[1]
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```
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> Shape of transformed y train: (60000, 10) 
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## 6. Реализация и обучение однослойной нейронной сети.
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```
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from keras.models import Sequential
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from keras.layers import Dense
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```
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* Создаем модель - объявляем ее объектом класса Sequential, добавляем выходной слой.
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```
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model = Sequential()
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model.add(Dense(units=num_classes, activation='softmax'))
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```
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* Компилируем модель.
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```
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model.compile(loss='categorical_crossentropy', optimizer='sgd', metrics=['accuracy'])
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print(model.summary())
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```
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>Model: "sequential"
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>┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
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>┃ Layer (type)                    ┃ Output Shape           ┃       Param # ┃
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>┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
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>│ dense (Dense)                   │ ?                      │   0 (unbuilt) │
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>└─────────────────────────────────┴────────────────────────┴───────────────┘
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> Total params: 0 (0.00 B)
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> Trainable params: 0 (0.00 B)
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> Non-trainable params: 0 (0.00 B)
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>None
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* Обучаем модель.
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```
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H = model.fit(X_train, y_train, validation_split=0.1, epochs=50)
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```
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* Выводим график функции ошибки
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```
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plt.plot(H.history['loss'])
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plt.plot(H.history['val_loss'])
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plt.grid()
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plt.xlabel('Epochs')
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plt.ylabel('loss')
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plt.legend(['train_loss', 'val_loss'])
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plt.title('Loss by epochs')
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plt.show()
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```
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## 7. Применение модели к тестовым данным.
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```
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scores = model.evaluate(X_test, y_test)
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print('Loss on test data:', scores[0])
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print('Accuracy on test data:', scores[1])
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```
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>accuracy: 0.9313 - loss: 0.2648
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>Loss on test data: 0.2729383409023285
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>Accuracy on test data: 0.9290000200271606
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## 8. Добавление одного скрытого слоя.
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* При 100 нейронах в скрытом слое.
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```
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model100 = Sequential()
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model100.add(Dense(units=100,input_dim=num_pixels, activation='sigmoid'))
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model100.add(Dense(units=num_classes, activation='softmax'))
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model100.compile(loss='categorical_crossentropy', optimizer='sgd', metrics=['accuracy']
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print(model100.summary())
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```
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>Model: "sequential_1"
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>┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
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>┃ Layer (type)                    ┃ Output Shape           ┃       Param # ┃
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>┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
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>│ dense_1 (Dense)                 │ (None, 100)            │        78,500 │
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>├─────────────────────────────────┼────────────────────────┼───────────────┤
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>│ dense_2 (Dense)                 │ (None, 10)             │         1,010 │
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>└─────────────────────────────────┴────────────────────────┴───────────────┘
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> Total params: 79,510 (310.59 KB)
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> Trainable params: 79,510 (310.59 KB)
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> Non-trainable params: 0 (0.00 B)
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>None
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* Обучение модели.
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```
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H = model100.fit(X_train, y_train, validation_split=0.1, epochs=50)
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```
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* График функции ошибки.
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```
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plt.plot(H.history['loss'])
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plt.plot(H.history['val_loss'])
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plt.grid()
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plt.xlabel('Epochs')
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plt.ylabel('loss')
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plt.legend(['train_loss', 'val_loss'])
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plt.title('Loss by epochs')
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plt.show()
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```
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```
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scores = model100.evaluate(X_test, y_test)
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print('Loss on test data:', scores[0])
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print('Accuracy on test data:', scores[1])
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```
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>accuracy: 0.9500 - loss: 0.1884
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>Loss on test data: 0.1930633932352066
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>Accuracy on test data: 0.9473999738693237
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* При 300 нейронах в скрытом слое.
