In this post you will get to know how to define a simple Neural Network with the Keras package by solving a binary classification problem on the pima-indians-diabetes dataset.
If you haven’t installed Keras, please walk through my general post about Keras.
1. Load the data
Loading the keras and numpy package
from keras.models import Sequential
from keras.layers import Dense
import numpy
# fix random seed for reproducibility
numpy.random.seed(7)
Using TensorFlow backend.
Loading the binary classification data set
# load pima indians dataset
dataset = numpy.loadtxt("pima-indians-diabetes.csv", delimiter=",")
# split into input (X) and output (Y) variables
X = dataset[:,0:8]
Y = dataset[:,8]
X
array([[ 6. , 148. , 72. , ..., 33.6 , 0.627, 50. ],
[ 1. , 85. , 66. , ..., 26.6 , 0.351, 31. ],
[ 8. , 183. , 64. , ..., 23.3 , 0.672, 32. ],
...,
[ 5. , 121. , 72. , ..., 26.2 , 0.245, 30. ],
[ 1. , 126. , 60. , ..., 30.1 , 0.349, 47. ],
[ 1. , 93. , 70. , ..., 30.4 , 0.315, 23. ]])
Y
array([ 1., 0., 1., 0., 1., 0., 1., 0., 1., 1., 0., 1., 0.,
1., 1., 1., 1., 1., 0., 1., 0., 0., 1., 1., 1., 1.,
1., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 1., 1.,
1., 0., 0., 0., 1., 0., 1., 0., 0., 1., 0., 0., 0.,
0., 1., 0., 0., 1., 0., 0., 0., 0., 1., 0., 0., 1.,
0., 1., 0., 0., 0., 1., 0., 1., 0., 0., 0., 0., 0.,
1., 0., 0., 0., 0., 0., 1., 0., 0., 0., 1., 0., 0.,
0., 0., 1., 0., 0., 0., 0., 0., 1., 1., 0., 0., 0.,
0., 0., 0., 0., 0., 1., 1., 1., 0., 0., 1., 1., 1.,
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1., 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
1., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 1., 1.,
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1., 0., 1., 0., 0., 1., 0., 1., 0., 1., 1., 1., 0.,
0., 1., 0., 1., 0., 0., 0., 1., 0., 0., 0., 0., 1.,
1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0.,
0., 0., 0., 0., 1., 1., 1., 0., 1., 1., 0., 0., 1.,
0., 0., 1., 0., 0., 1., 1., 0., 0., 0., 0., 1., 0.,
0., 1., 0., 0., 0., 0., 0., 0., 0., 1., 1., 1., 0.,
0., 1., 0., 0., 1., 0., 0., 1., 0., 1., 1., 0., 1.,
0., 1., 0., 1., 0., 1., 1., 0., 0., 0., 0., 1., 1.,
0., 1., 0., 1., 0., 0., 0., 0., 1., 1., 0., 1., 0.,
1., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 1., 0.,
0., 1., 1., 1., 0., 0., 1., 0., 0., 1., 0., 0., 0.,
1., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
1., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 1.,
0., 0., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 1.,
0., 0., 0., 0., 1., 0., 0., 0., 1., 0., 0., 0., 1.,
0., 0., 0., 1., 0., 0., 0., 0., 1., 1., 0., 0., 0.,
0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 1., 0., 0., 0., 1., 1., 1., 1., 0., 0., 1.,
1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.,
0., 0., 0., 0., 0., 1., 0., 1., 1., 0., 0., 0., 1.,
0., 1., 0., 1., 0., 1., 0., 1., 0., 0., 1., 0., 0.,
1., 0., 0., 0., 0., 1., 1., 0., 1., 0., 0., 0., 0.,
1., 1., 0., 1., 0., 0., 0., 1., 1., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 1., 0.,
0., 1., 0., 0., 0., 1., 0., 0., 0., 1., 1., 1., 0.,
0., 0., 0., 0., 0., 1., 0., 0., 0., 1., 0., 1., 1.,
1., 1., 0., 1., 1., 0., 0., 0., 0., 0., 0., 0., 1.,
1., 0., 1., 0., 0., 1., 0., 1., 0., 0., 0., 0., 0.,
1., 0., 1., 0., 1., 0., 1., 1., 0., 0., 0., 0., 1.,
1., 0., 0., 0., 1., 0., 1., 1., 0., 0., 1., 0., 0.,
1., 1., 0., 0., 1., 0., 0., 1., 0., 0., 0., 0., 0.,
0., 0., 1., 1., 1., 0., 0., 0., 0., 0., 0., 1., 1.,
0., 0., 1., 0., 0., 1., 0., 1., 1., 1., 0., 0., 1.,
1., 1., 0., 1., 0., 1., 0., 1., 0., 0., 0., 0., 1., 0.])
