One can leverage free Graphics Processing Units(GPUs) for machine, scientific computing and 3D visualizations. Scientists, Artists and Engineers need access to massively parallel computational power. Deep learning, physical simulation or molecular modelling are accelerated with several GPU types such as NVIDIA Tesla K80, P100, P4, T4 and V100 available depending on compute or visualization needs.

You should be very careful with recursion as it can be quite easy to slip into writing a function which never terminates, or one that uses excess amounts of memory or processor power. However, when written correctly recursion can be a very efficient and mathematically-elegant approach to programming.

In this example, tri_recursion() is a function that we have defined to call itself ("recurse"). We use the k variable as the data, which decrements (-1) every time we recurse. The recursion ends when the condition is not greater than 0 .

def tri_recursion(k):
  if(k > 0):
    result = k + tri_recursion(k - 1)
    print(result)
  else:
    result = 0
  return result

print("\n\nRecursion Example Results")
tri_recursion(6)

The output cell should be as below

Recursion Example Results
1
3
6
10
15
21
21

The reason why 1 is printed before the 21 is because of the stack that is formed and that puts it ontop of the rest of the numbers followed by 3 then 6 then 10 ....

Machine Learning Intro

By now you have all the notebook basics at your finger tips. Lets dive into some machine learning using scikit-learn. I assume you have a basic working knowledge of ML practices.

Scikit-Learn

Scikit-learn is an open source machine learning library that supports supervised and unsupervised learning. It also provides various tools for model fitting, data preprocessing, model selection and evaluation, and many other utilities.

By default, this library is pre installed in google colab so no need to run the pip installation command.
Scikit-Learn provides dozens of built-in machine learning algorithms and models, called estimators. Each estimator can be fitted to some data using its fit method.

Model Fitting

This is an example to fit a RandomForestClassifier with some very basic data. You should try it out in a new colab notebook. Type the code below in an input cell then run it.

from sklearn.ensemble import RandomForestClassifier
clf = RandomForestClassifier(random_state=0)
X = [[ 1,  2,  3],[11, 12, 13]]  # 2 samples, 3 features
y = [0, 1]  # classes of each sample
clf.fit(X, y)

The output cell should be:

The fit method generally accepts 2 inputs:

The samples matrix (or design matrix) X. The size of X is typically (n_samples, n_features), which means that samples are represented as rows and features are represented as columns.
The target values y which are real numbers for regression tasks, or integers for classification (or any other discrete set of values). For unsupervized learning tasks, y does not need to be specified. y is usually 1d array where the i th entry corresponds to the target of the i th sample (row) of X.

Both X and y are usually expected to be numpy arrays or equivalent array-like data types, though some estimators work with other formats such as sparse matrices.

Prediction

Once the estimator is fitted, it can be used for predicting target values of new data. You don’t need to re-train the estimator:

clf.predict(X)  # predict classes of the training data
clf.predict([[4, 5, 6], [14, 15, 16]])  # predict classes of new data

How to run a job with GPU

We will now do an example of image classification while running it on a GPU.

This example shows how to classify cats or dogs from images. We shall build an image classifier using tf.keras.sequential model and load the data using tf.keras.preprocessing.image.ImageDataGenerator. The following concepts will be emphasized :

Building data into pipelines to efficiently work with data on disk to use with the model.
Overfitting - How to identify and prevent it.
Data augmentation and dropout - Key techniques to fight overfitting in computer vision tasks to incorporate into the data pipeline and image classifier model.

Import Packages

Let's start by changing to a GPU runtime then importing the required packages into our colab notebook. The os package is used to read files and directory structure, NumPy is used to convert python list to numpy array and to perform required matrix operations and matplotlib.pyplot to plot the graph and display images in the training and validation data. Type the code below in an input cell and run it to import packages

import tensorflow as tf

from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense, Conv2D, Flatten, Dropout, MaxPooling2D
from tensorflow.keras.preprocessing.image import ImageDataGenerator

import os
import numpy as np
import matplotlib.pyplot as plt

Load Data

Begin by downloading the dataset. This tutorial uses a filtered version of Dogs vs Cats dataset from Kaggle. Download the archive version of the dataset and store it in the "/tmp/" directory.