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```
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model300 = Sequential()
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model300.add(Dense(units=300,input_dim=num_pixels, activation='sigmoid'))
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model300.add(Dense(units=num_classes, activation='softmax'))
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model300.compile(loss='categorical_crossentropy', optimizer='sgd', metrics=['accuracy'])
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print(model300.summary())
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```
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>Model: "sequential_2"
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>┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
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>┃ Layer (type)                    ┃ Output Shape           ┃       Param # ┃
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>┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
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>│ dense_3 (Dense)                 │ (None, 300)            │       235,500 │
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>├─────────────────────────────────┼────────────────────────┼───────────────┤
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>│ dense_4 (Dense)                 │ (None, 10)             │         3,010 │
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>└─────────────────────────────────┴────────────────────────┴───────────────┘
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> Total params: 238,510 (931.68 KB)
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> Trainable params: 238,510 (931.68 KB)
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> Non-trainable params: 0 (0.00 B)
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>None
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* Обучение модели.
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```
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H = model300.fit(X_train, y_train, validation_split=0.1, epochs=50)
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```
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* Вывод графиков функции ошибки.
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```
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plt.plot(H.history['loss'])
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plt.plot(H.history['val_loss'])
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plt.grid()
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plt.xlabel('Epochs')
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plt.ylabel('loss')
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plt.legend(['train_loss', 'val_loss'])
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plt.title('Loss by epochs')
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plt.show()
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```
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```
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scores = model300.evaluate(X_test, y_test)
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print('Loss on test data:', scores[0])
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print('Accuracy on test data:', scores[1])
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```
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>accuracy: 0.9444 - loss: 0.2126
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>Loss on test data: 0.2181043177843094
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>Accuracy on test data: 0.9419999718666077
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* При 500 нейронах в скрытом слое.
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```
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model500 = Sequential()
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model500.add(Dense(units=500,input_dim=num_pixels, activation='sigmoid'))
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model500.add(Dense(units=num_classes, activation='softmax'))
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model500.compile(loss='categorical_crossentropy', optimizer='sgd', metrics=['accuracy'])
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print(model500.summary())
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```
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>Model: "sequential_3"
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>┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
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>┃ Layer (type)                    ┃ Output Shape           ┃       Param # ┃
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>┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
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>│ dense_5 (Dense)                 │ (None, 500)            │       392,500 │
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>├─────────────────────────────────┼────────────────────────┼───────────────┤
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>│ dense_6 (Dense)                 │ (None, 10)             │         5,010 │
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>└─────────────────────────────────┴────────────────────────┴───────────────┘
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> Total params: 397,510 (1.52 MB)
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> Trainable params: 397,510 (1.52 MB)
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> Non-trainable params: 0 (0.00 B)
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>None
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* Обучение модели.
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```
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H = model500.fit(X_train, y_train, validation_split=0.1, epochs=50)
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```
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* Вывод графиков функции ошибки.
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```
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plt.plot(H.history['loss'])
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plt.plot(H.history['val_loss'])
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plt.grid()
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plt.xlabel('Epochs')
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plt.ylabel('loss')
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plt.legend(['train_loss', 'val_loss'])
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plt.title('Loss by epochs')
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plt.show()
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```
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```
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scores = model500.evaluate(X_test, y_test)
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print('Loss on test data:', scores[0])
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print('Accuracy on test data:', scores[1])
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```
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>accuracy: 0.9401 - loss: 0.2261
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>Loss on test data: 0.2324201464653015
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>Accuracy on test data: 0.9376000165939331
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Как мы видим, лучшая метрика получилась при архитектуре со 100 нейронами в скрытом слое:
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Ошибка на тестовых данных: 0.1930633932352066
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Точность тестовых данных: 0.9473999738693237
 | 
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## 9. Добавление второго скрытого слоя.
 | 
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* При 50 нейронах во втором скрытом слое.
 | 
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```
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model10050 = Sequential()
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model10050.add(Dense(units=100,input_dim=num_pixels, activation='sigmoid'))
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model10050.add(Dense(units=50,activation='sigmoid'))
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model10050.add(Dense(units=num_classes, activation='softmax'))
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model10050.compile(loss='categorical_crossentropy', optimizer='sgd', metrics=['accuracy'])
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print(model10050.summary())
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						|
```
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						|
 | 
						|
>Model: "sequential_4"
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>┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
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>┃ Layer (type)                    ┃ Output Shape           ┃       Param # ┃
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						|
>┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
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>│ dense_7 (Dense)                 │ (None, 100)            │        78,500 │
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						|
>├─────────────────────────────────┼────────────────────────┼───────────────┤
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>│ dense_8 (Dense)                 │ (None, 50)             │         5,050 │
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						|
>├─────────────────────────────────┼────────────────────────┼───────────────┤
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>│ dense_9 (Dense)                 │ (None, 10)             │           510 │
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						|
>└─────────────────────────────────┴────────────────────────┴───────────────┘
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						|
> Total params: 84,060 (328.36 KB)
 | 
						|
> Trainable params: 84,060 (328.36 KB)
 | 
						|
> Non-trainable params: 0 (0.00 B)
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						|
>None
 | 
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* Обучаем модель.
