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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Machine Learing, Gaussian Mixture Models\n",
    "## The Expectation-Maximization algorithm for Gaussian mixture models\n",
    "\n",
    "A **Gaussian Mixture Model** (GMM) is a probabilstic model that assumes the data points come from a mixture of several Gaussian (normal) distributions with unknown parameters. Each Gaussian distribution in this model is called a **component**, which has its own mean vector $\\mu_k$, covariance matrix $\\Sigma_k$, and mixture **weight** $\\pi_k$. Specifically, the probabilty function of a GMM with $K$ components is:\n",
    "<br>$p(x)=\\sum_{k=0}^{K-1}\\pi_k N(x|\\mu_k,\\Sigma_k)$\n",
    "<br>where $\\pi_k \\ge 0$ and $\\sum_{k=0}^{K-1}\\pi_k =1$. Also, $N(x|\\mu_k,\\Sigma_k)$ is the value of probability function of a Gaussian distribution with mean vector $\\mu_k$ and covariance matrix $\\Sigma_k$ at data point $x$.\n",
    "\n",
    "---\n",
    "The algorithm to estimate the unknown parameters of a GMM is called the **Expectation-Maximization** algorithm or the **EM algorithm** for short. The EM algorithm is an iterative emthod which alternates between two steps until convergence: The Expectation step (E-step) and the Maximization step (M-step). THe goal of the EM algorithom for a GMM is to find the local maximum of the likelihood (or the log-likelihood) function of the GMM given $n$ data points $X=\\{x_0,x_1,...,x_{n-1}\\}$.\n",
    "<br> **Hint:** The **log-likelihood** of a GMM with data points $X=\\{x_0,x_1,...,x_{n-1}\\}$ is expressed as:\n",
    "<br>$logp(X|\\mu,\\Sigma,\\pi)=\\sum_{i=0}^{n-1}log(\\sum_{k=0}^{K-1}\\pi_k N(x_i|\\mu_k,\\Sigma_k))$\n",
    "\n",
    "---\n",
    "The EM algorithm can be stated in the following steps:\n",
    "1. **Initialization:** The number of Gaussians is given in advance. So, initialize the unknown parameters: mean vectors, covariance matrices, and the weights.\n",
    "\n",
    "2. **Iteration:** Iterate the following two steps until **convergence**:\n",
    "      - **E-step:** Compute **responsibilities** (poster probabilities) with the current parameters\n",
    "      - **M-step:** Update the parameters with the computed responsibilities.\n",
    "\n",
    "---\n",
    "The details of the algorithm is given in the **pinterest** page mentioned below.\n",
    "<br>In the following, we implement the EM algorithm from scratch. We try the implemented EM with the iris datasets that has been reduced to 2-dimensional points by the **PCA** (Principal Components Analysis). At the end, we show the centroid (means) of each cluster along with its convaraince ellipse.\n",
    "\n",
    "<br>The code is at : https://github.com/ostad-ai/Machine-Learning\n",
    "<br>Explanation: https://www.pinterest.com/HamedShahHosseini/Machine-Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# importing the required modules\n",
    "import numpy as np\n",
    "from numpy.linalg import eig\n",
    "from scipy.stats import multivariate_normal\n",
    "from matplotlib import pyplot as plt\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of data points: 150\n",
      "The dimension of each data point: 4\n"
     ]
    }
   ],
   "source": [
    "# loading the iris dataset from scikit-learn datasets\n",
    "iris=load_iris()\n",
    "X,y=iris.data,iris.target\n",
    "print(f'The number of data points: {X.shape[0]}')\n",
    "print(f'The dimension of each data point: {X.shape[1]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the function to get the points of the ellipse of covariance\n",
    "def ellipse_covariance(mean,sigma,Npoints=100):\n",
    "    ts = np.linspace(0, 2*np.pi, Npoints);\n",
    "    eigvals,eigvecs=eig(sigma)\n",
    "    points = (np.sqrt(eigvals[np.newaxis,:]) * eigvecs) @ [np.cos(ts), np.sin(ts)]\n",
    "    return points[0]+mean[0],points[1]+mean[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class EM:\n",
    "    def __init__(self,n_components=3,max_iter=100,tolerance=1e-5):\n",
    "        self.K=n_components # number of Gaussians\n",
    "        self.maxIter=max_iter # maximum iteration\n",
    "        self.tol=tolerance # maximum tolerance for convergence\n",
    "        \n",
    "        #---initialize parameters\n",
    "    def initialization(self,X): # initialzie paramters \n",
    "        n,q=X.shape  # n is th number of samples, q is the dimension of each sample\n",
    "        self.weights = np.ones(self.K) /K  # weights become equal with their sum is one\n",
