Multiclass classificaton

In [20]:

import numpy as np
import keras
from sklearn import datasets
import matplotlib.pyplot as plt
from keras.models import Sequential
from keras.layers import Dense
from keras.optimizers import Adam
# add categorical module for multiclass cross entropy
from keras.utils.np_utils import to_categorical

import numpy as np import keras from sklearn import datasets import matplotlib.pyplot as plt from keras.models import Sequential from keras.layers import Dense from keras.optimizers import Adam # add categorical module for multiclass cross entropy from keras.utils.np_utils import to_categorical

In [21]:

# numbers of points
n_pts = 500
# coordinators of center of blob cluster
# cluster index or positions: [0, 1, 2, 3, 4] for the output label
# centers = [[-1, 1], [-1, -1], [1, -1], [1, 1], [0, 0]]
centers = [[-1, 1], [-1, -1], [1, -1]]

"""
 - make blobs() fun :  Generate isotropic Gaussian blobs for clustering.
 - n_samples : 
 - random_state : 
 - centers : center coordinators position
 - cluster_std : distance between points clustered 
"""
X, y = datasets.make_blobs(n_samples=n_pts, random_state = 123, centers=centers, cluster_std=0.4)
# print(X)
# print(y) 

# plot the dataset cluster of the 3 classes
# plot the data of coordinator index [0] i.e : [-1, 1]
plt.scatter(X[y==0, 0], X[y==0, 1])
# plot the data of coordinator index [1] i.e : [-1, -1]
plt.scatter(X[y==1, 0], X[y==1, 1])
# plot the data of coordinator index [2] i.e : [1, -1]
plt.scatter(X[y==2, 0], X[y==2, 1])
# plot the data of coordinator index [3] i.e : [1, 1]
# plt.scatter(X[y==3, 0], X[y==3, 1])
# plot the data of coordinator index [4] i.e : [0, 0]
# plt.scatter(X[y==4, 0], X[y==4, 1])
 

# numbers of points n_pts = 500 # coordinators of center of blob cluster # cluster index or positions: [0, 1, 2, 3, 4] for the output label # centers = [[-1, 1], [-1, -1], [1, -1], [1, 1], [0, 0]] centers = [[-1, 1], [-1, -1], [1, -1]] """ - make blobs() fun : Generate isotropic Gaussian blobs for clustering. - n_samples : - random_state : - centers : center coordinators position - cluster_std : distance between points clustered """ X, y = datasets.make_blobs(n_samples=n_pts, random_state = 123, centers=centers, cluster_std=0.4) # print(X) # print(y) # plot the dataset cluster of the 3 classes # plot the data of coordinator index [0] i.e : [-1, 1] plt.scatter(X[y==0, 0], X[y==0, 1]) # plot the data of coordinator index [1] i.e : [-1, -1] plt.scatter(X[y==1, 0], X[y==1, 1]) # plot the data of coordinator index [2] i.e : [1, -1] plt.scatter(X[y==2, 0], X[y==2, 1]) # plot the data of coordinator index [3] i.e : [1, 1] # plt.scatter(X[y==3, 0], X[y==3, 1]) # plot the data of coordinator index [4] i.e : [0, 0] # plt.scatter(X[y==4, 0], X[y==4, 1])

Out[21]:

<matplotlib.collections.PathCollection at 0x7f6ce3691810>

In [22]:

# printing actual labels
print(y)
# reformate the label into hot encoding form
"""
to_categorical(y, arg2)
 - y : actual label
 - arg2 : if empty => 3 classes , others the number of specified classes 
"""
y_cat = to_categorical(y, 3)
print(y_cat)

# printing actual labels print(y) # reformate the label into hot encoding form """ to_categorical(y, arg2) - y : actual label - arg2 : if empty => 3 classes , others the number of specified classes """ y_cat = to_categorical(y, 3) print(y_cat)

