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cv_total_least_squares_regression.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": [],
"authorship_tag": "ABX9TyOYq86GFxfnrqpMj/TGxbsq",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/dsaint31x/9215404d5f84c063942c9c48666b4794/cv_total_least_squares_regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from sklearn.linear_model import LinearRegression\n",
"\n",
"# OLS를 사용한 회귀\n",
"def ols_regression(X, y):\n",
" ols = LinearRegression()\n",
" ols.fit(X, y)\n",
" return ols.coef_[0], ols.intercept_\n",
"\n",
"# TLS를 사용한 회귀 (EVD 이용)\n",
"def tls_regression(X, y):\n",
" # 평균을 원점으로 맞추기 (Mean Centering)\n",
" X_mean = np.mean(X)\n",
" y_mean = np.mean(y)\n",
" X_centered = X - X_mean\n",
" y_centered = y - y_mean\n",
"\n",
" # 데이터 행렬 생성\n",
" A = np.hstack((X_centered, y_centered))\n",
"\n",
" # 공분산 행렬 계산\n",
" cov_matrix = np.cov(A.T)\n",
"\n",
" # Eigen Value Decomposition\n",
" eigenvalues, eigenvectors = np.linalg.eig(cov_matrix)\n",
"\n",
" # Eigen values에 따라 정렬\n",
" idx = np.argsort(eigenvalues)\n",
" eigenvectors = eigenvectors[:, idx]\n",
"\n",
" # TLS 회귀 계수 계산 (작은 eigenvalue에 대응하는 eigenvector 사용)\n",
" tls_direction = eigenvectors[:, 0]\n",
" a_tls = -tls_direction[0] / tls_direction[1]\n",
" b_tls = y_mean - a_tls * X_mean\n",
"\n",
" return a_tls, b_tls, tls_direction\n",
"\n",
"# 데이터 생성\n",
"np.random.seed(0)\n",
"X = np.linspace(0, 10, 20)\n",
"y = 2 * X + 1 + np.random.normal(scale=2, size=X.shape)\n",
"\n",
"X = X.reshape(-1, 1) # X를 2차원 배열로 변환\n",
"y = y.reshape(-1, 1) # y를 2차원 배열로 변환\n",
"\n",
"# OLS 회귀\n",
"a_ols, b_ols = ols_regression(X, y)\n",
"y_pred_ols = a_ols * X + b_ols\n",
"\n",
"# TLS 회귀\n",
"a_tls, b_tls, tls_direction = tls_regression(X, y)\n",
"y_pred_tls = a_tls * X + b_tls\n",
"\n",
"# 그래프 그리기\n",
"plt.scatter(X, y, label='Data')\n",
"plt.plot(X, y_pred_ols, color='red', label='OLS fit')\n",
"plt.plot(X, y_pred_tls, color='blue', label='TLS fit')\n",
"\n",
"# OLS residuals\n",
"for i in range(len(X)):\n",
" plt.plot([X[i], X[i]], [y[i], y_pred_ols[i]], color='red', linestyle='dotted')\n",
"\n",
"# TLS residuals in the direction of the eigen vector\n",
"tls_direction = tls_direction / np.linalg.norm(tls_direction) # Normalize the direction vector\n",
"for i in range(len(X)):\n",
" point = np.array([X[i], y[i]]).flatten()\n",
" proj_length = np.dot(point - np.array([X[i], a_tls * X[i] + b_tls]).flatten(), tls_direction)\n",
" proj_point = point - proj_length * tls_direction\n",
" plt.plot([point[0], proj_point[0]], [point[1], proj_point[1]], color='blue', linestyle='dotted')\n",
"\n",
"plt.xlabel('X')\n",
"plt.ylabel('y')\n",
"plt.legend()\n",
"plt.title('Comparison of OLS and TLS with Residuals')\n",
"plt.show()\n",
"\n",
"print(f'OLS 회귀 계수: 기울기={a_ols}, 절편={b_ols}')\n",
"print(f'TLS 회귀 계수: 기울기={a_tls}, 절편={b_tls}')"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 508
},
"id": "l3Qa3KGLKkfB",
