Pengelompokan data (GMM) dengan mean-field.

gmm-mf.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "910f0ec2-af02-4425-a0b7-2c9cda9cf262",
   "metadata": {},
   "source": [
    "# Implementasi GMM dgn mean-field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "26bedf45-af02-472c-bcfe-695894b9b249",
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import HTML\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from scipy.special import digamma\n",
    "from scipy.stats import multivariate_normal\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2d4ce74f-773a-4146-be63-79bedcb1eb00",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng(12345)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8fa65aa-fa83-4513-ba6f-a7aa33f3b6af",
   "metadata": {},
   "source": [
    "## Aturan pembaruan"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2d05c89-6388-418c-8e00-6b551b96de72",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{E}_q\\log\\pi_k\n",
    "=\\psi\\left(\\alpha_k+\\sum_iq(z_i=k)\\right)-\\psi\\left(\\sum_{k^\\prime}\\alpha_{k^\\prime}+N\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "08500f86-a341-4249-96a4-06989760da97",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_Eq_pi(q_z, alpha):\n",
    "    n_items, n_labels = q_z.shape\n",
    "    assert alpha.shape == (n_labels,)\n",
    "    return digamma(alpha + q_z.sum(axis=0)) - digamma(alpha.sum() + n_items)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa644fa5-8198-4ab5-b3a2-7bff390c0be6",
   "metadata": {},
   "source": [
    "$$\\omega_k^2=\\left(\\frac{1}{\\lambda^2}+\\frac{1}{\\sigma^2}\\sum_iq(z_i=k)\\right)^{-1}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a9ac2aa6-329a-4811-9ade-ce224ea645ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_omega2(q_z, lambda2=1, sigma2=1):\n",
    "    assert q_z.ndim == 2\n",
    "    return 1 / (1/lambda2 + 1/sigma2 * q_z.sum(axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3695a988-b333-45ac-9374-f73cf325698d",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{\\theta}_k\n",
    "=\\omega_k^2\\left(\\frac{1}{\\lambda^2}\\boldsymbol{\\gamma}_k+\\frac{1}{\\sigma^2}\\sum_iq(z_i=k)\\mathbf{x}_i\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6c6087ff-ab75-4ea0-a20a-6591e74b9e75",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_theta(q_z, omega2, X, gamma, lambda2=1, sigma2=1):\n",
    "    n_items, n_labels = q_z.shape\n",
    "    _, n_dims = X.shape\n",
    "    assert omega2.shape == (n_labels,)\n",
    "    assert X.shape[0] == n_items\n",
    "    assert gamma.shape == (n_labels, n_dims)\n",
    "\n",
    "    return omega2[:, np.newaxis] * (1/lambda2 * gamma + 1/sigma2 * q_z.T @ X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1dd3a73-0b0c-464e-9431-42c5ad2da720",
   "metadata": {},
   "source": [
    "$$\\mathbb{E}_q[\\boldsymbol{\\mu}_k^\\top\\boldsymbol{\\mu}_k]=D\\sigma^2+\\boldsymbol{\\theta}_k^\\top\\boldsymbol{\\theta}_k$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "16661fec-7aea-4ebb-8384-2f8f3ae0bf95",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_Eq_mu2(theta, sigma2=1):\n",
    "    assert theta.ndim == 2\n",
    "    return theta.shape[1] * sigma2 + (theta**2).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2becc0a1-8050-4d1b-b361-b104f235f44d",
   "metadata": {},
   "source": [
    "$$\n",
    "q(z_i=k)\n",
    "\\propto\\exp\\left\\lbrace\n",
    "  \\mathbb{E}_{q(\\boldsymbol{\\pi})}\\log\\pi_k-\\frac{1}{2\\sigma^2}\\left(\n",
    "     \\mathbb{E}_q[\\boldsymbol{\\mu}_k^\\top\\boldsymbol{\\mu}_k]\n",
    "     -2\\mathbb{E}_q[\\boldsymbol{\\mu}_k]^\\top\\mathbf{x}_i\n",
    "  \\right)\n",
    "\\right\\rbrace\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7956412f-88df-42b7-91d9-ccef0996ada6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_q_z(Eq_pi, Eq_mu2, theta, X, sigma2=1):\n",
    "    n_labels, n_dims = theta.shape\n",
    "    assert Eq_pi.shape == (n_labels,)\n",