 | 
						|
```
 | 
						|
H = model10050.fit(X_train, y_train, validation_split=0.1, epochs=50)
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						|
```
 | 
						|
 | 
						|
* Выводим график функции ошибки.
 | 
						|
```
 | 
						|
plt.plot(H.history['loss'])
 | 
						|
plt.plot(H.history['val_loss'])
 | 
						|
plt.grid()
 | 
						|
plt.xlabel('Epochs')
 | 
						|
plt.ylabel('loss')
 | 
						|
plt.legend(['train_loss', 'val_loss'])
 | 
						|
plt.title('Loss by epochs')
 | 
						|
plt.show()
 | 
						|
```
 | 
						|
 | 
						|

 | 
						|
 | 
						|
```
 | 
						|
scores = model10050.evaluate(X_test, y_test)
 | 
						|
print('Loss on test data:', scores[0])
 | 
						|
print('Accuracy on test data:', scores[1])
 | 
						|
```
 | 
						|
 | 
						|
>accuracy: 0.9476 - loss: 0.1931
 | 
						|
>Loss on test data: 0.1974852979183197
 | 
						|
>Accuracy on test data: 0.9449999928474426
 | 
						|
 | 
						|
* При 100 нейронах во втором скрытом слое.
 | 
						|
```
 | 
						|
model100100 = Sequential()
 | 
						|
model100100.add(Dense(units=100,input_dim=num_pixels, activation='sigmoid'))
 | 
						|
model100100.add(Dense(units=100,activation='sigmoid'))
 | 
						|
model100100.add(Dense(units=num_classes, activation='softmax'))
 | 
						|
 | 
						|
model100100.compile(loss='categorical_crossentropy', optimizer='sgd', metrics=['accuracy'])
 | 
						|
 | 
						|
print(model100100.summary())
 | 
						|
```
 | 
						|
 | 
						|
>Model: "sequential_5"
 | 
						|
>┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
 | 
						|
>┃ Layer (type)                    ┃ Output Shape           ┃       Param # ┃
 | 
						|
>┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
 | 
						|
>│ dense_10 (Dense)                │ (None, 100)            │        78,500 │
 | 
						|
>├─────────────────────────────────┼────────────────────────┼───────────────┤
 | 
						|
>│ dense_11 (Dense)                │ (None, 100)            │        10,100 │
 | 
						|
>├─────────────────────────────────┼────────────────────────┼───────────────┤
 | 
						|
>│ dense_12 (Dense)                │ (None, 10)             │         1,010 │
 | 
						|
>└─────────────────────────────────┴────────────────────────┴───────────────┘
 | 
						|
> Total params: 89,610 (350.04 KB)
 | 
						|
> Trainable params: 89,610 (350.04 KB)
 | 
						|
> Non-trainable params: 0 (0.00 B)
 | 
						|
>None
 | 
						|
 | 
						|
* Обучаем модель.
 | 
						|
```
 | 
						|
H = model100100.fit(X_train, y_train, validation_split=0.1, epochs=50)
 | 
						|
```
 | 
						|
 | 
						|
* Выводим график функции ошибки.
