diff --git a/README.md b/README.md
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--- a/README.md
+++ b/README.md
@@ -1,92 +1,341 @@
# Image classification
+Corentin MASSALA
+## Prepare the CIFAR dataset
+All the code can be found on the python file read_cifar.py
-## Getting started
+#### 2-
+```
+def read_cifar_batch(file):
+ with open(file, 'rb') as fo:
+ dict = pickle.load(fo, encoding='bytes')
+ return (np.array(dict[b'data']).astype('float32'), np.array(dict[b'labels']).astype('int64') )
+```
+#### 3-
+```
+def read_cifar(path):
+ data = []
+ labels = []
+
+ #Add the 5 batches
+ for i in range(1,6):
+ data_temp, labels_temps = read_cifar_batch(f'{path}/data_batch_{i}')
+ data.append(data_temp)
+ labels.append(labels_temps)
+
+ #Add the test batches
+ data_temp, labels_temps = read_cifar_batch(f'{path}/test_batch')
+ data.append(data_temp)
+ labels.append(labels_temps)
+
+ #Concatenate all the batches to create a big one
+ data = np.concatenate(data, axis = 0)
+ labels = np.concatenate(labels, axis = 0)
+
+ return(data, labels)
+```
+#### 4-
+
+To split the dataset we use the split function from the sklearn library
+
+```
+def split_dataset(data, labels, split):
+ X_train, X_test, y_train, y_test = train_test_split(
+ data, labels, test_size=(1 - split), random_state=0)
+
+ return(X_train, X_test, y_train, y_test)
+```
+
+
+## K-nearest neighbors
+All the code can be found on the python file knn.py
+#### 1-
+
+```
+def distance_matrix(matrix1, matrix2):
+ #X_test then X_train in this order
+ sum_of_squares_matrix1 = np.sum(np.square(matrix1), axis=1, keepdims=True) #A^2
+ sum_of_squares_matrix2 = np.sum(np.square(matrix2), axis=1, keepdims=True) #B^2
+
+ dot_product = np.dot(matrix1, matrix2.T) # A * B (matrix mutliplication)
+
+ dists = np.sqrt(sum_of_squares_matrix1 + sum_of_squares_matrix2.T - 2 * dot_product) # Compute the product
+ return dists
+```
+
+#### 2-
-To make it easy for you to get started with GitLab, here's a list of recommended next steps.
+```
+def knn_predict(dists, labels_train, k):
+ output = []
+ # Loop on all the images_test
+ for i in range(len(dists)):
+ # Innitialize table to store the neighbors
+ res = [0] * 10
+ # Get the closest neighbors
+ labels_close = np.argsort(dists[i])[:k]
+ for label in labels_close:
+ #add a label to the table of result
+ res[labels_train[label]] += 1
+ # Get the class with the maximum neighbors
+ label_temp = np.argmax(res) #Careful to the logic here, if there is two or more maximum, the function the first maximum encountered
+ output.append(label_temp)
+ return(np.array(output))
+```
-Already a pro? Just edit this README.md and make it your own. Want to make it easy? [Use the template at the bottom](#editing-this-readme)!
+#### 3-
-## Add your files
+```
+def evaluate_knn(data_train, labels_train, data_test, labels_tests, k):
+ dist = distance_matrix(data_test, data_train)
+ result_test = knn_predict(dist, labels_train, k)
-- [ ] [Create](https://docs.gitlab.com/ee/user/project/repository/web_editor.html#create-a-file) or [upload](https://docs.gitlab.com/ee/user/project/repository/web_editor.html#upload-a-file) files
-- [ ] [Add files using the command line](https://docs.gitlab.com/ee/gitlab-basics/add-file.html#add-a-file-using-the-command-line) or push an existing Git repository with the following command:
+ #accuracy
+ N = labels_tests.shape[0]
+ accuracy = (labels_tests == result_test).sum() / N
+ return(accuracy)
+```
+#### 4-
```
-cd existing_repo
-git remote add origin https://gitlab.ec-lyon.fr/cmassala/image-classification.git
-git branch -M main
-git push -uf origin main
+def bench_knn():
+
+ k_indices = [i for i in range(20) if i % 2 != 0]
+ accuracies = []
+
+ # Load data
+ data, labels = read_cifar.read_cifar('image-classification/data/cifar-10-batches-py')
+ X_train, X_test, y_train, y_test = read_cifar.split_dataset(data, labels, 0.9)
+
+ # Loop on the k_indices to get all the accuracies
+ for k in k_indices:
+ accuracy = evaluate_knn(X_train, y_train, X_test, y_test, k)
+ accuracies.append(accuracy)
+
+ # Save and show the graph of accuracies
+ fig = plt.figure()
+ plt.plot(k_indices, accuracies)
+ plt.title("Accuracy as function of k")
+ plt.show()
+ plt.savefig('image-classification/results/knn_batch_1.png')
+ plt.close(fig)
```
-## Integrate with your tools
+Here is the graph of the accuracy vs K for the whole Cifar dataset with a split factor of 0.9:
-- [ ] [Set up project integrations](https://gitlab.ec-lyon.fr/cmassala/image-classification/-/settings/integrations)
+
-## Collaborate with your team
+Here we can conclude that the best K is 9, (if we don't use k = 1) with a performace of 35% of accuracy.