2. Define Model
The Sequential model is a linear stack of layers. Dense(12) is a fully-connected layer with 12 hidden units. For the first layer, you must specify the expected input data shape: 8-dimensional vectors. You can simply add layers via the .add() method:
# create sequential model layer by layer
model = Sequential()
# 1. hidden layer with 12 neurons expects 8 inputs and rectifier activation function
model.add(Dense(12, input_dim=8, activation='relu'))
# 2. hidden layer with 8 neurons and rectifier activation function
model.add(Dense(8, activation='relu'))
# output layer with one neuron for the binary classification
model.add(Dense(1, activation='sigmoid'))
3. Compile Model
Before training a model, you need to configure the learning process, which is done via the compile method. It receives three arguments:
- An optimizer
- A loss function
- A list of metrics
# Compile the model with binary crossentropy as the evaluation function and adam as the weights optimizer. Report the accuracy metri
model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])
4. Fit Model
Keras models are trained on numpy arrays of input data and labels which we already prepared with the numpy.loadtxt() method. For training a model, you will typically use the fit function:
# Fit the model using 150 epochs and the batch size (#instances that are evaluated before a weight update) of 10
model.fit(X, Y, epochs=150, batch_size=10)
Epoch 1/150
768/768 [==============================] - 0s - loss: 3.7497 - acc: 0.6003
Epoch 2/150
768/768 [==============================] - 0s - loss: 0.9433 - acc: 0.5951
Epoch 3/150
768/768 [==============================] - 0s - loss: 0.7511 - acc: 0.6367
Epoch 4/150
768/768 [==============================] - 0s - loss: 0.7133 - acc: 0.6549
Epoch 5/150
768/768 [==============================] - 0s - loss: 0.6827 - acc: 0.6732
Epoch 6/150
768/768 [==============================] - 0s - loss: 0.6516 - acc: 0.6810
Epoch 7/150
768/768 [==============================] - 0s - loss: 0.6499 - acc: 0.6771
Epoch 8/150
768/768 [==============================] - 0s - loss: 0.6380 - acc: 0.6836
Epoch 9/150
768/768 [==============================] - 0s - loss: 0.6249 - acc: 0.6927
Epoch 10/150
768/768 [==============================] - 0s - loss: 0.6315 - acc: 0.6745
Epoch 11/150
768/768 [==============================] - 0s - loss: 0.6500 - acc: 0.6693
Epoch 12/150
768/768 [==============================] - 0s - loss: 0.6407 - acc: 0.6745
Epoch 13/150
768/768 [==============================] - 0s - loss: 0.6260 - acc: 0.6771
Epoch 14/150
768/768 [==============================] - 0s - loss: 0.6192 - acc: 0.6966
Epoch 15/150
768/768 [==============================] - 0s - loss: 0.6026 - acc: 0.6953
Epoch 16/150
768/768 [==============================] - 0s - loss: 0.5883 - acc: 0.6992
Epoch 17/150
768/768 [==============================] - 0s - loss: 0.5851 - acc: 0.6979
Epoch 18/150
768/768 [==============================] - 0s - loss: 0.5994 - acc: 0.6901
Epoch 19/150
768/768 [==============================] - 0s - loss: 0.5801 - acc: 0.7109
Epoch 20/150
768/768 [==============================] - 0s - loss: 0.5795 - acc: 0.7214
Epoch 21/150
768/768 [==============================] - 0s - loss: 0.5687 - acc: 0.7148
Epoch 22/150
768/768 [==============================] - 0s - loss: 0.5820 - acc: 0.6940
Epoch 23/150
768/768 [==============================] - 0s - loss: 0.5734 - acc: 0.7122
Epoch 24/150
768/768 [==============================] - 0s - loss: 0.5679 - acc: 0.7305
Epoch 25/150
768/768 [==============================] - 0s - loss: 0.5574 - acc: 0.7370
Epoch 26/150
768/768 [==============================] - 0s - loss: 0.5707 - acc: 0.7057
Epoch 27/150
768/768 [==============================] - 0s - loss: 0.5556 - acc: 0.7227
Epoch 28/150
