In this notebook, we'll be building a neural network that recognizes handwritten numbers 0-9.
This kind of neural network is used in a variety of real-world applications including: recognizing phone numbers and sorting postal mail by address. To build the network, we'll be using the MNIST data set, which consists of images of handwritten numbers and their correct labels 0-9.
We'll be using TFLearn, a high-level library built on top of TensorFlow to build the neural network. We'll start off by importing all the modules we'll need, then load the data, and finally build the network.
In [2]:
# Import Numpy, TensorFlow, TFLearn, and MNIST data
import numpy as np
import tensorflow as tf
import tflearn
import tflearn.datasets.mnist as mnist
The MNIST data set already contains both training and test data. There are 55,000 data points of training data, and 10,000 points of test data.
Each MNIST data point has:
We'll call the images, which will be the input to our neural network, X and their corresponding labels Y.
We're going to want our labels as one-hot vectors, which are vectors that holds mostly 0's and one 1. It's easiest to see this in a example. As a one-hot vector, the number 0 is represented as [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], and 4 is represented as [0, 0, 0, 0, 1, 0, 0, 0, 0, 0].
For this example, we'll be using flattened data or a representation of MNIST images in one dimension rather than two. So, each handwritten number image, which is 28x28 pixels, will be represented as a one dimensional array of 784 pixel values.
Flattening the data throws away information about the 2D structure of the image, but it simplifies our data so that all of the training data can be contained in one array whose shape is [55000, 784]; the first dimension is the number of training images and the second dimension is the number of pixels in each image. This is the kind of data that is easy to analyze using a simple neural network.
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# Retrieve the training and test data
trainX, trainY, testX, testY = mnist.load_data(one_hot=True)
In [4]:
# Visualizing the data
import matplotlib.pyplot as plt
%matplotlib inline
# Function for displaying a training image by it's index in the MNIST set
def show_digit(index):
label = trainY[index].argmax(axis=0)
# Reshape 784 array into 28x28 image
image = trainX[index].reshape([28,28])
plt.title('Training data, index: %d, Label: %d' % (index, label))
plt.imshow(image, cmap='gray_r')
plt.show()
# Display the first (index 0) training image
show_digit(0)
TFLearn lets you build the network by defining the layers in that network.
For this example, you'll define:
Let's start with the input layer; to define the input layer, you'll define the type of data that the network expects. For example,
net = tflearn.input_data([None, 100])would create a network with 100 inputs. The number of inputs to your network needs to match the size of your data. For this example, we're using 784 element long vectors to encode our input data, so we need 784 input units.
To add new hidden layers, you use
net = tflearn.fully_connected(net, n_units, activation='ReLU')This adds a fully connected layer where every unit (or node) in the previous layer is connected to every unit in this layer. The first argument net is the network you created in the tflearn.input_data call, it designates the input to the hidden layer. You can set the number of units in the layer with n_units, and set the activation function with the activation keyword. You can keep adding layers to your network by repeated calling tflearn.fully_connected(net, n_units).
Then, to set how you train the network, use:
net = tflearn.regression(net, optimizer='sgd', learning_rate=0.1, loss='categorical_crossentropy')Again, this is passing in the network you've been building. The keywords:
optimizer sets the training method, here stochastic gradient descentlearning_rate is the learning rateloss determines how the network error is calculated. In this example, with categorical cross-entropy.Finally, you put all this together to create the model with tflearn.DNN(net).
Exercise: Below in the build_model() function, you'll put together the network using TFLearn. You get to choose how many layers to use, how many hidden units, etc.
Hint: The final output layer must have 10 output nodes (one for each digit 0-9). It's also recommended to use a softmax activation layer as your final output layer.
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# Define the neural network
def build_model():
# This resets all parameters and variables, leave this here
tf.reset_default_graph()
#### Your code ####
# Include the input layer, hidden layer(s), and set how you want to train the model
net = tflearn.input_data([None, 784])
net = tflearn.fully_connected(net, 128, activation='ReLU')
net = tflearn.fully_connected(net, 32, activation='ReLU')
net = tflearn.fully_connected(net, 10, activation='softmax')
net = tflearn.regression(net, optimizer='sgd', learning_rate=0.1, loss='categorical_crossentropy')
# This model assumes that your network is named "net"
model = tflearn.DNN(net)
return model
In [6]:
# Build the model
model = build_model()
Now that we've constructed the network, saved as the variable model, we can fit it to the data. Here we use the model.fit method. You pass in the training features trainX and the training targets trainY. Below I set validation_set=0.1 which reserves 10% of the data set as the validation set. You can also set the batch size and number of epochs with the batch_size and n_epoch keywords, respectively.
Too few epochs don't effectively train your network, and too many take a long time to execute. Choose wisely!
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# Training
model.fit(trainX, trainY, validation_set=0.1, show_metric=True, batch_size=100, n_epoch=8)
After you're satisified with the training output and accuracy, you can then run the network on the test data set to measure it's performance! Remember, only do this after you've done the training and are satisfied with the results.
A good result will be higher than 98% accuracy! Some simple models have been known to get up to 99.7% accuracy.
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# Compare the labels that our model predicts with the actual labels
predictions = (np.array(model.predict(testX))[:,0] >= 0.5).astype(np.int_)
# Calculate the accuracy, which is the percentage of times the predicated labels matched the actual labels
test_accuracy = np.mean(predictions == testY[:,0], axis=0)
# Print out the result
print("Test accuracy: ", test_accuracy)
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np.bincount(testY[:,0].astype(np.int_))
Out[9]:
Column zero has 9020 zeros and 980 ones. So about one tenth of our 10000 images was a zero.
Column one is different:
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np.bincount(testY[:,1].astype(np.int_))
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It has over 1000 ones. So there are more ones than zeros in the testY set.
Let's look at ALL the digits:
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for i in range(10):
print(i, np.bincount(testY[:,i].astype(np.int_)))
As a check, adding up all the one-hot one's, we should get a total of 10000:
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980 + \
1135+ \
1032+ \
1010+ \
982 + \
892 + \
958 + \
1028+ \
974 + \
1009
Out[12]:
Now let's look at our predictions in the same way:
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for i in range(10):
print(i, np.bincount((np.array(model.predict(testX))[:,i] >= 0.5).astype(np.int_)))
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np.bincount(predictions == testY[:,0])
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But what about the other columns besides zero?
It turns out those other columns (the other digits) have different levels of error.
Up to 1.15% error for the nines.
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for i in range(10):
print(i, np.bincount((np.array(model.predict(testX))[:,i] >= 0.5).astype(np.int_) == testY[:,i]))