"outputId": "e62f4a0f-a7c2-44ce-cbca-fc9b3e5db1b7"
},
"execution_count": 30,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"OLS 회귀 계수: 기울기=[1.77255483], 절편=[3.27589504]\n",
"TLS 회귀 계수: 기울기=1.8864122408637019, 절편=2.706607981572759\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from sklearn.linear_model import LinearRegression\n",
"\n",
"# OLS를 사용한 회귀\n",
"def ols_regression(X, y):\n",
" ols = LinearRegression()\n",
" ols.fit(X, y)\n",
" return ols.coef_[0], ols.intercept_\n",
"\n",
"# TLS를 사용한 회귀 (SVD 이용)\n",
"def tls_regression_svd(X, y):\n",
" # 평균을 원점으로 맞추기 (Mean Centering)\n",
" X_mean = np.mean(X)\n",
" y_mean = np.mean(y)\n",
" X_centered = X - X_mean\n",
" y_centered = y - y_mean\n",
"\n",
" # 데이터 행렬 생성\n",
" A = np.hstack((X_centered, y_centered))\n",
"\n",
" # SVD 분해\n",
" U, S, Vt = np.linalg.svd(A, full_matrices=False)\n",
"\n",
" # TLS 회귀 계수 계산 (작은 singular value에 대응하는 singular vector 사용)\n",
" tls_direction = Vt[-1]\n",
" a_tls = -tls_direction[0] / tls_direction[1]\n",
" b_tls = y_mean - a_tls * X_mean\n",
"\n",
" return a_tls, b_tls, tls_direction\n",
"\n",
"# 데이터 생성\n",
"np.random.seed(0)\n",
"X = np.linspace(0, 10, 20)\n",
"y = 2 * X + 1 + np.random.normal(scale=2, size=X.shape)\n",
"\n",
"X = X.reshape(-1, 1) # X를 2차원 배열로 변환\n",
"y = y.reshape(-1, 1) # y를 2차원 배열로 변환\n",
"\n",
"# OLS 회귀\n",
"a_ols, b_ols = ols_regression(X, y)\n",
"y_pred_ols = a_ols * X + b_ols\n",
"\n",
"# TLS 회귀 (SVD)\n",
"a_tls, b_tls, tls_direction = tls_regression_svd(X, y)\n",
"y_pred_tls = a_tls * X + b_tls\n",
"\n",
"# 그래프 그리기\n",
"plt.scatter(X, y, label='Data')\n",
"plt.plot(X, y_pred_ols, color='red', label='OLS fit')\n",
"plt.plot(X, y_pred_tls, color='green', label='TLS fit (SVD)')\n",
"\n",
"# OLS residuals\n",
"for i in range(len(X)):\n",
" plt.plot([X[i], X[i]], [y[i], y_pred_ols[i]], color='red', linestyle='dotted')\n",
"\n",
"# TLS residuals in the direction of the singular vector\n",
"tls_direction = tls_direction / np.linalg.norm(tls_direction) # Normalize the direction vector\n",
"for i in range(len(X)):\n",
" point = np.array([X[i], y[i]]).flatten()\n",
" proj_length = np.dot(point - np.array([X[i], a_tls * X[i] + b_tls]).flatten(), tls_direction)\n",
" proj_point = point - proj_length * tls_direction\n",
" plt.plot([point[0], proj_point[0]], [point[1], proj_point[1]], color='green', linestyle='dotted')\n",
"\n",
"plt.xlabel('X')\n",
"plt.ylabel('y')\n",
"plt.legend()\n",
"plt.title('Comparison of OLS and TLS (SVD) with Residuals')\n",
"plt.show()\n",
"\n",
"print(f'OLS 회귀 계수: 기울기={a_ols}, 절편={b_ols}')\n",
"print(f'TLS 회귀 계수 (SVD): 기울기={a_tls}, 절편={b_tls}')"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 508
},
"id": "CgKLsBr3Misz",
"outputId": "1fa76473-fd6e-430c-d3f2-8ab6277a3b88"
},
"execution_count": 32,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"OLS 회귀 계수: 기울기=[1.77255483], 절편=[3.27589504]\n",