768/768 [==============================] - 0s - loss: 0.5555 - acc: 0.7305
Epoch 29/150
768/768 [==============================] - 0s - loss: 0.5728 - acc: 0.7174
Epoch 30/150
768/768 [==============================] - 0s - loss: 0.5611 - acc: 0.7214
Epoch 31/150
768/768 [==============================] - 0s - loss: 0.5683 - acc: 0.7188
Epoch 32/150
768/768 [==============================] - 0s - loss: 0.5651 - acc: 0.7096
Epoch 33/150
768/768 [==============================] - 0s - loss: 0.5515 - acc: 0.7227
Epoch 34/150
768/768 [==============================] - 0s - loss: 0.5479 - acc: 0.7292
Epoch 35/150
768/768 [==============================] - 0s - loss: 0.5492 - acc: 0.7240
Epoch 36/150
768/768 [==============================] - 0s - loss: 0.5652 - acc: 0.7070
Epoch 37/150
768/768 [==============================] - 0s - loss: 0.5339 - acc: 0.7383
Epoch 38/150
768/768 [==============================] - 0s - loss: 0.5410 - acc: 0.7253
Epoch 39/150
768/768 [==============================] - 0s - loss: 0.5465 - acc: 0.7214
Epoch 40/150
768/768 [==============================] - 0s - loss: 0.5451 - acc: 0.7240
Epoch 41/150
768/768 [==============================] - 0s - loss: 0.5426 - acc: 0.7331
Epoch 42/150
768/768 [==============================] - 0s - loss: 0.5377 - acc: 0.7448
Epoch 43/150
768/768 [==============================] - 0s - loss: 0.5306 - acc: 0.7539
Epoch 44/150
768/768 [==============================] - 0s - loss: 0.5329 - acc: 0.7474
Epoch 45/150
768/768 [==============================] - 0s - loss: 0.5322 - acc: 0.7474
Epoch 46/150
768/768 [==============================] - 0s - loss: 0.5310 - acc: 0.7526
Epoch 47/150
768/768 [==============================] - 0s - loss: 0.5316 - acc: 0.7409
Epoch 48/150
768/768 [==============================] - 0s - loss: 0.5319 - acc: 0.7422
Epoch 49/150
768/768 [==============================] - 0s - loss: 0.5335 - acc: 0.7474
Epoch 50/150
768/768 [==============================] - 0s - loss: 0.5265 - acc: 0.7357
Epoch 51/150
768/768 [==============================] - 0s - loss: 0.5262 - acc: 0.7474
Epoch 52/150
768/768 [==============================] - 0s - loss: 0.5323 - acc: 0.7448
Epoch 53/150
768/768 [==============================] - 0s - loss: 0.5384 - acc: 0.7487
Epoch 54/150
768/768 [==============================] - 0s - loss: 0.5382 - acc: 0.7240
Epoch 55/150
768/768 [==============================] - 0s - loss: 0.5217 - acc: 0.7500
Epoch 56/150
768/768 [==============================] - 0s - loss: 0.5286 - acc: 0.7422
Epoch 57/150
768/768 [==============================] - 0s - loss: 0.5309 - acc: 0.7344
Epoch 58/150
768/768 [==============================] - 0s - loss: 0.5215 - acc: 0.7513
Epoch 59/150
768/768 [==============================] - 0s - loss: 0.5128 - acc: 0.7604
Epoch 60/150
768/768 [==============================] - 0s - loss: 0.5352 - acc: 0.7396
Epoch 61/150
768/768 [==============================] - 0s - loss: 0.5264 - acc: 0.7305
Epoch 62/150
768/768 [==============================] - 0s - loss: 0.5170 - acc: 0.7578
Epoch 63/150
768/768 [==============================] - 0s - loss: 0.5430 - acc: 0.7383
Epoch 64/150
768/768 [==============================] - 0s - loss: 0.5328 - acc: 0.7370
Epoch 65/150
768/768 [==============================] - 0s - loss: 0.5197 - acc: 0.7474
Epoch 66/150
768/768 [==============================] - 0s - loss: 0.5066 - acc: 0.7487
Epoch 67/150
768/768 [==============================] - 0s - loss: 0.5162 - acc: 0.7331
Epoch 68/150
768/768 [==============================] - 0s - loss: 0.5131 - acc: 0.7526
Epoch 69/150
768/768 [==============================] - 0s - loss: 0.5128 - acc: 0.7526
Epoch 70/150
768/768 [==============================] - 0s - loss: 0.5346 - acc: 0.7188
Epoch 71/150
768/768 [==============================] - 0s - loss: 0.5191 - acc: 0.7435
Epoch 72/150