[2 2 2 0 1 0 0 2 2 2 1 1 0 0 1 2 2 2 2 0 2 0 1 2 1 2 0 0 2 1 1 0 0 2 1 0 2
 0 2 0 0 2 1 0 2 0 1 2 0 2 0 1 1 0 1 2 2 0 1 2 0 2 0 2 1 0 1 1 1 1 2 1 1 1
 1 1 2 1 1 2 0 1 2 2 1 0 2 1 1 2 0 0 2 1 2 2 0 1 2 0 2 1 1 2 2 0 0 1 2 1 1
 2 0 0 1 0 2 2 2 2 1 2 1 2 0 2 2 0 1 0 0 0 0 2 0 1 0 2 2 0 2 2 2 2 1 2 0 0
 0 2 1 0 2 0 0 1 1 0 2 0 0 1 1 2 2 0 2 1 2 2 2 1 1 1 2 0 0 1 0 1 2 2 1 1 2
 1 1 0 0 2 2 1 0 0 0 0 2 2 0 2 1 1 2 0 0 2 2 0 1 0 2 0 2 2 0 0 2 1 2 0 2 0
 1 1 2 0 0 0 2 1 2 2 2 0 0 1 0 2 0 2 0 2 1 1 1 2 2 1 1 1 0 1 2 1 0 1 2 2 0
 0 0 1 1 1 2 1 1 2 1 1 2 0 0 0 2 0 2 0 0 0 2 1 1 0 2 1 0 0 1 1 1 1 2 1 1 0
 0 0 2 1 1 1 0 0 0 0 0 0 0 1 2 1 2 1 0 2 0 0 1 2 0 1 2 2 2 2 2 0 1 2 0 2 1
 0 0 1 2 0 2 0 1 1 0 2 1 0 1 1 1 0 2 0 2 0 1 1 0 1 1 1 2 2 0 2 0 2 2 1 1 0
 2 2 2 1 1 1 2 2 0 1 2 1 2 0 1 2 2 2 0 1 1 1 2 0 2 0 0 2 1 1 1 2 0 1 0 0 1
 1 2 0 0 1 2 1 1 0 2 0 1 0 2 0 0 0 1 1 1 2 0 1 1 0 2 1 2 1 1 1 1 0 0 0 0 0
 2 2 1 1 0 1 0 2 2 2 2 0 0 1 1 0 0 1 1 1 2 2 1 1 1 1 0 0 2 0 1 0 1 0 1 1 2
 2 0 2 2 1 0 1 2 0 2 0 2 1 0 2 0 1 1 0]
[[0. 0. 1.]
 [0. 0. 1.]
 [0. 0. 1.]
 ...
 [0. 1. 0.]
 [0. 1. 0.]
 [1. 0. 0.]]

In [23]:

# create NN model
model = Sequential()
# create the layers with 'softmax' for multiclass classfication
# model.add(Dense(5, input_shape=(2,), activation='softmax'))
# height of the layer : 3 (2 inputs values + 1 bias)  
model.add(Dense(3, input_shape=(2,), activation='softmax'))
model.compile(Adam(lr=0.1), 'categorical_crossentropy', metrics=['accuracy'])

# create NN model model = Sequential() # create the layers with 'softmax' for multiclass classfication # model.add(Dense(5, input_shape=(2,), activation='softmax')) # height of the layer : 3 (2 inputs values + 1 bias) model.add(Dense(3, input_shape=(2,), activation='softmax')) model.compile(Adam(lr=0.1), 'categorical_crossentropy', metrics=['accuracy'])

In [24]:

# training the labels with hot coding processes
# one hot encode output
history = model.fit(X, y_cat, verbose=1, batch_size = 50, epochs=100)

# training the labels with hot coding processes # one hot encode output history = model.fit(X, y_cat, verbose=1, batch_size = 50, epochs=100)