    "    assert X.ndim == 2 and X.shape[1] == n_dims\n",
    "    \n",
    "    q_z = np.exp(Eq_pi - 1/(2*sigma2) * (Eq_mu2 - 2 * X @ theta.T))\n",
    "    return q_z / q_z.sum(axis=1, keepdims=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6ef2b92-fb4f-4cce-bcbc-5bf480325076",
   "metadata": {},
   "source": [
    "## Membangun data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7feae5b0-5658-40fc-abdd-810c3e32042a",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_items = 1000\n",
    "gamma = np.array([[1, 1], [10, 1], [1, 10], [10, 10]])\n",
    "n_labels = gamma.shape[0]\n",
    "lambda2, sigma2 = 1.5**2 , 1.5**2\n",
    "alpha = np.ones(n_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad21f7d1-9dfa-4c46-bfa9-f49f95b2ba81",
   "metadata": {},
   "source": [
    "$$\\boldsymbol{\\mu}_k\\sim\\mathcal{N}(\\boldsymbol{\\gamma}_k,\\lambda^2\\mathbf{I})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b7d3ffe8-9d62-4c52-9ba8-b5ebee937224",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.13573755,  2.89559269],\n",
       "       [ 8.69400739,  0.61124015],\n",
       "       [ 0.88698504,  8.88867302],\n",
       "       [ 7.94831095, 10.9733392 ]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu = rng.normal(gamma, np.sqrt(lambda2))\n",
    "mu"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a39f20b1-6c81-4d48-96f8-da0622496655",
   "metadata": {},
   "source": [
    "$$\\boldsymbol{\\pi}\\sim\\mathrm{Dirichlet}(\\boldsymbol{\\alpha})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "55992abe-c79e-433e-9537-0456a443a806",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.288709  , 0.23926787, 0.02033005, 0.45169308])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi = rng.dirichlet(alpha)\n",
    "pi"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "219c5cd5-7783-4ed6-b68b-34889be457b4",
   "metadata": {},
   "source": [
    "$$z_i\\sim\\mathrm{Categorical}(\\boldsymbol{\\pi})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c3c86fc0-69f3-4df1-97a2-57c2c7bc1468",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 0, 1, 3, 3, 1, 3, 0, 0, 0])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = rng.choice(n_labels, n_items, p=pi)\n",
    "z[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a772812-f2e9-4013-8a27-2b7845c5fe63",
   "metadata": {},
   "source": [
    "$$\\mathbf{x}_i\\sim\\mathcal{N}(\\boldsymbol{\\mu}_{z_i},\\sigma^2\\mathbf{I})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cc9688fe-20a0-4bbd-a7f0-4a3f789eeb48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8.38914584, 11.30198982],\n",
       "       [-2.09251275,  3.69193404],\n",
       "       [ 8.33819005, -1.1536928 ],\n",
       "       [ 9.75582509, 12.05015829],\n",
       "       [ 3.91890176,  8.17544853]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = rng.normal(mu[z], np.sqrt(sigma2))\n",
    "X[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c11f181f-464f-4491-8443-72850cfc533d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1267428d0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_title('Plot data dengan label asli')\n",
    "for l in range(n_labels):\n",
    "    ax.scatter(X[z == l, 0], X[z == l, 1], label=l)\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f715a63-adad-4953-ac51-c8c2e8b934e8",
   "metadata": {},
   "source": [
    "## Menjalankan algoritma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "bdaf9bad-fc7b-4a1f-91f2-75a16b889969",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Akurasi tebakan awal: 26.3%\n",
      "Macro-F1 tebakan awal: 26.0%\n"
     ]
    }
   ],
   "source": [
    "q_z = rng.random([n_items, n_labels])\n",
    "q_z /= q_z.sum(axis=1, keepdims=True)\n",
    "z_init = q_z.argmax(axis=1)\n",
    "\n",
    "prec = rec = 0\n",
    "for l in range(n_labels):\n",
    "    if (z_init == l).sum() == 0:\n",
    "        prec_ = 1\n",
    "    else:\n",
