1. Marchine_learning_and_linear_algebra.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b1620cdc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "D1 = np.array([[1.0, 1.2, 3, 4, 5, 6], [1.7, 3, 2.3, 5.3, 3.8, 5.5]])\n",
    "D2 = np.array([[-0.6, 1.0, 1.2, 3, 4, 5, 6], [2.9, 1.7, 3, 2.3, 5.3, 3.8, 5.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d057ad94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1,2,sharex=True, sharey=False)\n",
    "fig.set_size_inches((15,6))\n",
    "\n",
    "ax1.plot(D1[0], D1[1], 'ko', markersize=10)\n",
    "ax1.set_xlim([-1,7])\n",
    "ax1.set_ylim([1,6])\n",
    "ax1.set_title('D1', fontsize=18)\n",
    "\n",
    "ax2.plot(D2[0], D2[1], 'ko', markersize=10)\n",
    "ax2.set_xlim([-1,7])\n",
    "ax2.set_ylim([1,6])\n",
    "ax2.set_title('D2', fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "542afa5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D1.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "963c07a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def machine_learning(D):\n",
    "    N = D.shape[1]\n",
    "    X = np.c_[np.ones(N), D[0]]\n",
    "    y = D[1]\n",
    "    \n",
    "    w = np.linalg.solve(np.dot(X.T, X), np.dot(X.T, y))\n",
    "    return w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3944e5d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 0, 0, 4, 5, 6]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.c_[np.array([[1,2,3]]), 0, 0, np.array([[4,5,6]])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "2f9c954e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1.])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9b380131",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 1.2, 3. , 4. , 5. , 6. ],\n",
       "       [1.7, 3. , 2.3, 5.3, 3.8, 5.5]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d8ee0f04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 1.7],\n",
       "       [1.2, 3. ],\n",
       "       [3. , 2.3],\n",
       "       [4. , 5.3],\n",
       "       [5. , 3.8],\n",
       "       [6. , 5.5]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D1.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "068d09f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.89,  6.3 ,  6.91, 13.01, 11.46, 15.35],\n",
       "       [ 6.3 , 10.44, 10.5 , 20.7 , 17.4 , 23.7 ],\n",
       "       [ 6.91, 10.5 , 14.29, 24.19, 23.74, 30.65],\n",
       "       [13.01, 20.7 , 24.19, 44.09, 40.14, 53.15],\n",
       "       [11.46, 17.4 , 23.74, 40.14, 39.44, 50.9 ],\n",
       "       [15.35, 23.7 , 30.65, 53.15, 50.9 , 66.25]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(D1.T, D1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a5f8f7c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.89,  6.3 ,  6.91, 13.01, 11.46, 15.35],\n",
       "       [ 6.3 , 10.44, 10.5 , 20.7 , 17.4 , 23.7 ],\n",
       "       [ 6.91, 10.5 , 14.29, 24.19, 23.74, 30.65],\n",
       "       [13.01, 20.7 , 24.19, 44.09, 40.14, 53.15],\n",
       "       [11.46, 17.4 , 23.74, 40.14, 39.44, 50.9 ],\n",
       "       [15.35, 23.7 , 30.65, 53.15, 50.9 , 66.25]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.matmul(D1.T, D1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "0268aa60",
   "metadata": {},
   "outputs": [],
   "source": [
    "def more_clever(D):\n",
    "    first, last = D[:,0], D[:,-1]\n",
    "    w1 = (last[1]-first[1]) / (last[0]-first[0])\n",
    "    w0 = -w1 * first[0] + first[1]\n",
    "    return(w0, w1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "1ba81ab7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.51079935, 0.62055465])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "machine_learning(D1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "aa2f7a65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.94, 0.76)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "more_clever(D1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "932e2ef4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1. , 1.7])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D1[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "01fafe84",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D1[:,0][1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "772e8d03",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x,w):\n",
    "    return w[1] * x + w[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "0799119b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "w_ml_d1 = machine_learning(D1)\n",
    "w_mc_d1 = more_clever(D1)\n",
    "\n",
    "w_ml_d2 = machine_learning(D2)\n",
    "w_mc_d2 = more_clever(D2)\n",
    "\n",
    "x = np.linspace(-1,7, 100)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1,2, sharex=True, sharey=True)\n",
    "fig.set_size_inches((15,6))\n",
    "\n",
    "ax1.plot(D1[0], D1[1], 'ko', markersize=10)\n",