 | 
						|
```
 | 
						|
plt.plot(H.history['loss'])
 | 
						|
plt.plot(H.history['val_loss'])
 | 
						|
plt.grid()
 | 
						|
plt.xlabel('Epochs')
 | 
						|
plt.ylabel('loss')
 | 
						|
plt.legend(['train_loss', 'val_loss'])
 | 
						|
plt.title('Loss by epochs')
 | 
						|
plt.show()
 | 
						|
```
 | 
						|
 | 
						|

 | 
						|
 | 
						|
```
 | 
						|
scores = model100100.evaluate(X_test, y_test)
 | 
						|
print('Loss on test data:', scores[0])
 | 
						|
print('Accuracy on test data:', scores[1])
 | 
						|
```
 | 
						|
 | 
						|
>accuracy: 0.9485 - loss: 0.1814
 | 
						|
>Loss on test data: 0.18734164535999298
 | 
						|
>Accuracy on test data: 0.9470000267028809
 | 
						|
 | 
						|
## 10. Результаты исследования архитектур нейронной сети.
 | 
						|
 | 
						|
| Количество скрытых слоев | Количество нейронов в первом скрытом слое | Количество нейронов во втором скрытом слое | Значение метрики качества классификации |
 | 
						|
|--------------------------|-------------------------------------------|--------------------------------------------|------------------------------------------|
 | 
						|
| 0                        | -                                         | -                                          | 0.9290000200271606                       |
 | 
						|
| 1                        | 100                                       | -                                          | 0.9473999738693237                       |
 | 
						|
| 1                        | 300                                       | -                                          | 0.9419999718666077                       |
 | 
						|
| 1                        | 500                                       | -                                          | 0.9376000165939331                       |
 | 
						|
| 2                        | 100                                       | 50                                         | 0.9449999928474426                       |
 | 
						|
| 2                        | 100                                       | 100                                        | 0.9470000267028809                       |
 | 
						|
 | 
						|
Анализ результатов позволяет сделать вывод, что наилучшее качество классификации (порядка 94.7%) достигается при использовании моделей с относительно простой архитектурой. Наибольшую точность показали однослойная сеть со 100 нейронами и двухслойная конфигурация с 100 и 100 нейронами соответственно.
 | 
						|
 | 
						|
## 11. Сохранение наилучшей модели на диск.
 | 
						|
```
 | 
						|
model100.save('/content/drive/MyDrive/Colab Notebooks/best_model/model100.keras')
 | 
						|
```
 | 
						|
 | 
						|
* Загрузка лучшей модели с диска.
 | 
						|
```
 | 
						|
from keras.models import load_model
 | 
						|
model = load_model('/content/drive/MyDrive/Colab Notebooks/best_model/model100.keras')
 | 
						|
```
 | 
						|
 | 
						|
## 12. Вывод тестовых изображений и результатов распознаваний.
 | 
						|
```
 | 
						|
n = 222
 | 
						|
result = model.predict(X_test[n:n+1])
 | 
						|
print('NN output:', result)
 | 
						|
plt.imshow(X_test[n].reshape(28,28), cmap=plt.get_cmap('gray'))
 | 
						|
plt.show()
 | 
						|
print('Real mark: ', str(np.argmax(y_test[n])))
 | 
						|
print('NN answer: ', str(np.argmax(result)))
 | 
						|
```
 | 
						|
 | 
						|
>NN output: [[3.7926259e-03 9.0994104e-07 2.0981293e-04 2.9478846e-02 2.0727816e-06
 | 
						|
>  9.6508384e-01 7.6052487e-07 5.7595258e-05 1.0619552e-03 3.1140275e-04]]
 | 
						|

 | 
						|
>Real mark:  5
 | 
						|
>NN answer:  5
 | 
						|
 | 
						|
```
 | 
						|
n = 123
 | 
						|
result = model.predict(X_test[n:n+1])
 | 
						|
print('NN output:', result)
 | 
						|
plt.imshow(X_test[n].reshape(28,28), cmap=plt.get_cmap('gray'))
 | 
						|
plt.show()
 | 
						|
print('Real mark: ', str(np.argmax(y_test[n])))
 | 
						|
print('NN answer: ', str(np.argmax(result)))
 | 
						|
```
 | 
						|
 | 
						|
>NN output: [[7.6678516e-06 2.1507578e-06 2.5754166e-04 6.3994766e-04 2.8644723e-04
 | 
						|
> 2.3038971e-04 1.0776109e-05 2.3045135e-05 9.9186021e-01 6.6818334e-03]]
 | 
						|

 | 
						|
>Real mark:  8
 | 
						|
>NN answer:  8
 | 
						|
 | 
						|
## 13. Тестирование на собственных изображениях.
 | 
						|
* Загрузка 1 собственного изображения.