-- [ ] [Invite team members and collaborators](https://docs.gitlab.com/ee/user/project/members/)
-- [ ] [Create a new merge request](https://docs.gitlab.com/ee/user/project/merge_requests/creating_merge_requests.html)
-- [ ] [Automatically close issues from merge requests](https://docs.gitlab.com/ee/user/project/issues/managing_issues.html#closing-issues-automatically)
-- [ ] [Enable merge request approvals](https://docs.gitlab.com/ee/user/project/merge_requests/approvals/)
-- [ ] [Set auto-merge](https://docs.gitlab.com/ee/user/project/merge_requests/merge_when_pipeline_succeeds.html)
+## Artificial Neural Network
-## Test and Deploy
+### Math Theory
-Use the built-in continuous integration in GitLab.
+Here are all the answer for the theory of the backpropagation.
-- [ ] [Get started with GitLab CI/CD](https://docs.gitlab.com/ee/ci/quick_start/index.html)
-- [ ] [Analyze your code for known vulnerabilities with Static Application Security Testing(SAST)](https://docs.gitlab.com/ee/user/application_security/sast/)
-- [ ] [Deploy to Kubernetes, Amazon EC2, or Amazon ECS using Auto Deploy](https://docs.gitlab.com/ee/topics/autodevops/requirements.html)
-- [ ] [Use pull-based deployments for improved Kubernetes management](https://docs.gitlab.com/ee/user/clusters/agent/)
-- [ ] [Set up protected environments](https://docs.gitlab.com/ee/ci/environments/protected_environments.html)
+#### 1-
+
-***
+#### 2-
+
-# Editing this README
+#### 3-
+
-When you're ready to make this README your own, just edit this file and use the handy template below (or feel free to structure it however you want - this is just a starting point!). Thank you to [makeareadme.com](https://www.makeareadme.com/) for this template.
+#### 4-
+
-## Suggestions for a good README
-Every project is different, so consider which of these sections apply to yours. The sections used in the template are suggestions for most open source projects. Also keep in mind that while a README can be too long and detailed, too long is better than too short. If you think your README is too long, consider utilizing another form of documentation rather than cutting out information.
+#### 5-
+
-## Name
-Choose a self-explaining name for your project.
+#### 6-
+
-## Description
-Let people know what your project can do specifically. Provide context and add a link to any reference visitors might be unfamiliar with. A list of Features or a Background subsection can also be added here. If there are alternatives to your project, this is a good place to list differentiating factors.
+#### 7-
+
-## Badges
-On some READMEs, you may see small images that convey metadata, such as whether or not all the tests are passing for the project. You can use Shields to add some to your README. Many services also have instructions for adding a badge.
+#### 8-
+
-## Visuals
-Depending on what you are making, it can be a good idea to include screenshots or even a video (you'll frequently see GIFs rather than actual videos). Tools like ttygif can help, but check out Asciinema for a more sophisticated method.
+#### 9-
+
-## Installation
-Within a particular ecosystem, there may be a common way of installing things, such as using Yarn, NuGet, or Homebrew. However, consider the possibility that whoever is reading your README is a novice and would like more guidance. Listing specific steps helps remove ambiguity and gets people to using your project as quickly as possible. If it only runs in a specific context like a particular programming language version or operating system or has dependencies that have to be installed manually, also add a Requirements subsection.