The dataset has the following directory structure:

cats_and_dogs_filtered
|__ train
    |______ cats: [cat.0.jpg, cat.1.jpg, cat.2.jpg ....]
    |______ dogs: [dog.0.jpg, dog.1.jpg, dog.2.jpg ...]
|__ validation
    |______ cats: [cat.2000.jpg, cat.2001.jpg, cat.2002.jpg ....]
    |______ dogs: [dog.2000.jpg, dog.2001.jpg, dog.2002.jpg ...]

After extracting its contents, assign variables with the proper file path for the training and validation set.

train_dir = os.path.join(PATH, 'train')
validation_dir = os.path.join(PATH, 'validation')

train_cats_dir = os.path.join(train_dir, 'cats')  # directory with our training cat pictures
train_dogs_dir = os.path.join(train_dir, 'dogs')  # directory with our training dog pictures
validation_cats_dir = os.path.join(validation_dir, 'cats')  # directory with our validation cat pictures
validation_dogs_dir = os.path.join(validation_dir, 'dogs')  # directory with our validation dog pictures

Understanding the data

Let's look at how many cats and dogs images are in the training and validation directory:

num_cats_tr = len(os.listdir(train_cats_dir))
num_dogs_tr = len(os.listdir(train_dogs_dir))

num_cats_val = len(os.listdir(validation_cats_dir))
num_dogs_val = len(os.listdir(validation_dogs_dir))

total_train = num_cats_tr + num_dogs_tr
total_val = num_cats_val + num_dogs_val

print('total training cat images:', num_cats_tr)
print('total training dog images:', num_dogs_tr)

print('total validation cat images:', num_cats_val)
print('total validation dog images:', num_dogs_val)
print("--")
print("Total training images:", total_train)
print("Total validation images:", total_val)

The output cell should be as below

For convenience, set up variables to use while pre-processing the dataset and training the network.

batch_size = 128
epochs = 15
IMG_HEIGHT = 150
IMG_WIDTH = 150

Data preparation

Format the images into appropriately pre-processed floating point tensors before feeding to the network:

Read images from the disk.
Decode contents of these images and convert it into proper grid format as per their RGB content.
Convert them into floating point tensors.
Rescale the tensors from values between 0 and 255 to values between 0 and 1, as neural networks prefer to deal with small input values.

Fortunately, all these tasks can be done with the ImageDataGenerator class provided by tf.keras. It can read images from disk and preprocess them into proper tensors. It will also set up generators that convert these images into batches of tensors—helpful when training the network.

train_image_generator = ImageDataGenerator(rescale=1./255) # Generator for our training data
validation_image_generator = ImageDataGenerator(rescale=1./255) # Generator for our validation data

After defining the generators for training and validation images, the flow_from_directory method load images from the disk, applies rescaling, and resizes the images into the required dimensions.

train_data_gen = train_image_generator.flow_from_directory(batch_size=batch_size,directory=train_dir,shuffle=True,target_size=(IMG_HEIGHT, IMG_WIDTH),class_mode='binary')

val_data_gen = validation_image_generator.flow_from_directory(batch_size=batch_size,
directory=validation_dir,target_size=(IMG_HEIGHT, IMG_WIDTH),class_mode='binary')

Visualize training images

Visualize the training images by extracting a batch of images from the training generator—which is 32 images in this example—then plot five of them with matplotlib.

sample_training_images, _ = next(train_data_gen)

The next function returns a batch from the dataset. The return value of next function is in form of (x_train, y_train) where x_train is training features and y_train, its labels. Discard the labels to only visualize the training images.