 | 
						|
```
 | 
						|
from PIL import Image
 | 
						|
file_data = Image.open('test.png')
 | 
						|
file_data = file_data.convert('L') # перевод в градации серого
 | 
						|
test_img = np.array(file_data)
 | 
						|
```
 | 
						|
 | 
						|
* Вывод собственного изображения.
 | 
						|
```
 | 
						|
plt.imshow(test_img, cmap=plt.get_cmap('gray'))
 | 
						|
plt.show()
 | 
						|
```
 | 
						|
 | 
						|

 | 
						|
 | 
						|
* Предобработка.
 | 
						|
```
 | 
						|
test_img = test_img / 255
 | 
						|
test_img = test_img.reshape(1, num_pixels)
 | 
						|
```
 | 
						|
 | 
						|
* Распознавание.
 | 
						|
```
 | 
						|
result = model.predict(test_img)
 | 
						|
print('I think it\'s ', np.argmax(result))
 | 
						|
```
 | 
						|
>I think it's  2
 | 
						|
 | 
						|
* Тест 2 изображения.
 | 
						|
```
 | 
						|
from PIL import Image
 | 
						|
file2_data = Image.open('test2.png')
 | 
						|
file2_data = file2_data.convert('L') # перевод в градации серого
 | 
						|
test2_img = np.array(file2_data)
 | 
						|
```
 | 
						|
 | 
						|
```
 | 
						|
plt.imshow(test2_img, cmap=plt.get_cmap('gray'))
 | 
						|
plt.show()
 | 
						|
```
 | 
						|
 | 
						|

 | 
						|
 | 
						|
```
 | 
						|
test2_img = test2_img / 255
 | 
						|
test2_img = test2_img.reshape(1, num_pixels)
 | 
						|
```
 | 
						|
 | 
						|
```
 | 
						|
result_2 = model.predict(test2_img)
 | 
						|
print('I think it\'s ', np.argmax(result_2))
 | 
						|
```
 | 
						|
 | 
						|
>I think it's  8
 | 
						|
 | 
						|
Сеть корректно распознала цифры на изображениях.
 | 
						|
 | 
						|
## 14. Тестирование на повернутых изображениях.
 | 
						|
```
 | 
						|
from PIL import Image
 | 
						|
file90_data = Image.open('test90.png')
 | 
						|
file90_data = file90_data.convert('L') # перевод в градации серого
 | 
						|
test90_img = np.array(file90_data)
 | 
						|
 | 
						|
plt.imshow(test90_img, cmap=plt.get_cmap('gray'))
 | 
						|
plt.show()
 | 
						|
```
 | 
						|
 | 
						|

 | 
						|
 | 
						|
```
 | 
						|
test90_img = test90_img / 255
 | 
						|
test90_img = test90_img.reshape(1, num_pixels)
 | 
						|
 | 
						|
result_3 = model.predict(test90_img)
 | 
						|
print('I think it\'s ', np.argmax(result_3))
 | 
						|
```
 | 
						|
 | 
						|
>I think it's  8
 | 
						|
 | 
						|
```
 | 
						|
from PIL import Image
 | 
						|
file902_data = Image.open('test90_2.png')
 | 
						|
file902_data = file902_data.convert('L') # перевод в градации серого
 | 
						|
test902_img = np.array(file902_data)
 | 
						|
 | 
						|
plt.imshow(test902_img, cmap=plt.get_cmap('gray'))
 | 
						|
plt.show()
 | 
						|
```
 | 
						|
 | 
						|

 | 
						|
 | 
						|
```
 | 
						|
test902_img = test902_img / 255
 | 
						|
test902_img = test902_img.reshape(1, num_pixels)
 | 
						|
 | 
						|
result_4 = model.predict(test902_img)
 | 
						|
print('I think it\'s ', np.argmax(result_4))
 | 
						|
```
 | 
						|
 | 
						|
>I think it's  4
 | 
						|
 | 
						|
Сеть не распознала цифры на изображениях корректно. |