Just focus on your works. DATUMO<\/em><\/strong> got your back!<\/p>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n<\/article>\n [\/vc_column_text] To sum it all up, we started off by discussing what image classification in general is and how it is carried out by a model i.e., based on the pixel values in an image. We also talked about the very popular MNIST dataset, which is basically a dataset of handwritten digits and is used commonly in the handwritten digit classification problem. We thoroughly discussed the details and particulars of this dataset and went through each step of handwritten digit classification in Python. Lastly, we talked about how we can improve the test accuracy by introducing some changes in the model as well as in the dataset, for example, by creating an augmented dataset.<\/p>\n [\/vc_column_text] Build smarter AI with us.<\/p>See what we can do for you.<\/h3>
\ud83d\udd11<\/strong> In 9 minutes you will learn:<\/strong><\/span><\/p>\n <\/p>\n [\/vc_column_text]<\/div><\/div>[\/vc_column][\/vc_row][vc_row pix_particles_check=””][vc_column] Modified National Institute of Standards and Technology, known as MNIST in short, is a dataset containing handwritten images of digits from 0 to 9 (made by the guru, Professor\u00a0Yann LeCun<\/em><\/a>, and his colleagues). To be more precise, the dataset contains a total of 70,000 square, grayscale images of dimensions 28 x 28 pixels each. Each image comprises 784 features, and each feature corresponds to a pixel\u2019s intensity, which is from 0 to 255. Out of the total 70,000 images in the dataset, 60,000 are for training, and the remaining 10,000 images are for testing. The total number of classes is 10, signifying the output i.e., the digits from 0 to 9 inclusive.<\/p>\n THE MNIST database of handwritten digits<\/p>\n [\/vc_column_text][\/vc_column][\/vc_row][\/vc_section][vc_row pix_particles_check=””][vc_column] <\/p>\n [\/vc_column_text][vc_column_text css=”.vc_custom_1655919237412{border-top-width: 1px !important;padding-top: 60px !important;padding-bottom: 30px !important;border-top-color: rgba(0,0,0,0.2) !important;border-top-style: solid !important;}”]<\/p>\n <\/p>\n Since the MNIST dataset is hugely popular, it can easily be easily accessed from different sources. Even\u00a0TensorFlow<\/a>\u00a0and\u00a0Keras<\/a>\u00a0allow us to download it through their respective API directly. Thus, we will download it through Keras\u2019 API.<\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n We have decided to go for a 4-layered model i.e., having two hidden layers and an input and output layer. The rectifier activation function is chosen for the neurons in the hidden layers.<\/p>\n <\/p>\n [\/vc_column_text][vc_column_text css=”.vc_custom_1655919448439{border-top-width: 1px !important;padding-top: 60px !important;padding-bottom: 30px !important;border-top-color: rgba(0,0,0,0.2) !important;border-top-style: solid !important;}”]<\/p>\n <\/p>\n It is considered a good practice to scale input values when it comes to neural networks. Thus we will normalize our data.<\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n The training dataset is structured to be a 3-dimensional array. To be able to use the dataset in Keras API, we need 4-dimensional NumPy arrays. Therefore, we need to flatten or reduce the images so that they represent a vector of pixels. In this case, since the image is 28 x 28, there will be 784-pixel values.<\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n We will now fit the model.<\/p>\n <\/p>\n <\/p>\n <\/p>\n Step 7: Evaluate the model accuracy on test data<\/strong><\/p>\n <\/p>\n We will now evaluate the accuracy of the model.<\/p>\n <\/p>\n <\/p>\n 97.85% seems quite great? Isn\u2019t it? No, never satisfy! In the next section, we will discuss how to improve it even more!<\/p>\n [\/vc_column_text][\/vc_column][\/vc_row][\/vc_section][vc_row pix_particles_check=””][vc_column]\n
About MNIST dataset<\/h2><\/div>[vc_column_text css=”.vc_custom_1655918751170{padding-top: 40px !important;padding-bottom: 40px !important;}”]<\/p>\n
![\"\"](\"https:\/\/blog.datumo.com\/en\/wp-content\/uploads\/2022\/06\/1-300x214.jpg\")
![\"\"](\"https:\/\/blog.datumo.com\/en\/wp-content\/uploads\/2022\/06\/2-300x214.png\")
![\"\"](\"https:\/\/blog.datumo.com\/en\/wp-content\/uploads\/2022\/06\/3-300x214.png\")