"TLS 회귀 계수 (SVD): 기울기=1.886412240863701, 절편=2.7066079815727644\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from sklearn.linear_model import LinearRegression\n",
"\n",
"# OLS를 사용한 회귀\n",
"def ols_regression(X, y):\n",
" ols = LinearRegression()\n",
" ols.fit(X, y)\n",
" return ols.coef_[0], ols.intercept_\n",
"\n",
"# TLS를 사용한 회귀 (EVD 이용)\n",
"def tls_regression_without_mean_centering(X, y):\n",
" # 데이터 행렬 생성\n",
" A = np.hstack((X, y))\n",
"\n",
" # 공분산 행렬 계산\n",
" cov_matrix = np.cov(A.T)\n",
"\n",
" # Eigen Value Decomposition\n",
" eigenvalues, eigenvectors = np.linalg.eig(cov_matrix)\n",
"\n",
" # Eigen values에 따라 정렬\n",
" idx = np.argsort(eigenvalues)\n",
" eigenvectors = eigenvectors[:, idx]\n",
"\n",
" # TLS 회귀 계수 계산 (작은 eigenvalue에 대응하는 eigenvector 사용)\n",
" tls_direction = eigenvectors[:, 0]\n",
" a_tls = -tls_direction[0] / tls_direction[1]\n",
" b_tls = np.mean(y) - a_tls * np.mean(X)\n",
"\n",
" return a_tls, b_tls, tls_direction\n",
"\n",
"# 데이터 생성\n",
"np.random.seed(0)\n",
"X = np.linspace(0, 10, 20)\n",
"y = 2 * X + 1 + np.random.normal(scale=2, size=X.shape)\n",
"\n",
"X = X.reshape(-1, 1) # X를 2차원 배열로 변환\n",
"y = y.reshape(-1, 1) # y를 2차원 배열로 변환\n",
"\n",
"# OLS 회귀\n",
"a_ols, b_ols = ols_regression(X, y)\n",
"y_pred_ols = a_ols * X + b_ols\n",
"\n",
"# TLS 회귀\n",
"a_tls, b_tls, tls_direction = tls_regression_without_mean_centering(X, y)\n",
"y_pred_tls = a_tls * X + b_tls\n",
"\n",
"# 그래프 그리기\n",
"plt.scatter(X, y, label='Data')\n",
"plt.plot(X, y_pred_ols, color='red', label='OLS fit')\n",
"plt.plot(X, y_pred_tls, color='blue', label='TLS fit')\n",
"\n",
"# OLS residuals\n",
"for i in range(len(X)):\n",
" plt.plot([X[i], X[i]], [y[i], y_pred_ols[i]], color='red', linestyle='dotted')\n",
"\n",
"# TLS residuals in the direction of the eigen vector\n",
"tls_direction = tls_direction / np.linalg.norm(tls_direction) # Normalize the direction vector\n",
"for i in range(len(X)):\n",
" point = np.array([X[i], y[i]]).flatten()\n",
" proj_length = np.dot(point - np.array([X[i], a_tls * X[i] + b_tls]).flatten(), tls_direction)\n",
" proj_point = point - proj_length * tls_direction\n",
" plt.plot([point[0], proj_point[0]], [point[1], proj_point[1]], color='blue', linestyle='dotted')\n",
"\n",
"plt.xlabel('X')\n",
"plt.ylabel('y')\n",
"plt.legend()\n",
"plt.title('Comparison of OLS and TLS with Residuals (Without Mean Centering)')\n",
"plt.show()\n",
"\n",
"print(f'OLS 회귀 계수: 기울기={a_ols}, 절편={b_ols}')\n",
"print(f'TLS 회귀 계수: 기울기={a_tls}, 절편={b_tls}')"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 508
},
"id": "QCCt_9G5NgzA",
"outputId": "55e782ab-1563-47de-a5f9-ba51ea458341"
},
"execution_count": 33,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"OLS 회귀 계수: 기울기=[1.77255483], 절편=[3.27589504]\n",
"TLS 회귀 계수: 기울기=1.8864122408637019, 절편=2.706607981572759\n"
]
}
]
},
{
"cell_type": "code",
"source": [],
"metadata": {
"id": "gREWFDPm1niz"
},
"execution_count": null,
"outputs": []
}
]
}
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