    "ax1.plot(x, f(x, w_ml_d1), c='k', lw=2, label='machine learning')\n",
    "ax1.plot(x, f(x, w_mc_d1), '--', c='k', lw=2, label='more clever')\n",
    "ax1.set_xlim([-1,7])\n",
    "ax1.set_ylim([1,6])\n",
    "ax1.legend(fontsize=18)\n",
    "\n",
    "ax2.plot(D2[0], D2[1], 'ko', markersize=10)\n",
    "ax2.plot(x, f(x, w_ml_d2), c='k', lw=2, label='machine learning')\n",
    "ax2.plot(x, f(x, w_mc_d2), '--', c='k', lw=2, label='more clever')\n",
    "ax2.set_xlim([-1,7])\n",
    "ax2.set_ylim([1,6])\n",
    "ax2.legend(fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd293eed",
   "metadata": {},
   "source": [
    "## 150번 반복해서 선을 그리며 점점 최적의 선을 찾아가는 과정"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "700f5c4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "D1 = np.array([[1.0, 1.2, 3, 4, 5, 6],\n",
    "             [1.5, 3, 2.3, 5.3, 3.8, 5.5]])\n",
    "\n",
    "num_iters = 150\n",
    "eta = 0.02\n",
    "\n",
    "np.random.seed(2)\n",
    "w = np.random.randn(2)\n",
    "N = D1.shape[1]\n",
    "\n",
    "ws, L = [], []\n",
    "\n",
    "# 1열에는 숫자 1이 있고, 2열에는 데이터의 x좌표가 있는 행렬 X를 만듭니다.\n",
    "# X: (N,2), Y: (N,)\n",
    "X = np.c_[np.ones(N), D1[0]]\n",
    "y = D1[1]\n",
    "\n",
    "# 여기서 우리의 경험 E를 반복하면서  태스크 T를 개선합니다.\n",
    "for i in range(num_iters):\n",
    "    # grad L\n",
    "    c = (1/N) * np.dot(X.T, np.dot(X, w) - y)\n",
    "    # 안전장치 grad L을 이용해서 w를 수정합니다.\n",
    "    w -= eta * c\n",
    "    # w가 변화되는 과정을 저장합니다.\n",
    "    ws.append(w)\n",
    "    \n",
    "    # 손실을 계산합니다.\n",
    "    L.append( ((np.dot(X, w)-y)**2).sum()/(2*N) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "0b9c2167",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 1. ],\n",
       "       [1. , 1.2],\n",
       "       [1. , 3. ],\n",
       "       [1. , 4. ],\n",
       "       [1. , 5. ],\n",
       "       [1. , 6. ]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "37ca21d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.58801406, 0.83186127])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "f75825b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 1. , 1. , 1. , 1. , 1. ],\n",
       "       [1. , 1.2, 3. , 4. , 5. , 6. ]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "369c1049",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.41987533, 1.58624759, 3.08359787, 3.91545914, 4.74732041,\n",
       "       5.57918168])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(X, w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "005477da",
   "metadata": {},
   "outputs": [],
   "source": [
    "test = np.array([1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "9993ee77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5862475853230076"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[1,0]*w[0]+X[1,1]*w[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "570b1059",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0835978703415035"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[2,0]*w[0]+X[2,1]*w[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "5e8fa77d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 1. , 1. , 1. , 1. , 1. ],\n",
       "       [1. , 1.2, 3. , 4. , 5. , 6. ]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "7478525b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 6)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.T.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "fef21734",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6,)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.dot(X, w) - y).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "6a7d5905",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-1, 7, 100)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1,2)\n",
    "fig.set_size_inches((15,6))\n",
    "\n",
    "ax1.plot(D1[0], D1[1], 'ko', markersize=8)\n",
    "ax1.plot(x, f(x, w), c='k', lw=2, label='machine learning')\n",
    "ax1.set_xlim([-1,7])\n",
    "ax1.set_ylim([1,6])\n",
    "ax1.legend(fontsize=18)\n",
    "\n",
    "ax2.plot(L[:50], '--', c='k', label='loss')\n",
    "ax2.legend(fontsize=18)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "cf4b31ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# num_iters = 250으로 했을 때\n",
    "\n",
    "x = np.linspace(-1, 7, 100)\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1,2)\n",
    "fig.set_size_inches((15,6))\n",
    "\n",
    "ax1.plot(D1[0], D1[1], 'ko', markersize=8)\n",
    "ax1.plot(x, f(x, w), c='k', lw=2, label='machine learning')\n",
    "ax1.set_xlim([-1,7])\n",
    "ax1.set_ylim([1,6])\n",
    "ax1.legend(fontsize=18)\n",
    "\n",
    "ax2.plot(L[:50], '--', c='k', label='loss')\n",
    "ax2.legend(fontsize=18)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e577b5fe",
   "metadata": {},
   "outputs": [],
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