768/768 [==============================] - 0s - loss: 0.5164 - acc: 0.7513
Epoch 73/150
768/768 [==============================] - 0s - loss: 0.5167 - acc: 0.7435
Epoch 74/150
768/768 [==============================] - 0s - loss: 0.5091 - acc: 0.7604
Epoch 75/150
768/768 [==============================] - 0s - loss: 0.5122 - acc: 0.7552
Epoch 76/150
768/768 [==============================] - 0s - loss: 0.5141 - acc: 0.7513
Epoch 77/150
768/768 [==============================] - 0s - loss: 0.5151 - acc: 0.7591
Epoch 78/150
768/768 [==============================] - 0s - loss: 0.5140 - acc: 0.7487
Epoch 79/150
768/768 [==============================] - 0s - loss: 0.5150 - acc: 0.7357
Epoch 80/150
768/768 [==============================] - 0s - loss: 0.5109 - acc: 0.7539
Epoch 81/150
768/768 [==============================] - 0s - loss: 0.5061 - acc: 0.7695
Epoch 82/150
768/768 [==============================] - 0s - loss: 0.5030 - acc: 0.7500
Epoch 83/150
768/768 [==============================] - 0s - loss: 0.5020 - acc: 0.7565
Epoch 84/150
768/768 [==============================] - 0s - loss: 0.4980 - acc: 0.7539
Epoch 85/150
768/768 [==============================] - 0s - loss: 0.5060 - acc: 0.7487
Epoch 86/150
768/768 [==============================] - 0s - loss: 0.5080 - acc: 0.7487
Epoch 87/150
768/768 [==============================] - 0s - loss: 0.4998 - acc: 0.7565
Epoch 88/150
768/768 [==============================] - 0s - loss: 0.5013 - acc: 0.7669
Epoch 89/150
768/768 [==============================] - 0s - loss: 0.5065 - acc: 0.7591
Epoch 90/150
768/768 [==============================] - 0s - loss: 0.5105 - acc: 0.7461
Epoch 91/150
768/768 [==============================] - 0s - loss: 0.5002 - acc: 0.7487
Epoch 92/150
768/768 [==============================] - 0s - loss: 0.5055 - acc: 0.7435
Epoch 93/150
768/768 [==============================] - 0s - loss: 0.4983 - acc: 0.7565
Epoch 94/150
768/768 [==============================] - 0s - loss: 0.4989 - acc: 0.7578
Epoch 95/150
768/768 [==============================] - 0s - loss: 0.5065 - acc: 0.7435
Epoch 96/150
768/768 [==============================] - 0s - loss: 0.4937 - acc: 0.7604
Epoch 97/150
768/768 [==============================] - 0s - loss: 0.4970 - acc: 0.7708
Epoch 98/150
768/768 [==============================] - 0s - loss: 0.4902 - acc: 0.7578
Epoch 99/150
768/768 [==============================] - 0s - loss: 0.4900 - acc: 0.7656
Epoch 100/150
768/768 [==============================] - 0s - loss: 0.4848 - acc: 0.7760
Epoch 101/150
768/768 [==============================] - 0s - loss: 0.4898 - acc: 0.7734
Epoch 102/150
768/768 [==============================] - 0s - loss: 0.4981 - acc: 0.7565
Epoch 103/150
768/768 [==============================] - 0s - loss: 0.4986 - acc: 0.7526
Epoch 104/150
768/768 [==============================] - 0s - loss: 0.4929 - acc: 0.7865
Epoch 105/150
768/768 [==============================] - 0s - loss: 0.5259 - acc: 0.7461
Epoch 106/150
768/768 [==============================] - 0s - loss: 0.4914 - acc: 0.7708
Epoch 107/150
768/768 [==============================] - 0s - loss: 0.4885 - acc: 0.7721
Epoch 108/150
768/768 [==============================] - 0s - loss: 0.5021 - acc: 0.7630
Epoch 109/150
768/768 [==============================] - 0s - loss: 0.4871 - acc: 0.7591
Epoch 110/150
768/768 [==============================] - 0s - loss: 0.4876 - acc: 0.7669
Epoch 111/150
768/768 [==============================] - 0s - loss: 0.4829 - acc: 0.7786
Epoch 112/150
768/768 [==============================] - 0s - loss: 0.4914 - acc: 0.7773
Epoch 113/150
768/768 [==============================] - 0s - loss: 0.4971 - acc: 0.7591
Epoch 114/150
768/768 [==============================] - 0s - loss: 0.4912 - acc: 0.7526
Epoch 115/150
768/768 [==============================] - 0s - loss: 0.4917 - acc: 0.7643
