{
"cells": [
{
"cell_type": "code",
"execution_count": 97,
"id": "e2813538",
"metadata": {},
"outputs": [],
"source": [
"import time\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"import seaborn as sns\n",
"from scipy.linalg import svd\n",
"\n",
"from sklearn.datasets import load_svmlight_file\n",
"from sklearn.metrics.pairwise import rbf_kernel\n",
"from sklearn.model_selection import train_test_split\n",
"from sklearn.preprocessing import StandardScaler\n",
"\n",
"rng = np.random.default_rng(42)"
]
},
{
"cell_type": "code",
"execution_count": 98,
"id": "641aeaac",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(49990, 22) (49990,)\n"
]
}
],
"source": [
"X, y = load_svmlight_file(\"./data/ijcnn1.bz2\")\n",
"print(X.shape, y.shape)"
]
},
{
"cell_type": "code",
"execution_count": 99,
"id": "0e003e1e",
"metadata": {},
"outputs": [],
"source": [
"scaler = StandardScaler(with_mean=False)\n",
"X_scaled = scaler.fit_transform(X)"
]
},
{
"cell_type": "code",
"execution_count": 100,
"id": "a3a85d20",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"((20000, 22), (29990, 22))"
]
},
"execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X_train, X_test, y_train, y_test = train_test_split(\n",
" X_scaled,\n",
" y,\n",
" test_size=29990 / 49990,\n",
" random_state=42,\n",
")\n",
"\n",
"X_train.shape, X_test.shape"
]
},
{
"cell_type": "code",
"execution_count": 101,
"id": "b78a08ae",
"metadata": {},
"outputs": [],
"source": [
"from sklearn.metrics import accuracy_score\n",
"from sklearn.svm import LinearSVC\n",
"\n",
"clf = LinearSVC(dual=False, random_state=42)\n",
"\n",
"start_time = time.time()\n",
"clf.fit(X_train, y_train)\n",
"training_time_svc = time.time() - start_time\n",
"y_pred_svc = clf.predict(X_test)\n",
"accuracy_svc = accuracy_score(y_test, y_pred_svc)"
]
},
{
"cell_type": "code",
"execution_count": 102,
"id": "8cb70eb0",
"metadata": {},
"outputs": [],
"source": [
"from sklearn.svm import SVC\n",
"\n",
"clf_rbf = SVC(kernel=\"rbf\", random_state=42)\n",
"\n",
"start_time = time.time()\n",
"clf_rbf.fit(X_train, y_train)\n",
"training_time_rbf = time.time() - start_time\n",
"y_pred_rbf = clf_rbf.predict(X_test)\n",
"accuracy_rbf = accuracy_score(y_test, y_pred_rbf)"
]
},
{
"cell_type": "code",
"execution_count": 103,
"id": "cf96d113",
"metadata": {},
"outputs": [],
"source": [
"def compute_rkf(\n",
" X_train: np.ndarray,\n",
" X_test: np.ndarray,\n",
" c: int = 300,\n",
" gamma: float | None = None,\n",
") -> tuple[np.ndarray, np.ndarray]:\n",
" \"\"\"Compute Random Kitchen Features for RBF kernel approximation.\n",
"\n",
" Args:\n",
" X_train (np.ndarray): Training data of shape (n1, p).\n",
" X_test (np.ndarray): Test data of shape (n2, p).\n",
" c (int): Number of random features to generate.\n",
" gamma (float | None): Kernel coefficient for RBF kernel. If None, defaults to 1/p.\n",
"\n",
" Returns:\n",
" tuple[np.ndarray, np.ndarray]: Transformed training and test data of shapes (n1, c) and (n2, c).\n",
"\n",
" \"\"\"\n",
" p = X_train.shape[1]\n",
"\n",
" if gamma is None:\n",
" gamma = 1 / p\n",
"\n",
" W = rng.normal(0, np.sqrt(2 * gamma), size=(p, c))\n",
" b = rng.uniform(0, 2 * np.pi, size=(1, c))\n",
"\n",
" def transform(X: np.ndarray) -> np.ndarray:\n",
" \"\"\"Transform the input data using Random Kitchen Features.\"\"\"\n",
" return np.sqrt(2 / c) * np.cos(np.dot(X, W) + b)\n",
"\n",
" return transform(X_train), transform(X_test)\n"
]
},
{
"cell_type": "code",
"execution_count": 104,
"id": "d0487ec1",
"metadata": {},
"outputs": [],
"source": [
"Z_train, Z_test = compute_rkf(X_train.toarray(), X_test.toarray(), c=300)\n",
"\n",
"clf_rkf = LinearSVC(dual=False, random_state=42)\n",
"\n",
"start_time = time.time()\n",
"clf_rkf.fit(Z_train, y_train)\n",
"training_time_rkf = time.time() - start_time\n",
"\n",
"y_pred_rkf = clf_rkf.predict(Z_test)\n",
"accuracy_rkf = accuracy_score(y_test, y_pred_rkf)"
]
},
{
"cell_type": "code",
"execution_count": 105,
"id": "bf07c16e",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.microsoft.datawrangler.viewer.v0+json": {
"columns": [
{
"name": "index",
"rawType": "int64",
"type": "integer"
},
{
"name": "Méthode",
"rawType": "object",
"type": "string"
},
{
"name": "Accuracy",
"rawType": "float64",
"type": "float"
},
{
"name": "Temps (s)",
"rawType": "float64",
"type": "float"
}
],
"ref": "5e2536cf-d951-4c4a-9a11-c620b11f6cce",
"rows": [
[
"0",
"Linear SVM (Raw)",
"0.9221407135711904",
"0.08201122283935547"
],
[
"1",
"Full RBF SVM",
"0.9737912637545849",
"1.1328659057617188"
],
[
"2",
"RKF (c=300)",
"0.9551517172390797",
"0.713508129119873"
]
],
"shape": {
"columns": 3,
"rows": 3
}
},
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" Méthode | \n",
" Accuracy | \n",
" Temps (s) | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" Linear SVM (Raw) | \n",
" 0.922141 | \n",
" 0.082011 | \n",
"
\n",
" \n",
" | 1 | \n",
" Full RBF SVM | \n",
" 0.973791 | \n",
" 1.132866 | \n",
"
\n",
" \n",
" | 2 | \n",
" RKF (c=300) | \n",
" 0.955152 | \n",
" 0.713508 | \n",
"
\n",
" \n",
"
\n",
"