Epoch 1/100
10/10 [==============================] - 0s 1ms/step - loss: 0.9412 - accuracy: 0.6378
Epoch 2/100
10/10 [==============================] - 0s 1ms/step - loss: 0.2560 - accuracy: 0.9814
Epoch 3/100
10/10 [==============================] - 0s 2ms/step - loss: 0.1176 - accuracy: 0.9902
Epoch 4/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0898 - accuracy: 0.9886
Epoch 5/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0661 - accuracy: 0.9933
Epoch 6/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0697 - accuracy: 0.9846
Epoch 7/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0626 - accuracy: 0.9893
Epoch 8/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0538 - accuracy: 0.9897
Epoch 9/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0448 - accuracy: 0.9913
Epoch 10/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0503 - accuracy: 0.9861
Epoch 11/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0483 - accuracy: 0.9899
Epoch 12/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0468 - accuracy: 0.9905
Epoch 13/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0455 - accuracy: 0.9908
Epoch 14/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0463 - accuracy: 0.9908
Epoch 15/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0399 - accuracy: 0.9908
Epoch 16/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0388 - accuracy: 0.9915
Epoch 17/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0369 - accuracy: 0.9907
Epoch 18/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0317 - accuracy: 0.9949
Epoch 19/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0388 - accuracy: 0.9878
Epoch 20/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0369 - accuracy: 0.9901
Epoch 21/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0378 - accuracy: 0.9891
Epoch 22/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0366 - accuracy: 0.9925
Epoch 23/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0332 - accuracy: 0.9916
Epoch 24/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0373 - accuracy: 0.9883
Epoch 25/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0315 - accuracy: 0.9916
Epoch 26/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0367 - accuracy: 0.9885
Epoch 27/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0359 - accuracy: 0.9848
Epoch 28/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0336 - accuracy: 0.9899
Epoch 29/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0423 - accuracy: 0.9847
Epoch 30/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0283 - accuracy: 0.9931
Epoch 31/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0317 - accuracy: 0.9897
Epoch 32/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0234 - accuracy: 0.9946
Epoch 33/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0314 - accuracy: 0.9889
Epoch 34/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0249 - accuracy: 0.9935
Epoch 35/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0241 - accuracy: 0.9947
Epoch 36/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0314 - accuracy: 0.9904
Epoch 37/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0292 - accuracy: 0.9894
Epoch 38/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0307 - accuracy: 0.9896
Epoch 39/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0254 - accuracy: 0.9919
Epoch 40/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0307 - accuracy: 0.9890
Epoch 41/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0386 - accuracy: 0.9876
Epoch 42/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0275 - accuracy: 0.9924
Epoch 43/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0253 - accuracy: 0.9938
Epoch 44/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0212 - accuracy: 0.9930
Epoch 45/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0293 - accuracy: 0.9908
Epoch 46/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0224 - accuracy: 0.9953
Epoch 47/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0316 - accuracy: 0.9863
Epoch 48/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0244 - accuracy: 0.9946
Epoch 49/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0449 - accuracy: 0.9825
Epoch 50/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0300 - accuracy: 0.9896
Epoch 51/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0195 - accuracy: 0.9949
Epoch 52/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0427 - accuracy: 0.9828
Epoch 53/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0159 - accuracy: 0.9969
Epoch 54/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0375 - accuracy: 0.9817
Epoch 55/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0161 - accuracy: 0.9955
Epoch 56/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0398 - accuracy: 0.9857
Epoch 57/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0270 - accuracy: 0.9911
Epoch 58/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0293 - accuracy: 0.9885
Epoch 59/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0266 - accuracy: 0.9895
Epoch 60/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0224 - accuracy: 0.9940
Epoch 61/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0405 - accuracy: 0.9813
Epoch 62/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0211 - accuracy: 0.9928
Epoch 63/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0208 - accuracy: 0.9935
Epoch 64/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0232 - accuracy: 0.9929
Epoch 65/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0201 - accuracy: 0.9949
Epoch 66/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0220 - accuracy: 0.9928
Epoch 67/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0267 - accuracy: 0.9893
Epoch 68/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0177 - accuracy: 0.9948
Epoch 69/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0172 - accuracy: 0.9950
Epoch 70/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0268 - accuracy: 0.9878
Epoch 71/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0203 - accuracy: 0.9942
Epoch 72/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0275 - accuracy: 0.9884
Epoch 73/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0381 - accuracy: 0.9864
Epoch 74/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0241 - accuracy: 0.9885
Epoch 75/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0278 - accuracy: 0.9853
Epoch 76/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0280 - accuracy: 0.9913
Epoch 77/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0236 - accuracy: 0.9931
Epoch 78/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0285 - accuracy: 0.9888
Epoch 79/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0330 - accuracy: 0.9864
Epoch 80/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0291 - accuracy: 0.9879
Epoch 81/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0273 - accuracy: 0.9918
Epoch 82/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0305 - accuracy: 0.9899
Epoch 83/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0338 - accuracy: 0.9869
Epoch 84/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0242 - accuracy: 0.9918
Epoch 85/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0369 - accuracy: 0.9849
Epoch 86/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0247 - accuracy: 0.9891
Epoch 87/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0274 - accuracy: 0.9885
Epoch 88/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0338 - accuracy: 0.9835
Epoch 89/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0217 - accuracy: 0.9915
Epoch 90/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0219 - accuracy: 0.9939
Epoch 91/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0357 - accuracy: 0.9860
Epoch 92/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0185 - accuracy: 0.9939
Epoch 93/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0208 - accuracy: 0.9910
Epoch 94/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0221 - accuracy: 0.9932
Epoch 95/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0234 - accuracy: 0.9907
Epoch 96/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0267 - accuracy: 0.9923
Epoch 97/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0280 - accuracy: 0.9916
Epoch 98/100
10/10 [==============================] - 0s 3ms/step - loss: 0.0256 - accuracy: 0.9882
Epoch 99/100
10/10 [==============================] - 0s 1ms/step - loss: 0.0260 - accuracy: 0.9862
Epoch 100/100
10/10 [==============================] - 0s 2ms/step - loss: 0.0280 - accuracy: 0.9879

