Refactor code for improved readability and consistency across multiple Jupyter notebooks

- Added missing commas in various print statements and function calls for better syntax.
- Reformatted code to enhance clarity, including breaking long lines and aligning parameters.
- Updated function signatures to use float type for sigma parameters instead of int for better precision.
- Cleaned up comments and documentation strings for clarity and consistency.
- Ensured consistent formatting in plotting functions and data handling.

M2/Unsupervised Learning/spectral_clustering.ipynb

@@ -9,6 +9,7 @@
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
+    "\n",
     "from sklearn.cluster import KMeans"
    ]
   },
@@ -77,11 +78,11 @@
     "    return eigenvalues[idx_L], eigenvectors[:, idx_L]\n",
     "\n",
     "\n",
-    "def compute_W_matrix(sigma: int, X: np.ndarray) -> np.ndarray:\n",
+    "def compute_W_matrix(sigma: float, X: np.ndarray) -> np.ndarray:\n",
     "    \"\"\"Fill the similarity matrix W.\n",
     "\n",
     "    Args:\n",
-    "        sigma (int): Parameter for the Gaussian kernel.\n",
+    "        sigma (float): Parameter for the Gaussian kernel.\n",
     "        X (np.ndarray): Input data.\n",
     "\n",
     "    Returns:\n",
@@ -94,7 +95,7 @@
     "            W[i, j] = (\n",
     "                0 if i == j else np.exp(-(np.abs(X[i] - X[j]) ** 2) / (2 * sigma**2))\n",
     "            )\n",
-    "    return W\n"
+    "    return W"
    ]
   },
   {
@@ -104,11 +105,11 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "def create_X(sigma: int, n: int, m: int) -> np.ndarray:\n",
+    "def create_X(sigma: float, n: int, m: int) -> np.ndarray:\n",
     "    \"\"\"Create a dataset with 4 Gaussian clusters.\n",
     "\n",
     "    Args:\n",
-    "        sigma (int): Standard deviation of the clusters.\n",
+    "        sigma (float): Standard deviation of the clusters.\n",
     "        n (int): Total number of data points.\n",
     "        m (int): Number of clusters.\n",
     "\n",
@@ -125,11 +126,11 @@
     "    return np.concatenate([norm_1, norm_2, norm_3, norm_4])\n",
     "\n",
     "\n",
-    "def plot_eigenvalues(sigma: int, n: int, m: int, k: int) -> None:\n",
+    "def plot_eigenvalues(sigma: float, n: int, m: int, k: int) -> None:\n",
     "    \"\"\"Plot the eigenvalues of the Laplacian for different sigma values.\n",
     "\n",
     "    Args:\n",
-    "        sigma (int): Standard deviation of the clusters.\n",
+    "        sigma (float): Standard deviation of the clusters.\n",
     "        n (int): Total number of data points.\n",
     "        m (int): Number of clusters.\n",
     "        k (int): Number of eigenvalues to compute.\n",
@@ -153,7 +154,7 @@
     "    plt.xlabel(\"Index\")\n",
     "    plt.ylabel(\"Eigenvalue\")\n",
     "\n",
-    "    plt.show()\n"
+    "    plt.show()"
    ]
   },
   {
@@ -236,7 +237,7 @@
     "n = 200\n",
     "m = 4\n",
     "for sigma in [0.1, 1 / 4, 0.5, 1]:\n",
-    "    plot_eigenvalues(sigma, n=n, m=m, k=k)\n"
+    "    plot_eigenvalues(sigma, n=n, m=m, k=k)"
    ]
   },
   {
@@ -246,14 +247,14 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "def spectral_clustering(sigma, n: int, m: int, k: int) -> np.ndarray:\n",
+    "def spectral_clustering(sigma: float, n: int, m: int, k: int) -> np.ndarray:\n",
     "    \"\"\"Perform spectral clustering on the data.\n",
     "\n",
     "    Args:\n",
-    "        sigma: The sigma value for the similarity matrix.\n",
-    "        n: Number of data points.\n",
-    "        m: Number of clusters.\n",
-    "        k: Number of eigenvectors to use.\n",
+    "        sigma (float): The sigma value for the similarity matrix.\n",
+    "        n (int): Number of data points.\n",
+    "        m (int): Number of clusters.\n",
+    "        k (int): Number of eigenvectors to use.\n",
     "\n",
     "    Returns:\n",
     "        X: The data points.\n",
@@ -269,7 +270,7 @@
     "\n",
     "    kmeans = KMeans(n_clusters=k)\n",
     "\n",
-    "    return X, kmeans.fit_predict(U_normalized)\n"
+    "    return X, kmeans.fit_predict(U_normalized)"
    ]
   },
   {
@@ -312,7 +313,7 @@
     "\n",
     "plt.scatter(X, np.zeros_like(X), c=clusters, cmap=\"magma\")\n",
     "plt.title(\"Spectral Clustering Results\")\n",
-    "plt.xlabel(\"Data Points\")\n"
+    "plt.xlabel(\"Data Points\")"
    ]
   },
   {