-## Usage
-Use examples liberally, and show the expected output if you can. It's helpful to have inline the smallest example of usage that you can demonstrate, while providing links to more sophisticated examples if they are too long to reasonably include in the README.
+### Coding part
+All the code can be found on the file mlp.py
-## Support
-Tell people where they can go to for help. It can be any combination of an issue tracker, a chat room, an email address, etc.
+```
+def learn_once_mse(w1, b1, w2, b2, data, targets, learning_rate):
+
+ N_out = len(targets) #number of training examples
+
+ # Forward pass
+ a0 = data # the data are the input of the first layer
+ z1 = np.matmul(a0, w1) + b1 # input of the hidden layer
+ a1 = sigmoid(z1) # output of the hidden layer (sigmoid activation function)
+ z2 = np.matmul(a1, w2) + b2 # input of the output layer
+ a2 = sigmoid(z2) # output of the output layer (sigmoid activation function)
+ predictions = a2 # the predicted values are the outputs of the output layer
+
+ # Compute loss (MSE)
+ loss = np.mean(np.square(predictions - targets))
+ print(f'loss: {loss}')
+ # print('shape a1', a1.shape)
+ # print('shape w1', w1.shape)
+ # print('shape b1', b1.shape)
+
+ # print('shape a2', a2.shape)
+ # print('shape w2', w2.shape)
+ # print('shape b2', b2.shape)
+
+ # Backpropagation
+ delta_a2 = 2 / N_out * (a2 - targets)
+ # print('shape delta_a2', delta_a2.shape)
+ delta_z2 = delta_a2 * (a2 * (1 - a2))
+ # print('shape delta_z2', delta_z2.shape)
+ delta_w2 = np.dot(a1.T, delta_z2)
+ # print('shape delta_w2', delta_w2.shape)
+ delta_b2 = delta_z2
+
+ delta_a1 = np.dot(delta_z2, w2.T)
+ # print('shape delta_a1', delta_a1.shape)
+ delta_z1 = delta_a1 * (a1 * (1- a1))
+ # print('shape delta_z1', delta_z1.shape)
+ delta_w1 = np.dot(a0.T, delta_z1)
+ # print('shape delta_w1', delta_w2.shape)
+ delta_b1 = delta_z1
+
+ # Update weights and biases
+ w2 -= learning_rate * delta_w2
+ b2 -= learning_rate * np.sum(delta_b2, axis = 0, keepdims = True)
+
+ w1 -= learning_rate * delta_w1
+ b1 -= learning_rate * np.sum(delta_b1, axis = 0, keepdims = True)
+
+ return w1, b1, w2, b2, loss
+```
-## Roadmap
-If you have ideas for releases in the future, it is a good idea to list them in the README.
+#### 11-
+```
+def one_hot(labels):
+ #num_classes = np.max(labels) + 1 on va le hardcoder ici
+ num_classes = 10
+ one_hot_matrix = np.eye(num_classes)[labels]
+ return one_hot_matrix
+```
-## Contributing
-State if you are open to contributions and what your requirements are for accepting them.
+#### 12-
+The cross_entropy_loss is :
+```
+def cross_entropy_loss(y_pred, y_true):
+ loss = -np.sum(y_true * np.log(y_pred)) / len(y_pred)
+ return loss
+```
+The new learning function is :
+
+```
+def learn_once_cross_entropy(w1, b1, w2, b2, data, labels_train, learning_rate):
+
+ N_out = len(labels_train) #number of training examples
+
+ # Forward pass
+ a0 = data # the data are the input of the first layer
+ z1 = np.matmul(a0, w1) + b1 # input of the hidden layer
+ a1 = sigmoid(z1) # output of the hidden layer (sigmoid activation function)
+ z2 = np.matmul(a1, w2) + b2 # input of the output layer
+ a2 = softmax_stable(z2) # output of the output layer (sigmoid activation function)
+ predictions = a2 # the predicted values are the outputs of the output layer
+
+
+ # Compute loss (cross-entropy loss)
+ y_true_one_hot = one_hot(labels_train)
+ loss = cross_entropy_loss(predictions, y_true_one_hot)
+
+
+ # Backpropagation
+ delta_z2 = (a2 - y_true_one_hot)
+ delta_w2 = np.dot(a1.T, delta_z2) / N_out # We divide by the sample size to have an average on the error and avoid big gradient jumps
+ delta_b2 = delta_z2 / N_out
+
+
+ delta_a1 = np.dot(delta_z2, w2.T)
+ delta_z1 = delta_a1 * (a1 * (1 - a1))