    "        self.means = X[np.random.choice(n, self.K, replace=False)]  #  K means randomly taken from X\n",
    "        self.covariances = [np.eye(q) for _ in range(self.K)]  # Identity covariances of size q*q\n",
    "    \n",
    "    # the Expectation-step\n",
    "    def e_step(self,X):\n",
    "        n = X.shape[0] # number of samples in X\n",
    "        self.responsibilities = np.zeros((n, self.K))\n",
    "        # compute responsibilities for each component (Gaussian)\n",
    "        for k in range(self.K):\n",
    "            self.responsibilities[:, k] = self.weights[k] * multivariate_normal.pdf(\n",
    "                X, mean=self.means[k], cov=self.covariances[k])\n",
    "\n",
    "        # normalize responsibilities\n",
    "        self.responsibilities /= self.responsibilities.sum(axis=1, keepdims=True)\n",
    "    \n",
    "    def m_step(self, X):\n",
    "        n,q = X.shape # n is the no. of samples. q is the dimension of each sample \n",
    "\n",
    "        # the effective number of samples for each component\n",
    "        effective_numbers=self.responsibilities.sum(axis=0)\n",
    "        # Update weights: for each k, effective number of samples for component k/total number of sampples\n",
    "        self.weights = effective_numbers / n\n",
    "\n",
    "        # update means\n",
    "        self.means = np.zeros((self.K, q))\n",
    "        for k in range(self.K):\n",
    "            self.means[k] = (self.responsibilities[:, k].reshape(1,-1)@X)/ effective_numbers[k]\n",
    "\n",
    "        # update covariances\n",
    "        self.covariances = [np.zeros((q,q)) for _ in range(self.K)]\n",
    "        for k in range(self.K):\n",
    "            diff = X - self.means[k]\n",
    "            for i in range(n):\n",
    "                self.covariances[k]+=self.responsibilities[i,k]*diff[i].reshape(-1,1)@diff[i].reshape(1,-1)\n",
    "            self.covariances[k]/=effective_numbers[k]\n",
    "            \n",
    "    def fit(self, X):\n",
    "        # initialize parameters\n",
    "        self.initialization(X)\n",
    "\n",
    "        # iterate until convergence or max iteration is reached\n",
    "        for iter in range(self.maxIter):\n",
    "            prevMeans = self.means.copy()\n",
    "            # E-step\n",
    "            self.e_step(X)\n",
    "            # M-step\n",
    "            self.m_step(X)\n",
    "            # Check for convergence with the Frobenius norm\n",
    "            if np.linalg.norm(self.means - prevMeans) < self.tol:\n",
    "                #print(f\"The EM has converged at iteration {iter}\")\n",
    "                break\n",
    "                \n",
    "    def predict(self, X): #hard assignment\n",
    "        # the component (Gaussian) with the highest responsibility is chosen\n",
    "        # for each row of X\n",
    "        # label is the index of the chosen component, counted from zero\n",
    "        self.e_step(X)\n",
    "        return np.argmax(self.responsibilities, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  We use PCA to reduce the dimension (number of features) of data points from 4 to 2\n",
    "pca=PCA(n_components=2)\n",
    "X2d=pca.fit_transform(X) # transformed data points with dimension 2\n",
    "K=3  # the number of components (clusters)\n",
    "gmm=EM(K)\n",
    "gmm.fit(X2d)\n",
    "# we can find the labels (clusters) of data points\n",
    "# labels are the index of clusters\n",
    "labels=gmm.predict(X2d)\n",
    "means=gmm.means\n",
    "covs=gmm.covariances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The centroids of clusters (the means of the Gaussians) are :\n",
      "[[-2.64241546  0.19088505]\n",
      " [ 0.47757825 -0.22918603]\n",
      " [ 1.96962883  0.00735392]]\n"
     ]
    }
   ],
   "source": [
    "print(f'The centroids of clusters (the means of the Gaussians) are :\\n{means}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# displaying the transformed 2-d data points along with the centroids (means) and covariance ellipses \n",
    "plt.scatter(X2d[:,0],X2d[:,1],c=labels,alpha=.5)\n",
    "plt.scatter(means[:,0],means[:,1],marker='*',c='red',s=150)\n",
    "for mean,cov in zip(means,covs):\n",
    "    points=ellipse_covariance(mean,cov)\n",
    "    plt.plot(points[0],points[1],c='black')\n",
    "plt.title('The EM for the GMM with the iris dataset'+\\\n",
    "          '\\nThe centroids shown with stars, the covariance ellipses in black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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