In [25]:

# ploting decision boundaries 
def plot_multiclass_decision_boundary(X, y, model):
    x_span = np.linspace(min(X[:,0]) - 1, max(X[:,0]) + 1)
    y_span = np.linspace(min(X[:,1]) - 1, max(X[:,1]) + 1)
    xx, yy = np.meshgrid(x_span, y_span)
    grid = np.c_[xx.ravel(), yy.ravel()]
    pred_func = model.predict_classes(grid)
    z = pred_func.reshape(xx.shape)
    plt.contourf(xx, yy, z)

# ploting decision boundaries def plot_multiclass_decision_boundary(X, y, model): x_span = np.linspace(min(X[:,0]) - 1, max(X[:,0]) + 1) y_span = np.linspace(min(X[:,1]) - 1, max(X[:,1]) + 1) xx, yy = np.meshgrid(x_span, y_span) grid = np.c_[xx.ravel(), yy.ravel()] pred_func = model.predict_classes(grid) z = pred_func.reshape(xx.shape) plt.contourf(xx, yy, z)

In [26]:

plot_multiclass_decision_boundary(X, y_cat, model)
plt.scatter(X[y==0, 0], X[y==0, 1])
plt.scatter(X[y==1, 0], X[y==1, 1])
plt.scatter(X[y==2, 0], X[y==2, 1])
# plt.scatter(X[y==3, 0], X[y==3, 1])
# plt.scatter(X[y==4, 0], X[y==4, 1])

# adding twice for new point classification
plot_multiclass_decision_boundary(X, y_cat, model)
plt.scatter(X[y==0, 0], X[y==0, 1])
plt.scatter(X[y==1, 0], X[y==1, 1])
plt.scatter(X[y==2, 0], X[y==2, 1])
# plt.scatter(X[y==3, 0], X[y==3, 1])
# plt.scatter(X[y==4, 0], X[y==4, 1])
 
x = -0.5
y = -0.5

# adding twice for new point classification
point = np.array([[x, y]])
prediction = model.predict_classes(point)
plt.plot([x], [y], marker='o', markersize=10, color="red")
print("Prediction is: ", prediction)

# 0 : violet zone
# 1 : blue
# 2 : yellow

# So model is working great!!!

plot_multiclass_decision_boundary(X, y_cat, model) plt.scatter(X[y==0, 0], X[y==0, 1]) plt.scatter(X[y==1, 0], X[y==1, 1]) plt.scatter(X[y==2, 0], X[y==2, 1]) # plt.scatter(X[y==3, 0], X[y==3, 1]) # plt.scatter(X[y==4, 0], X[y==4, 1]) # adding twice for new point classification plot_multiclass_decision_boundary(X, y_cat, model) plt.scatter(X[y==0, 0], X[y==0, 1]) plt.scatter(X[y==1, 0], X[y==1, 1]) plt.scatter(X[y==2, 0], X[y==2, 1]) # plt.scatter(X[y==3, 0], X[y==3, 1]) # plt.scatter(X[y==4, 0], X[y==4, 1]) x = -0.5 y = -0.5 # adding twice for new point classification point = np.array([[x, y]]) prediction = model.predict_classes(point) plt.plot([x], [y], marker='o', markersize=10, color="red") print("Prediction is: ", prediction) # 0 : violet zone # 1 : blue # 2 : yellow # So model is working great!!!

/usr/local/lib/python3.7/dist-packages/tensorflow/python/keras/engine/sequential.py:450: UserWarning: `model.predict_classes()` is deprecated and will be removed after 2021-01-01. Please use instead:* `np.argmax(model.predict(x), axis=-1)`,   if your model does multi-class classification   (e.g. if it uses a `softmax` last-layer activation).* `(model.predict(x) > 0.5).astype("int32")`,   if your model does binary classification   (e.g. if it uses a `sigmoid` last-layer activation).
  warnings.warn('`model.predict_classes()` is deprecated and '

Prediction is:  [1]

In [26]: