style: amélioration de la mise en forme et des espaces dans le code

M2/Unsupervised Learning/spectral_clustering.ipynb

@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": null,
    "id": "c1b23a23",
    "metadata": {},
    "outputs": [],
@@ -24,6 +24,7 @@
     "    D = np.diag(np.sum(W, axis=1))\n",
     "    return D - W\n",
     "\n",
+    "\n",
     "def compute_symmetric_laplacian(W: np.ndarray) -> np.ndarray:\n",
     "    \"\"\"Compute the symmetric normalized graph Laplacian.\"\"\"\n",
     "    D_inv_sqrt = np.diag(1.0 / np.sqrt(np.sum(W, axis=1)))\n",
@@ -35,24 +36,28 @@
     "    D_inv = np.diag(1.0 / np.sum(W, axis=1))\n",
     "    return np.eye(W.shape[0]) - D_inv @ W\n",
     "\n",
+    "\n",
     "def sort_eigenvalues(M: np.ndarray, k: int):\n",
     "    \"\"\"Sort eigenvalues and eigenvectors in ascending order.\"\"\"\n",
     "    eigenvalues, eigenvectors = np.linalg.eigh(M)\n",
     "    idx_L = np.argsort(eigenvalues)[:k]\n",
     "    return eigenvalues[idx_L], eigenvectors[:, idx_L]\n",
     "\n",
+    "\n",
     "def compute_W_matrix(sigma: int, X: np.ndarray) -> np.ndarray:\n",
     "    \"\"\"Fill the similarity matrix W.\"\"\"\n",
     "    W = np.zeros((len(X), len(X)))\n",
     "    for i in range(len(X)):\n",
     "        for j in range(len(X)):\n",
-    "            W[i, j] = 0 if i == j else np.exp(-(np.abs(X[i] - X[j]) ** 2) / (2 * sigma**2))\n",
-    "    return W"
+    "            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"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": null,
    "id": "9e7e4ffa",
    "metadata": {},
    "outputs": [],
@@ -67,6 +72,7 @@
     "\n",
     "    return np.concatenate([norm_1, norm_2, norm_3, norm_4])\n",
     "\n",
+    "\n",
     "def plot_eigenvalues(sigma: int, n: int, k: int):\n",
     "    \"\"\"Plot the eigenvalues of the Laplacian for different sigma values.\"\"\"\n",
     "    print(f\"Plotting the eigenvalues and the distribution for Sigma: {sigma}\")\n",
@@ -87,12 +93,12 @@
     "    plt.xlabel(\"Index\")\n",
     "    plt.ylabel(\"Eigenvalue\")\n",
     "\n",
-    "    plt.show()"
+    "    plt.show()\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": null,
    "id": "b3871450",
    "metadata": {},
    "outputs": [
@@ -168,13 +174,13 @@
    "source": [
     "k = 10\n",
     "n = 200\n",
-    "for sigma in [0.1, 1/4, 0.5, 1]:\n",
-    "    plot_eigenvalues(sigma, n, k)"
+    "for sigma in [0.1, 1 / 4, 0.5, 1]:\n",
+    "    plot_eigenvalues(sigma, n, k)\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": null,
    "id": "0fb32d82",
    "metadata": {},
    "outputs": [],
@@ -190,12 +196,12 @@
     "\n",
     "    kmeans = KMeans(n_clusters=k)\n",
     "\n",
-    "    return X, kmeans.fit_predict(U_normalized)"
+    "    return X, kmeans.fit_predict(U_normalized)\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": null,
    "id": "57c342d0",
    "metadata": {},
    "outputs": [
@@ -229,11 +235,11 @@
     }
    ],
    "source": [
-    "X, clusters = spectral_clustering(1/4, k=4)\n",
+    "X, clusters = spectral_clustering(1 / 4, k=4)\n",
     "\n",
     "plt.scatter(X, np.zeros_like(X), c=clusters, cmap=\"magma\")\n",
     "plt.title(\"Spectral Clustering Results\")\n",
-    "plt.xlabel(\"Data Points\")"
+    "plt.xlabel(\"Data Points\")\n"
    ]
   },
   {