Keras neural network example

points.py

# standard libraries in Anaconda Python

import numpy as np
import matplotlib.pyplot as plt

#keras imports - requires keras and tensorflow
import keras
from keras.models import Sequential
from keras.layers import Dense, Dropout
from keras.optimizers import RMSprop

def f(x, y):
    '''auxiliary function to categorize points into blue and orange dots'''
    return np.sin(x*np.pi*4)*np.sin(y*np.pi*4) > 0

#how many points should be shown
Nshow = 10000
#how many training points should be generated
N = 100000

#how many points of neural network output should be on one axis
M = 1024
batch_size = 512
num_classes = 2
epochs = 50

X = np.random.uniform(0, 1, size=N).reshape((-1, 2))
Y = np.array([[f(x, y), not f(x, y)] for x, y in X]).astype('float32')

#half of data is training, half is test

x_train = X[:len(X)//2]
x_test = X[len(X)//2:]

y_train = Y[:len(Y)//2]
y_test = Y[len(Y)//2:]

#we create neural network 2 x 1024 x 1024 x 2

model = Sequential()
model.add(Dense(1024, activation='relu', input_shape=(2,)))
model.add(Dropout(0.2))
model.add(Dense(1024, activation='relu'))
model.add(Dropout(0.2))
model.add(Dense(2, activation='softmax'))

model.summary()

model.compile(loss='categorical_crossentropy',
              optimizer=RMSprop(),
              metrics=['accuracy'])

# training time

history = model.fit(x_train, y_train,
                    batch_size=batch_size,
                    epochs=epochs,
                    validation_data=(x_test, y_test))

# we test how good is our neural network

score = model.evaluate(x_test, y_test, verbose=0)
print('Test loss:', score[0])
print('Test accuracy:', score[1])

data = [[[x, y] for x in np.linspace(0, 1, M)]
                                     for y in np.linspace(0, 1, M)]
data = np.array(data).reshape((-1, 2))

# now we get output to get info where network is expecting for blue points to show up

result = model.predict(data)
result = np.array([x for x, y in result])

# we plot network expectations onto the graph

plt.imshow(result.reshape(M, M))

# we divided before points into two sets, now we do it again for the sake of plot

X_red=[[x, y] for x, y in X[::N//Nshow] if f(x, y) == True]
X_blue=[[x, y] for x, y in X[::N//Nshow] if f(x, y) == False]

X_red=np.array(X_red).T
X_blue=np.array(X_blue).T

# we add initial points into plot to show part of training data

plt.scatter(X_red[0]*M, X_red[1]*M, s = 1)
plt.scatter(X_blue[0]*M, X_blue[1]*M, s = 1)

# now we show visualization of our data
plt.show()