    "        prec_ = ((z == l) & (z_init == l)).sum() / (z_init == l).sum()\n",
    "    rec_ = ((z == l) & (z_init == l)).sum() / (z == l).sum()\n",
    "    prec += prec_\n",
    "    rec += rec_\n",
    "prec /= n_labels\n",
    "rec /= n_labels\n",
    "\n",
    "acc = (z == z_init).mean()\n",
    "f1 = (2*prec*rec) / (prec+rec)\n",
    "print(f'Akurasi tebakan awal: {acc:.1%}')\n",
    "print(f'Macro-F1 tebakan awal: {f1:.1%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ecc6f487-9e8f-4db3-83b5-72a9d8906367",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iterasi 20/500\n",
      "Konvergen di iterasi 20\n"
     ]
    }
   ],
   "source": [
    "theta_hist = []\n",
    "for it in range(500):\n",
    "    if (it + 1) % 20 == 0:\n",
    "        print(f'Iterasi {it+1}/500')\n",
    "    Eq_pi = get_Eq_pi(q_z, alpha)\n",
    "    omega2 = get_omega2(q_z, lambda2, sigma2)\n",
    "    theta = get_theta(q_z, omega2, X, gamma, lambda2, sigma2)\n",
    "    Eq_mu2 = get_Eq_mu2(theta, sigma2)\n",
    "    old_q_z = q_z\n",
    "    q_z = get_q_z(Eq_pi, Eq_mu2, theta, X, sigma2)\n",
    "    theta_hist.append((it + 1, theta))\n",
    "    if np.allclose(old_q_z, q_z):\n",
    "        print('Konvergen di iterasi', it + 1)\n",
    "        break\n",
    "else:\n",
    "    print('Belum konvergen dalam 500 iterasi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "80335a3d-9307-4da2-9eb8-6b74366564f0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Akurasi tebakan akhir: 67.8%\n",
      "Macro-F1 tebakan akhir: 56.1%\n"
     ]
    }
   ],
   "source": [
    "z_hat = q_z.argmax(axis=1)\n",
    "\n",
    "prec = rec = 0\n",
    "for l in range(n_labels):\n",
    "    if (z_hat == l).sum() == 0:\n",
    "        prec_ = 1\n",
    "    else:\n",
    "        prec_ = ((z == l) & (z_hat == l)).sum() / (z_hat == l).sum()\n",
    "    rec_ = ((z == l) & (z_hat == l)).sum() / (z == l).sum()\n",
    "    prec += prec_\n",
    "    rec += rec_\n",
    "prec /= n_labels\n",
    "rec /= n_labels\n",
    "\n",
    "acc = (z == z_hat).mean()\n",
    "f1 = (2*prec*rec) / (prec+rec)\n",
    "print(f'Akurasi tebakan akhir: {acc:.1%}')\n",
    "print(f'Macro-F1 tebakan akhir: {f1:.1%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2e95c65e-c1ca-4450-9ae4-15ef35106747",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12684f080>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_title('Plot data dgn label prediksi')\n",
    "for l in range(n_labels):\n",
    "    ax.scatter(X[z_hat == l, 0], X[z_hat == l, 1], label=l)\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62ea4e48-385e-456a-87eb-cc2fe10d0c28",
   "metadata": {},
   "source": [
    "## Menampilkan perubahan distribusi Gaussian per kelompok"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1be35080-786a-448f-94e1-ba1ca8f29eb4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xmin, xmax = X[:, 0].min(), X[:, 0].max()\n",
    "ymin, ymax = X[:, 1].min(), X[:, 1].max()\n",
    "xv, yv = np.meshgrid(np.linspace(xmin-2, xmax+2, num=100), np.linspace(ymin-2, ymax+2, num=100))\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.axis('square')\n",
    "\n",
    "def plot_gauss(args):\n",
    "    it, theta = args\n",
    "    ax.clear()\n",
    "    ax.set_prop_cycle(None)\n",
    "    ax.set_title(f'Iterasi {it}')\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])\n",
    "    for l in range(n_labels):\n",
    "        ax.scatter(X[z == l, 0], X[z == l, 1], label=l)\n",
    "        zv = multivariate_normal.pdf(np.stack([xv, yv], axis=2), theta[l], sigma2)\n",
    "        ax.contour(xv, yv, zv)\n",
    "\n",
    "anim = FuncAnimation(fig, plot_gauss, theta_hist)\n",
    "plt.close()\n",
    "HTML(anim.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e6330a8a-cfd1-4f9d-b813-f53e7da5fda4",
   "metadata": {},
   "outputs": [],
   "source": [
    "anim.save('../content/images/gmm-mf.gif', writer='imagemagick')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}