# This function will plot images in the form of a grid with 1 row and 5 columns where images are placed in each column.
def plotImages(images_arr):
    fig, axes = plt.subplots(1, 5, figsize=(20,20))
    axes = axes.flatten()
    for img, ax in zip( images_arr, axes):
        ax.imshow(img)
        ax.axis('off')
    plt.tight_layout()
    plt.show()

plotImages(sample_training_images[:5])

Your output should be five different images in a row as shown below

Create the model

The model consists of three convolution blocks with a max pool layer in each of them. There's a fully connected layer with 512 units on top of it that is activated by a relu activation function.

model = Sequential([
    Conv2D(16, 3, padding='same', activation='relu', input_shape=(IMG_HEIGHT, IMG_WIDTH ,3)),
    MaxPooling2D(),
    Conv2D(32, 3, padding='same', activation='relu'),
    MaxPooling2D(),
    Conv2D(64, 3, padding='same', activation='relu'),
    MaxPooling2D(),
    Flatten(),
    Dense(512, activation='relu'),
    Dense(1)
])

Compile the model

For this tutorial, choose the ADAM optimizer and binary cross entropy loss function. To view training and validation accuracy for each training epoch, pass the metrics argument.

model.compile(optimizer='adam',
              loss=tf.keras.losses.BinaryCrossentropy(from_logits=True),
              metrics=['accuracy'])

Model summary

View all the layers of the network using the model's summary method:

model.summary()

The output cell should show

Train the model

Use the fit_generator method of the ImageDataGenerator class to train the network.

history = model.fit_generator(
    train_data_gen,
    steps_per_epoch=total_train // batch_size,
    epochs=epochs,
    validation_data=val_data_gen,
    validation_steps=total_val // batch_size
)

The output cell should show the outputs below.Allow it to run until it completes all the 15 epochs

Visualize training results

Now visualize the results after training the network by typing the code below.

acc = history.history['accuracy']
val_acc = history.history['val_accuracy']

loss=history.history['loss']
val_loss=history.history['val_loss']

epochs_range = range(epochs)

plt.figure(figsize=(8, 8))
plt.subplot(1, 2, 1)
plt.plot(epochs_range, acc, label='Training Accuracy')
plt.plot(epochs_range, val_acc, label='Validation Accuracy')
plt.legend(loc='lower right')
plt.title('Training and Validation Accuracy')

plt.subplot(1, 2, 2)
plt.plot(epochs_range, loss, label='Training Loss')
plt.plot(epochs_range, val_loss, label='Validation Loss')
plt.legend(loc='upper right')
plt.title('Training and Validation Loss')
plt.show()

As you can see from the plots, training accuracy and validation accuracy are off by large margin and the model has achieved only around 70% accuracy on the validation set.

Let's look at what went wrong and try to increase overall performance of the model.

Overfitting

In the plots above, the training accuracy is increasing linearly over time, whereas validation accuracy stalls around 70% in the training process. Also, the difference in accuracy between training and validation accuracy is noticeable—a sign of overfitting.

When there are a small number of training examples, the model sometimes learns from noises or unwanted details from training examples—to an extent that it negatively impacts the performance of the model on new examples. This phenomenon is known as overfitting. It means that the model will have a difficult time generalizing on a new dataset.

There are multiple ways to fight overfitting in the training process. In this tutorial, you'll use data augmentation and add dropout to our model.

Data augmentation

Overfitting generally occurs when there are a small number of training examples. One way to fix this problem is to augment the dataset so that it has a sufficient number of training examples. Data augmentation takes the approach of generating more training data from existing training samples by augmenting the samples using random transformations that yield believable-looking images. The goal is the model will never see the exact same picture twice during training. This helps expose the model to more aspects of the data and generalize better.

Implement this in tf.keras using the ImageDataGenerator class. Pass different transformations to the dataset and it will take care of applying it during the training process.

Augment and visualize Data

Begin by applying random horizontal flip augmentation to the dataset and see how individual images look like after the transformation.