Epoch 116/150
768/768 [==============================] - 0s - loss: 0.4907 - acc: 0.7721
Epoch 117/150
768/768 [==============================] - 0s - loss: 0.4919 - acc: 0.7617
Epoch 118/150
768/768 [==============================] - 0s - loss: 0.4881 - acc: 0.7760
Epoch 119/150
768/768 [==============================] - 0s - loss: 0.4842 - acc: 0.7604
Epoch 120/150
768/768 [==============================] - 0s - loss: 0.4952 - acc: 0.7708
Epoch 121/150
768/768 [==============================] - 0s - loss: 0.4931 - acc: 0.7747
Epoch 122/150
768/768 [==============================] - 0s - loss: 0.4831 - acc: 0.7747
Epoch 123/150
768/768 [==============================] - 0s - loss: 0.4870 - acc: 0.7617
Epoch 124/150
768/768 [==============================] - 0s - loss: 0.4845 - acc: 0.7734
Epoch 125/150
768/768 [==============================] - 0s - loss: 0.4877 - acc: 0.7799
Epoch 126/150
768/768 [==============================] - 0s - loss: 0.4818 - acc: 0.7669
Epoch 127/150
768/768 [==============================] - 0s - loss: 0.4897 - acc: 0.7617
Epoch 128/150
768/768 [==============================] - 0s - loss: 0.4726 - acc: 0.7747
Epoch 129/150
768/768 [==============================] - 0s - loss: 0.4831 - acc: 0.7682
Epoch 130/150
768/768 [==============================] - 0s - loss: 0.4729 - acc: 0.7878
Epoch 131/150
768/768 [==============================] - 0s - loss: 0.4846 - acc: 0.7630
Epoch 132/150
768/768 [==============================] - 0s - loss: 0.4818 - acc: 0.7812
Epoch 133/150
768/768 [==============================] - 0s - loss: 0.4857 - acc: 0.7682
Epoch 134/150
768/768 [==============================] - 0s - loss: 0.4858 - acc: 0.7721
Epoch 135/150
768/768 [==============================] - 0s - loss: 0.4776 - acc: 0.7643
Epoch 136/150
768/768 [==============================] - 0s - loss: 0.4747 - acc: 0.7695
Epoch 137/150
768/768 [==============================] - 0s - loss: 0.4695 - acc: 0.7826
Epoch 138/150
768/768 [==============================] - 0s - loss: 0.4804 - acc: 0.7773
Epoch 139/150
768/768 [==============================] - 0s - loss: 0.4664 - acc: 0.7773
Epoch 140/150
768/768 [==============================] - 0s - loss: 0.4831 - acc: 0.7747
Epoch 141/150
768/768 [==============================] - 0s - loss: 0.4713 - acc: 0.7826
Epoch 142/150
768/768 [==============================] - 0s - loss: 0.4819 - acc: 0.7682
Epoch 143/150
768/768 [==============================] - 0s - loss: 0.4760 - acc: 0.7695
Epoch 144/150
768/768 [==============================] - 0s - loss: 0.4732 - acc: 0.7747
Epoch 145/150
768/768 [==============================] - 0s - loss: 0.4958 - acc: 0.7552
Epoch 146/150
768/768 [==============================] - 0s - loss: 0.4917 - acc: 0.7695
Epoch 147/150
768/768 [==============================] - 0s - loss: 0.4844 - acc: 0.7721
Epoch 148/150
768/768 [==============================] - 0s - loss: 0.4715 - acc: 0.7786
Epoch 149/150
768/768 [==============================] - 0s - loss: 0.4742 - acc: 0.7656
Epoch 150/150
768/768 [==============================] - 0s - loss: 0.4784 - acc: 0.7812
<keras.callbacks.History at 0x118859dd8>
5. Evaluate the Model
We have trained our neural network on the entire dataset and we can evaluate the performance of the network on the same dataset.
We have done this for simplicity, but ideally, you should separate your data into train and test data for training and evaluation of your model.
# evaluate the model
scores = model.evaluate(X, Y)
print("\n%s: %.2f%%" % (model.metrics_names[1], scores[1]*100))
32/768 [>.............................] - ETA: 0s
acc: 77.99%
6. Model Predictions
# calculate predictions
predictions = model.predict(X)
# round predictions
rounded = [round(x[0]) for x in predictions]
print(rounded)
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