+ delta_w1 = np.dot(a0.T, delta_z1) / N_out
+ delta_b1 = delta_z1 / N_out
+
+ # Update weights and biases
+ w2 -= learning_rate * delta_w2
+ b2 -= learning_rate * np.sum(delta_b2, axis = 0, keepdims = True)
+
+ w1 -= learning_rate * delta_w1
+ b1 -= learning_rate * np.sum(delta_b1, axis = 0, keepdims = True)
+
+ return w1, b1, w2, b2, loss
+```
+
+#### 13-
+```
+def forward(w1, b1, w2, b2, data):
+ # Forward pass
+ a0 = data # the data are the input of the first layer
+ z1 = np.matmul(a0, w1) + b1 # input of the hidden layer
+ a1 = sigmoid(z1) # output of the hidden layer (sigmoid activation function)
+ z2 = np.matmul(a1, w2) + b2 # input of the output layer
+ a2 = softmax_stable(z2) # output of the output layer (sigmoid activation function)
+ predictions = a2 # the predicted values are the outputs of the output layer
+ return(predictions)
+```
+```
+def train_mlp(w1, b1, w2, b2, data_train, labels_train, learning_rate, num_epoch):
+ train_accuracies = []
+ for epoch in range(num_epoch):
+ w1, b1, w2, b2, loss = learn_once_cross_entropy(w1, b1, w2, b2, data_train, labels_train, learning_rate)
+
+ # Compute accuracy
+ predictions = forward(w1, b1, w2, b2, data_train)
+ predicted_labels = np.argmax(predictions, axis=1)
+ # print(predictions.shape)
+ # print(predicted_labels.shape)
+ # print(labels_train.shape)
+ accuracy = np.mean(predicted_labels == labels_train)
+ train_accuracies.append(accuracy)
+
+ print(f'Epoch {epoch + 1}/{num_epoch}, Loss: {loss:.3f}, Train Accuracy: {accuracy:.2f}')
+
+ return w1, b1, w2, b2, train_accuracies
+```
+#### 14-
+```def test_mlp(w1, b1, w2, b2, data_test, labels_test):
+
+ # Compute accuracy
+ predictions = forward(w1, b1, w2, b2, data_test)
+ predicted_labels = np.argmax(predictions, axis=1)
+ print(predicted_labels)
+ test_accuracy = np.mean(predicted_labels == labels_test)
+ print(f'Train Accuracy: {test_accuracy:.2f}')
+ return test_accuracy
+```
+
+#### 15-
+
+```
+def run_mlp_training(data_train, labels_train, data_test, labels_test, d_h,learning_rate, num_epoch):
-For people who want to make changes to your project, it's helpful to have some documentation on how to get started. Perhaps there is a script that they should run or some environment variables that they need to set. Make these steps explicit. These instructions could also be useful to your future self.
+ d_in = data_train.shape[1]
+ d_out = 10 #we can hard code it here or len(np.unique(label_train))
-You can also document commands to lint the code or run tests. These steps help to ensure high code quality and reduce the likelihood that the changes inadvertently break something. Having instructions for running tests is especially helpful if it requires external setup, such as starting a Selenium server for testing in a browser.
+ #Random initialisation of weights
+ w1 = np.random.randn(d_in, d_h)
+ b1 = np.random.randn(1, d_h)
-## Authors and acknowledgment
-Show your appreciation to those who have contributed to the project.
+ w2 = np.random.randn(d_h, d_out)
+ b2 = np.random.randn(1, d_out)
-## License
-For open source projects, say how it is licensed.
+ # Train MLP
+ w1, b1, w2, b2, train_accuracies = train_mlp(w1, b1, w2, b2, data_train, labels_train, learning_rate, num_epoch)
-## Project status
-If you have run out of energy or time for your project, put a note at the top of the README saying that development has slowed down or stopped completely. Someone may choose to fork your project or volunteer to step in as a maintainer or owner, allowing your project to keep going. You can also make an explicit request for maintainers.
+ # Test MLP
+ test_accuracy = test_mlp(w1, b1, w2, b2, data_test, labels_test)
+ return train_accuracies, test_accuracy
+```
\ No newline at end of file