Apply Horizontal Flip

Pass horizontal_flip as an argument to the ImageDataGenerator class and set it to True to apply this augmentation.

image_gen = ImageDataGenerator(rescale=1./255, horizontal_flip=True)

train_data_gen = image_gen.flow_from_directory(batch_size=batch_size,directory=train_dir,shuffle=True,target_size=(IMG_HEIGHT, IMG_WIDTH))

Take one sample image from the training examples and repeat it five times so that the augmentation is applied to the same image five times.

augmented_images = [train_data_gen[0][0][0] for i in range(5)]

# Re-use the same custom plotting function defined and used
# above to visualize the training images
plotImages(augmented_images)

Randomly rotate the image

Let's take a look at a different augmentation called rotation and apply 45 degrees of rotation randomly to the training examples.

image_gen = ImageDataGenerator(rescale=1./255, rotation_range=45)

train_data_gen = image_gen.flow_from_directory(batch_size=batch_size,directory=train_dir,shuffle=True,target_size=(IMG_HEIGHT, IMG_WIDTH))

augmented_images = [train_data_gen[0][0][0] for i in range(5)]

plotImages(augmented_images)

Apply Zoom Augmentation

Apply a zoom augmentation to the dataset to zoom images up to 50% randomly.

# zoom_range from 0 - 1 where 1 = 100%.
image_gen = ImageDataGenerator(rescale=1./255, zoom_range=0.5) #

train_data_gen = image_gen.flow_from_directory(batch_size=batch_size,directory=train_dir,shuffle=True,target_size=(IMG_HEIGHT, IMG_WIDTH))

augmented_images = [train_data_gen[0][0][0] for i in range(5)]

plotImages(augmented_images)

Putting it all together

Apply all the previous augmentations. Here, you applied rescale, 45 degree rotation, width shift, height shift, horizontal flip and zoom augmentation to the training images.

image_gen_train = ImageDataGenerator(
                    rescale=1./255,
                    rotation_range=45,
                    width_shift_range=.15,
                    height_shift_range=.15,
                    horizontal_flip=True,
                    zoom_range=0.5
                    )

train_data_gen = image_gen_train.flow_from_directory(batch_size=batch_size,
                                                     directory=train_dir,
                                                     shuffle=True,
                                                     target_size=(IMG_HEIGHT, IMG_WIDTH),
                                                     class_mode='binary')

Visualize how a single image would look five different times when passing these augmentations randomly to the dataset.

augmented_images = [train_data_gen[0][0][0] for i in range(5)]
plotImages(augmented_images)

Create validation data generator

Generally, only apply data augmentation to the training examples. In this case, only rescale the validation images and convert them into batches using ImageDataGenerator.

image_gen_val = ImageDataGenerator(rescale=1./255)

val_data_gen = image_gen_val.flow_from_directory(batch_size=batch_size,
                                                 directory=validation_dir,
                                                 target_size=(IMG_HEIGHT, IMG_WIDTH),
                                                 class_mode='binary')

Dropout

Another technique to reduce overfitting is to introduce dropout to the network. It is a form of regularization that forces the weights in the network to take only small values, which makes the distribution of weight values more regular and the network can reduce overfitting on small training examples. Dropout is one of the regularization technique used in this tutorial

When you apply dropout to a layer it randomly drops out (set to zero) number of output units from the applied layer during the training process. Dropout takes a fractional number as its input value, in the form such as 0.1, 0.2, 0.4, etc. This means dropping out 10%, 20% or 40% of the output units randomly from the applied layer.

When appling 0.1 dropout to a certain layer, it randomly kills 10% of the output units in each training epoch.

Create a network architecture with this new dropout feature and apply it to different convolutions and fully-connected layers.

