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@Jean-KOUAGOU
Jean-KOUAGOU committed Nov 23, 2019
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247 changes: 247 additions & 0 deletions .ipynb_checkpoints/Gaussian Discriminant Analysis-checkpoint.ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"class GDA(object):\n",
" \n",
" def __init__(self, features, target):\n",
" self.features=features\n",
" self.target=target\n",
" self.mu0=self.features.iloc[[i for i in range(self.target.shape[0]) if self.target.iloc[i]==0.0]].mean()\n",
" self.mu1=self.features.iloc[[i for i in range(self.target.shape[0]) if self.target.iloc[i]==1.0]].mean()\n",
" self.phi=(1.0/self.target.shape[0])*self.target[self.target==1.0].count()\n",
"\n",
" def P_y(self, y, phi):\n",
" return phi**y * (1-phi)**(1-y)\n",
" \n",
" def P_x_y(self, sigma, x, mu):\n",
" comp1 = 1.0/(np.sqrt((2*np.pi)**self.features.shape[1]) * np.sqrt(np.linalg.det(sigma)))\n",
" comp2 = float(np.exp(np.dot(-0.5*np.dot(x-mu, np.linalg.inv(sigma)), x-mu)))\n",
" return comp1*comp2\n",
"\n",
" \n",
" def Sigma(self):\n",
" sigma=np.matrix(np.zeros([self.features.shape[1], self.features.shape[1]]))\n",
" for i in range(self.target.shape[0]):\n",
" if self.target.iloc[i]==0:\n",
" sigma += np.dot(np.matrix(self.features.iloc[i, :]-self.mu0).T, np.matrix(self.features.iloc[i, :]-self.mu0))\n",
" \n",
" else:\n",
" sigma += np.dot(np.matrix(self.features.iloc[i, :]-self.mu1).T, np.matrix(self.features.iloc[i, :]-self.mu1))\n",
" \n",
" return (1.0/self.target.shape[0])*sigma\n",
" \n",
" def predict(self, X):\n",
" predictions=[]\n",
" for i in range(X.shape[0]):\n",
" Prob0=self.P_x_y(self.Sigma(), X.iloc[i, :], self.mu0)*self.P_y(0, self.phi)\n",
" Prob1=self.P_x_y(self.Sigma(), X.iloc[i, :], self.mu1)*self.P_y(1, self.phi)\n",
" if Prob0>Prob1:\n",
" predictions.append(0.0)\n",
" else:\n",
" predictions.append(1.0)\n",
" return np.array(predictions)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"mu1 = -1\n",
"mu2 = 3\n",
"sig1 = 0.5\n",
"sig2 = 1\n",
"N = 150\n",
"np.random.seed(10)\n",
"x11=np.random.randn(N,1)*sig1 + mu1\n",
"x12=np.random.randn(N,1)*sig1 + mu1+3\n",
"x21=np.random.randn(N,1)*sig2 + mu2\n",
"x22=np.random.randn(N,1)*sig2 + mu2+3\n",
"c = np.vstack((np.zeros((N,1)), np.ones((N,1))))\n",
"x1 = np.hstack((x11,x12))\n",
"x2 = np.hstack((x21,x21))\n",
"\n",
"X = np.hstack( (np.vstack( (x1,x2) ),c) )\n",
"np.random.shuffle(X)\n",
"dataset = pd.DataFrame(data=X, columns=['x','y','c'])\n"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"Data_xy=dataset.drop('c', axis=1)\n",
"target=dataset['c']"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"mu1 = -1\n",
"mu2 = 3\n",
"sig1 = 0.5\n",
"sig2 = 1\n",
"N1 = 100\n",
"np.random.seed(10)\n",
"x11=np.random.randn(N1,1)*sig1 + mu1\n",
"x12=np.random.randn(N1,1)*sig1 + mu1+3\n",
"x21=np.random.randn(N1,1)*sig2 + mu2\n",
"x22=np.random.randn(N1,1)*sig2 + mu2+3\n",
"c = np.vstack((np.zeros((N1,1)), np.ones((N1,1))))\n",
"x1 = np.hstack((x11,x12))\n",
"x2 = np.hstack((x21,x22))\n",
"\n",
"X = np.hstack( (np.vstack( (x1,x2) ),c) )\n",
"np.random.shuffle(X)\n",
"dataset1 = pd.DataFrame(data=X, columns=['x','y','c'])"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Accuracy: 66.5 %\n"
]
}
],
"source": [
"Gaussian=GDA(Data_xy, target)\n",
"\n",
"Features_test=dataset1[['x', 'y']]\n",
"Target_test=dataset1[['c']]\n",
"\n",
"predictions=Gaussian.predict(Features_test)\n",
"predictions=predictions.reshape(-1,1)\n",
"print(\"Accuracy: \", ((predictions==np.array(Target_test)).sum()/Target_test.shape[0])*100, \"%\")"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Train data is 10% of the data (10, 5)\n",
"Test data is 90% of the data (90, 5)\n"
]
}
],
"source": [
"from sklearn import datasets\n",
"\n",
"Iris=datasets.load_iris()\n",
"data=Iris['data']\n",
"Data=np.hstack([data, Iris['target'].reshape(-1,1)])\n",
"Random=list(range(data.shape[0]))\n",
"np.random.shuffle(Random)\n",
"Data=Data[Random]\n",
"Data\n",
"Col=Iris['feature_names']\n",
"Col.insert(len(Col), 'target')\n",
"Data=pd.DataFrame(Data, columns=Col)\n",
"Data.head()\n",
"Data=Data[(Data['target']==0) | (Data['target']==1)]\n",
"\n",
"Train_data=Data.iloc[0:10]\n",
"Test_data=Data.iloc[10:]\n",
"print(\"Train data is 10% of the data \",Train_data.shape)\n",
"print(\"Test data is 90% of the data \",Test_data.shape)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Accuracy: 100.0 %\n"
]
}
],
"source": [
"GaussianIris=GDA(Train_data.iloc[:,:-1], Train_data.iloc[:,-1])\n",
"\n",
"#GaussianIris.Sigma()\n",
"\n",
"pred=GaussianIris.predict(Test_data.iloc[:,:-1])\n",
"pred=pred.reshape(-1,1)\n",
"print(\"Accuracy: \", (pred==np.array(Test_data.iloc[:,-1]).reshape(-1,1)).sum()/Test_data.iloc[:,-1].shape[0]*100, \"%\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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"display_name": "Python 3",
"language": "python",
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},
"language_info": {
"codemirror_mode": {
"name": "ipython",
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},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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