Pep8

.vscode/settings.json

+{
+    "python.analysis.autoImportCompletions": true,
+    "python.analysis.typeCheckingMode": "off"
+}
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README.md

@@ -3,10 +3,22 @@
 ## Setup
 
 1. Download the [CIFAR dataset](https://www.cs.toronto.edu/~kriz/cifar.html) `cifar-10-batches-py` in the [data](./data/) folder.
-1. You might want to create a venv with `python -m venv .venv` and activate it with `source .venv/bin/activate`.
+1. (*optionnal*) You might want to create a venv with `python -m venv .venv` and activate it with `source .venv/bin/activate`.
 1. Install the requirements using `pip install -r requirements.txt`.
 
 ## Usage
 
 To test knn, simply run [knn.py](./knn.py) using `python knn.py`.  
 Otherwise here is a test result: ![knn test result](./results/knn.png)
+
+## Some proofs
+
+### *1. Prove that $`\sigma' = \sigma \times (1-\sigma)`$*
+
+To prove that, let's firt derive the sigmoid function:  
+$\sigma(x) = \frac{1}{1+e^{-x}}$  
+so $\sigma'(x)=\frac{e^{-x}}{(1+e^{-x})^2}$  
+$\sigma'(x)=\frac{1}{1+e^{-x}}\times\frac{e^{-x}}{1+e^{-x}}$  
+Here we can identify $\frac{1}{1+e^{-x}} = \sigma(x)$  
+And $\frac{e^{-x}}{1+e^{-x}} = 1 - \frac{1}{1+e^{x}}$  
+So $\sigma'(x) = \sigma(x) \times (1 - \sigma(x))$
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knn.py

-import read_cifar
-import numpy as np
 import matplotlib.pyplot as plt
+import numpy as np
+
+import read_cifar
+
 
 def distance_matrix(X: np.array, Y: np.array):
     """Compute the L2 distance between two matricies
@@ -12,9 +14,12 @@ def distance_matrix(X: np.array, Y: np.array):
         dist -- distance matrix (shape: (X.shape[0], Y.shape[0])) => dist[i, j] = L2(X[i], Y[j])
     """
     return np.sqrt(
-        np.sum(np.square(X), axis=1).reshape((-1, 1))@np.ones((1, Y.shape[0])) + # X²
-        np.ones((X.shape[0], 1))@np.sum(np.square(Y), axis=1).reshape((1, -1))   # Y²
-        - 2*X@Y.T)                                                       # -2XY
+        # X² + Y² - 2XY
+        np.sum(np.square(X), axis=1).reshape((-1, 1))@np.ones((1, Y.shape[0])) +
+        np.ones((X.shape[0], 1))@np.sum(np.square(Y),
+                                        axis=1).reshape((1, -1))
+        - 2*X@Y.T)
+
 
 def knn_predict(dist: np.array, labels_train: np.array, k: int):
     """Predict the labels of the test set using the k-nearest neighbors algorithm
@@ -31,10 +36,12 @@ def knn_predict(dist: np.array, labels_train: np.array, k: int):
     # Get the labels of the k nearest neighbors
     labels = labels_train[indices]
     # Get the most frequent label
-    labels = np.apply_along_axis(lambda x: np.bincount(x).argmax(), axis=1, arr=labels)
+    labels = np.apply_along_axis(
+        lambda x: np.bincount(x).argmax(), axis=1, arr=labels)
 
     return labels
 
+
 def evaluate_knn(data_train: np.array, labels_train: np.array, data_test: np.array, labels_test: np.array, k: int, dist=None):
     """Evaluate the k-nearest neighbors algorithm
 
@@ -62,7 +69,8 @@ if __name__ == "__main__":
 
     # Split the data into training and testing sets
     print("Splitting sets")
-    images_train, labels_train, images_test, labels_test = read_cifar.split_dataset(images, labels, split_factor)
+    images_train, labels_train, images_test, labels_test = read_cifar.split_dataset(
+        images, labels, split_factor)
 
     # Compute the distance matrix
     print("Computing the distance matrix...")
@@ -72,7 +80,8 @@ if __name__ == "__main__":
     accuracies = []  # List of the accuracy
     ks = []  # List to make sure the plot starts at one and not 0
     for k in range(1, 21):
-        accuracy = evaluate_knn(images_train, labels_train, images_test, labels_test, k)
+        accuracy = evaluate_knn(
+            images_train, labels_train, images_test, labels_test, k)
         print(f"Accuracy for k = {k}: {accuracy}")
         accuracies.append(accuracy)
         ks.append(k)

requirements.txt

 numpy
+matplotlib
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