Creating a new network with Dropouts

Here, you apply dropout to first and last max pool layers. Applying dropout will randomly set 20% of the neurons to zero during each training epoch. This helps to avoid overfitting on the training dataset.

model_new = Sequential([
    Conv2D(16, 3, padding='same', activation='relu', 
           input_shape=(IMG_HEIGHT, IMG_WIDTH ,3)),
    MaxPooling2D(),
    Dropout(0.2),
    Conv2D(32, 3, padding='same', activation='relu'),
    MaxPooling2D(),
    Conv2D(64, 3, padding='same', activation='relu'),
    MaxPooling2D(),
    Dropout(0.2),
    Flatten(),
    Dense(512, activation='relu'),
    Dense(1)
])

Compile the model

After introducing dropouts to the network, compile the model and view the layers summary.

model_new.compile(optimizer='adam',
                  loss=tf.keras.losses.BinaryCrossentropy(from_logits=True),
                  metrics=['accuracy'])

model_new.summary()

Train the model

After successfully introducing data augmentations to the training examples and adding dropouts to the network, train this new network:

history = model_new.fit_generator(
    train_data_gen,
    steps_per_epoch=total_train // batch_size,
    epochs=epochs,
    validation_data=val_data_gen,
    validation_steps=total_val // batch_size
)

Visualize the model

Visualize the new model after training, you can see that there is significantly less overfitting than before. The accuracy should go up after training the model for more epochs.

acc = history.history['accuracy']
val_acc = history.history['val_accuracy']

loss = history.history['loss']
val_loss = history.history['val_loss']

epochs_range = range(epochs)

plt.figure(figsize=(8, 8))
plt.subplot(1, 2, 1)
plt.plot(epochs_range, acc, label='Training Accuracy')
plt.plot(epochs_range, val_acc, label='Validation Accuracy')
plt.legend(loc='lower right')
plt.title('Training and Validation Accuracy')

plt.subplot(1, 2, 2)
plt.plot(epochs_range, loss, label='Training Loss')
plt.plot(epochs_range, val_loss, label='Validation Loss')
plt.legend(loc='upper right')
plt.title('Training and Validation Loss')
plt.show()

Author Details

Am a senior student of Makerere University pursuing a Bachelor of Science degree in Telecommunications Engineering at the College of Engineering ,Design, Art and Technology.

Links to above ipython notebook tutorials

MyFirstNotebook : https://colab.research.google.com/drive/1zO7_uiTQ40lcxuv4OtaOe3vtKgoXYW0-

ML Intro: https://colab.research.google.com/drive/12KXXvzdV_2GSmqvwVoZPqSlVHOVe9Hpe?usp=sharing

Image Classifier : https://colab.research.google.com/drive/1m0VNPN5rg-l23y3zVk6vlQj9cbgDy1SH?usp=sharing

Github Repo

You can checkout this page's repository on Github by clicking the link below.

👉 https://github.com/KakoozaJerry/getting_started_with_colab

Contact Me

If you have any questions about this guide , do not hesitate to contact me on whichever platform you prefer below :) 👇

Email📧 : [email protected]

Twitter🐤 : @KakoozaJerry

Facebook😉 : @KakoozaJerry

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Why Colab?

Table of Contents

Basic Python Operations in Notebooks

My First Notebook

Uploading data to your Colab environment from your local machine.

Downloading Datasets into Google Drive via Google Colab

Saving your notebook to Google drive

Saving your notebook to Github

Getting started with running a GPU job on Google Colab.

Enabling GPU

Variables and Arithmetic

Functions

Machine Learning Intro

Scikit-Learn

Model Fitting

Prediction

How to run a job with GPU

Import Packages

Load Data

Understanding the data

Data preparation

Visualize training images

Create the model

Compile the model

Model summary

Train the model

Visualize training results

Overfitting

Data augmentation

Augment and visualize Data

Apply Horizontal Flip

Randomly rotate the image

Apply Zoom Augmentation

Putting it all together

Create validation data generator

Dropout

Creating a new network with Dropouts

Compile the model

Train the model

Visualize the model

Author Details

Links to above ipython notebook tutorials

Github Repo

Contact Me

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