<\/p>\nPrerequisites<\/h2><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1655918801284{padding-top: 40px !important;}”]Before you move ahead with this tutorial, you need to have basic programming knowledge in any language, preferably in Python 3, as well as some understanding of Machine Learning and Deep Learning concepts. Our code will be using\u00a0Google Colab<\/a>, but you can work on any code editor of your choice. We will be using Keras.[\/vc_column_text]
Python Code for Handwritten Digit Classification<\/h2><\/div><\/div><\/div>[vc_column_text css=”.vc_custom_1655919126613{padding-top: 60px !important;padding-bottom: 30px !important;}”]<\/p>\n
Step 1: Import essential libraries and packages<\/strong><\/h5>\n
import tensorflow\nimport tensorflow.keras\nfrom keras import models\nfrom keras import layers\nfrom keras.utils import normalize\nfrom keras.utils import to_categorical\nimport matplotlib.pyplot as plt<\/pre>\n
Step 2: Load the MNIST dataset<\/strong><\/h5>\n
mnist_dataset = tensorflow.keras.datasets.mnist\n# Split the data into training and test sets.\n(train_X, train_Y), (test_X, test_Y) = mnist_dataset.load_data()\n# train_X represents the pixel values (feautures) of the 28 x 28 image.\nprint(train_X[3])\nplt.imshow(train_X[3],cmap=plt.cm.binary)\nplt.show()<\/pre>\n
Output:<\/strong><\/h5>\n
![\"\"](\"https:\/\/blog.datumo.com\/en\/wp-content\/uploads\/2022\/06\/o1-500x1024.jpg\")
[\/vc_column_text][vc_column_text css=”.vc_custom_1655919280902{border-top-width: 1px !important;padding-top: 60px !important;padding-bottom: 30px !important;border-top-color: rgba(0,0,0,0.2) !important;border-top-style: solid !important;}”]<\/p>\nStep 3: Build the Model<\/strong><\/h5>\n
# 4-layered model\nmodel = models.Sequential()\n# Hidden layer containing 512 units. Rectifier linear function is used as the activation function. \nmodel.add(layers.Dense(512, activation='relu', input_shape=(28 * 28, )))\nmodel.add(layers.Dense(128, activation=tensorflow.nn.relu))\n# Dropout is a regularization technique that is used to reduce overfitting.\nmodel.add(layers.Dropout(0.2))\n# Output layer which is 10-way softmax layer, which returns an array of 10 probability scores displaying the probabability of image of the digit belonging to which of the 10 classes.\nmodel.add(layers.Dense(10, activation='softmax'))<\/pre>\n
Step 4: Normalize the data i.e., change the current data range from 0 to 255 to 0 and 1 inclusive.<\/strong><\/h5>\n
train_X = normalize(train_X, axis=1)\ntest_X = normalize(test_X, axis=1)\nprint(train_X[3])\nprint(\" \")\nprint('Shape of train_X: ', train_X.shape)\nprint('Number of images in train_x: ', train_X.shape[0])\nprint('Number of images in test_X: ', test_X.shape[0])<\/pre>\nOutput:<\/strong><\/h5>\n
![\"\"](\"https:\/\/blog.datumo.com\/en\/wp-content\/uploads\/2022\/06\/o2.jpg\")
[\/vc_column_text][vc_column_text css=”.vc_custom_1655919542695{border-top-width: 1px !important;padding-top: 60px !important;padding-bottom: 30px !important;border-top-color: rgba(0,0,0,0.2) !important;border-top-style: solid !important;}”]<\/p>\nStep 5: Flatten each 28 x 28 image to 1 x 784 image<\/strong><\/h5>\n
train_X = train_X.reshape(train_X.shape[0], -1)\ntest_X= test_X.reshape(test_X.shape[0], -1)\n# Encode labels\ntrain_Y = to_categorical(train_Y)\ntest_Y = to_categorical(test_Y)\nprint('Shape of train_X: ', train_X.shape)\nprint('Number of images in train_x: ', train_X.shape[0])\nprint('Number of images in test_X: ', test_X.shape[0])<\/pre>\nOutput:<\/strong><\/h5>\n
![\"\"](\"https:\/\/blog.datumo.com\/en\/wp-content\/uploads\/2022\/06\/0_EtE8XFkbzspzri4O.png\")
[\/vc_column_text][vc_column_text css=”.vc_custom_1655919624093{border-top-width: 1px !important;padding-top: 60px !important;padding-bottom: 30px !important;border-top-color: rgba(0,0,0,0.2) !important;border-top-style: solid !important;}”]<\/p>\nStep 6: Train the model<\/strong><\/h5>\n
model.fit(train_X, train_Y, epochs=7)<\/pre>\n
Output:<\/strong><\/h5>\n
![\"\"](\"https:\/\/blog.datumo.com\/en\/wp-content\/uploads\/2022\/06\/o3-1024x350.png\")
[\/vc_column_text][vc_column_text css=”.vc_custom_1655919748449{border-top-width: 1px !important;padding-top: 60px !important;padding-bottom: 30px !important;border-top-color: rgba(0,0,0,0.2) !important;border-top-style: solid !important;}”]<\/p>\n_, test_accuracy = model.evaluate(test_X, test_Y, verbose=0)\nprint(f\"\\nTest Accuracy : {test_accuracy * 100} %\")<\/pre>\nOutput:<\/strong><\/h5>\n
![\"\"](\"https:\/\/blog.datumo.com\/en\/wp-content\/uploads\/2022\/06\/04.png\")
<\/pre>\n