From 6e2e532b6dc24ed62b9acad4bbb1d3d3585184ac Mon Sep 17 00:00:00 2001
From: "Jangberry (Nomad-Debian)" <matt2001@hotmail.fr>
Date: Thu, 9 Nov 2023 15:52:18 +0100
Subject: [PATCH] Pep8
---
.vscode/settings.json | 4 ++++
README.md | 14 +++++++++++++-
knn.py | 41 +++++++++++++++++++++++++----------------
requirements.txt | 3 ++-
4 files changed, 44 insertions(+), 18 deletions(-)
create mode 100644 .vscode/settings.json
diff --git a/.vscode/settings.json b/.vscode/settings.json
new file mode 100644
index 0000000..56c56a0
--- /dev/null
+++ b/.vscode/settings.json
@@ -0,0 +1,4 @@
+{
+ "python.analysis.autoImportCompletions": true,
+ "python.analysis.typeCheckingMode": "off"
+}
\ No newline at end of file
diff --git a/README.md b/README.md
index fbaab16..a0ac53b 100644
--- a/README.md
+++ b/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: 
+
+## 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 $\sigma'(x) = \sigma(x) \times (1 - \sigma(x))$
\ No newline at end of file
diff --git a/knn.py b/knn.py
index 9d67d29..9ba4dbf 100644
--- a/knn.py
+++ b/knn.py
@@ -1,6 +1,8 @@
-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
@@ -12,10 +14,13 @@ 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
@@ -31,11 +36,13 @@ 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):
+
+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
Arguments:
@@ -59,24 +66,26 @@ if __name__ == "__main__":
print("Reading data")
images, labels = read_cifar.read_cifar("data/cifar-10-batches-py/")
split_factor = 0.9
-
+
# 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...")
dist = distance_matrix(images_test, images_train)
-
+
# Evaluate the k-nearest neighbors algorithm
- accuracies = [] # List of the accuracy
- ks = [] # List to make sure the plot starts at one and not 0
+ 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)
fig = plt.figure()
plt.plot(ks, accuracies)
fig.savefig(fname="results/knn.png")
- plt.show()
\ No newline at end of file
+ plt.show()
diff --git a/requirements.txt b/requirements.txt
index 296d654..806f221 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1 +1,2 @@
-numpy
\ No newline at end of file
+numpy
+matplotlib
\ No newline at end of file
--
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