Perpectron model keras

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import numpy as np
import tensorflow.keras
# linear model
from tensorflow.keras.models import Sequential
# every neuron in the input layer is connected to each neuron in the next layer
from tensorflow.keras.layers import Dense
# adaptive learning optmization method algorithm==Stochastic gradient descent > vanilla gradient descent 
from tensorflow.keras.optimizers import Adam
import matplotlib.pyplot as plt
%matplotlib inline

import numpy as np import tensorflow.keras # linear model from tensorflow.keras.models import Sequential # every neuron in the input layer is connected to each neuron in the next layer from tensorflow.keras.layers import Dense # adaptive learning optmization method algorithm==Stochastic gradient descent > vanilla gradient descent from tensorflow.keras.optimizers import Adam import matplotlib.pyplot as plt %matplotlib inline

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# number of points to train
n_pts = 500
# to display the same random point
np.random.seed(0)
Xa = np.array([np.random.normal(13, 2, n_pts), 
               np.random.normal(12, 2, n_pts)]).T
Xb = np.array([np.random.normal(8, 2, n_pts), 
               np.random.normal(6, 2, n_pts)]).T

# dataset
# vstack : matrix concatenation vertically into a single one
X = np.vstack((Xa, Xb))
# print(X)
# labeling : bottom = 1, top = 0
y = np.matrix(np.append(np.zeros(n_pts), np.ones(n_pts))).T
# print(y)

# display points
plt.scatter(X[:n_pts, 0], X[:n_pts, 1])
plt.scatter(X[n_pts:, 0], X[n_pts:, 1])

# number of points to train n_pts = 500 # to display the same random point np.random.seed(0) Xa = np.array([np.random.normal(13, 2, n_pts), np.random.normal(12, 2, n_pts)]).T Xb = np.array([np.random.normal(8, 2, n_pts), np.random.normal(6, 2, n_pts)]).T # dataset # vstack : matrix concatenation vertically into a single one X = np.vstack((Xa, Xb)) # print(X) # labeling : bottom = 1, top = 0 y = np.matrix(np.append(np.zeros(n_pts), np.ones(n_pts))).T # print(y) # display points plt.scatter(X[:n_pts, 0], X[:n_pts, 1]) plt.scatter(X[n_pts:, 0], X[n_pts:, 1])

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<matplotlib.collections.PathCollection at 0x7f9255ef4550>

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# linear model
model = Sequential()
# creating a perceptron (one layer) with 2 inputs and 1 output based on sigmoid activation function
model.add(Dense(units = 1, input_shape = (2,), activation='sigmoid'))
# Stochastic gradient descent or error optimizer = fonction de minimisation
adam = Adam(lr = 0.1)
# loss function = fonction de coût
model.compile(adam, loss='binary_crossentropy', metrics=['accuracy'])
# training
# verbose=1
# epoch is when a model reach the total dataset in one iteration
# epoch can be divided into batch for training optimization
# shuffle to force the gradient to go to/find the minimun value
h=model.fit(x=X, y=y, verbose=0, batch_size=50, epochs=500, shuffle='true')

# linear model model = Sequential() # creating a perceptron (one layer) with 2 inputs and 1 output based on sigmoid activation function model.add(Dense(units = 1, input_shape = (2,), activation='sigmoid')) # Stochastic gradient descent or error optimizer = fonction de minimisation adam = Adam(lr = 0.1) # loss function = fonction de coût model.compile(adam, loss='binary_crossentropy', metrics=['accuracy']) # training # verbose=1 # epoch is when a model reach the total dataset in one iteration # epoch can be divided into batch for training optimization # shuffle to force the gradient to go to/find the minimun value h=model.fit(x=X, y=y, verbose=0, batch_size=50, epochs=500, shuffle='true')

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plt.plot(h.history['accuracy'])
plt.title('accuracy')
plt.xlabel('epoch')
plt.legend(['accuracy'])

plt.plot(h.history['accuracy']) plt.title('accuracy') plt.xlabel('epoch') plt.legend(['accuracy'])

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<matplotlib.legend.Legend at 0x7f91dea643c8>

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plt.plot(h.history['loss'])
plt.title('loss')
plt.xlabel('epoch')
plt.legend(['loss'])

plt.plot(h.history['loss']) plt.title('loss') plt.xlabel('epoch') plt.legend(['loss'])

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<matplotlib.legend.Legend at 0x7f91dea29898>

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# display the score / prediction of the or the model results
def plot_decision_boundary(X, y, model):
  x_span = np.linspace(min(X[:, 0]) - 1, max(X[:, 0]) + 1, 50)
  y_span = np.linspace(min(X[:, 1]) - 1, max(X[:, 1]) + 1, 50)
  # convert our point to a 50x50 matrix
  xx, yy = np.meshgrid(x_span, y_span)
  xx_, yy_  = xx.ravel(), yy.ravel() 
  grid = np.c_[xx_, yy_]
  # prediction
  pred_func = model.predict(grid)
  z = pred_func.reshape(xx.shape)
  # different probabilities found by the model for both labels : 1 and 0
  plt.contourf(xx, yy, z)

# display the score / prediction of the or the model results def plot_decision_boundary(X, y, model): x_span = np.linspace(min(X[:, 0]) - 1, max(X[:, 0]) + 1, 50) y_span = np.linspace(min(X[:, 1]) - 1, max(X[:, 1]) + 1, 50) # convert our point to a 50x50 matrix xx, yy = np.meshgrid(x_span, y_span) xx_, yy_ = xx.ravel(), yy.ravel() grid = np.c_[xx_, yy_] # prediction pred_func = model.predict(grid) z = pred_func.reshape(xx.shape) # different probabilities found by the model for both labels : 1 and 0 plt.contourf(xx, yy, z)

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plot_decision_boundary(X, y, model)
# display points
plt.scatter(X[:n_pts, 0], X[:n_pts, 1])
plt.scatter(X[n_pts:, 0], X[n_pts:, 1])

plot_decision_boundary(X, y, model) # display points plt.scatter(X[:n_pts, 0], X[:n_pts, 1]) plt.scatter(X[n_pts:, 0], X[n_pts:, 1])

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<matplotlib.collections.PathCollection at 0x7f92400f7860>

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plot_decision_boundary(X, y, model)
# display points
plt.scatter(X[:n_pts, 0], X[:n_pts, 1])
plt.scatter(X[n_pts:, 0], X[n_pts:, 1])
# display a classified single model
x = 7.5
y = 5 
point = np.array([[x,y]])
prediction = model.predict(point)
plt.plot([x], [y], marker="o", markersize=10, color="red")
print("Prediction is:", prediction)

plot_decision_boundary(X, y, model) # display points plt.scatter(X[:n_pts, 0], X[:n_pts, 1]) plt.scatter(X[n_pts:, 0], X[n_pts:, 1]) # display a classified single model x = 7.5 y = 5 point = np.array([[x,y]]) prediction = model.predict(point) plt.plot([x], [y], marker="o", markersize=10, color="red") print("Prediction is:", prediction)

Prediction is: [[0.9999938]]

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