A Convolutional Neural Network is built using the Tensorflow-Keras framework. The MNIST dataset is used to build this model. This dataset has 70,000 handwritten samples of numbers from 0-9. Each image in the dataset is of 28x28 grayscale pixels size.
MNIST Data set can be imported as from tensorflow.keras.datasets import mnist. This dataset comprises of 70,000 images.The size of each image is 28 * 28 pixels and each pixel has a value in the range of 0 to 255 where, 0 pixel value represents black colour and 255 pixel value represents white colour.
This project is completed in TensorFlow environment. In the first step I have installed the required libraries which will be used in completing this project. After installing libraries I have imported MNIST (Modified National Institute of Standards and Technology database) from Keras library.
We are considering the data in the form of 2D images (28x28 pixels) instead of a flattened stream of 784 pixels. As, we have greyscale images so dimension of colour will be set to 1. The resultant data would be of the form (60000 * 28 * 28 * 1), where 1 signifies greyscale images and 60000 signifies total number of instances in training set.
As we have pixel values from 0 to 255, so, I am normalizing feature data (X_train and X_test) by dividing each pixel value with maximum possible pixel value. Instead of using MinMaxScalar for Normalizing feature data, I have divided all the pixel values by maximum pixel value (i.e., 255), because MinMaxScalar requires a 2-D array to normalize data. However, I have previously reshaped the data into 28 * 28 * 1 form.
I have used np_utils package to convert train and test labels in One-Hot Encoding format. After performing this step we will get 10 labels (from 0-9) and each image will be labelled between 0-9.
I have used Sequential model to define the model. In sequential model we can add each layer sequentially. Brief description about the model:
- 2 Convolutional Layer with ReLU activation function.
- MaxPool2D layer (It is used to reduce the size of image by keeping only important features from the image).
- 1st Dropout Layer to prevent Overfitting.
- Flattening layer (It is used to transform 2D array to 1-D which will be used as input for Neural Network).
- 2nd Dropout Layer to prevent Overfitting.
- Dense Layer or Full Connection Layer.
- Output Layer has 10 nodes. I have used sofmax activation function because there are total 10 classes and I want sum of probabilities to be 1.
- Model Compilation using adam optimizer and loss = 'categorical_crossentropy' instead of 'binary_crossentropy' because there are 10 different classes.
a. Input Image shape : (28 * 28 * 1)
b. 1st Convolution layer : (3,3) kernel size, Number of filter =32, Stride length=1 c. Output of 1st Convolution layer: (28 – 3) +1 = 26
d. Outputof2ndConvolutionlayer:(26–3)+1 = 24
e. Output of MaxPool2D Layer: (24-2)/2 +1 = 12
f. Flatten Layer: 121264 = 9216
So, Output of 1st convolution layer is (262632), where 32 is number of filters and output of 2nd convolution layer is (242464), where 64 is number of filters. Similarly, output of all other layers is also calculated in the same way.
I have trained the model with batch size of 32. For testing the results of model, I took 10 epochs in first attempt and 12 epochs in second attempt.
Number of epochs : 12
a. Loss after 12th Epoch - 0.0083
b. Accuracy after 12th Epoch - 0.9975 (or 99.75%)
c. Validation/Test loss after 12th Epoch – 0.0489
d. Validation/Test accuracy after 12th Epoch – 0.9886 (or 98.86%)
After 10 epochs validation loss increase and validation accuracy decreases.
a. Randomly chosen digit
Size of Confusion Matrix = (Number of unique classes * Number of unique classes). In my testing dataset there are 10000 rows. Results of my model are:
