20. PCA_practice_with_digits.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "feb17e59",
   "metadata": {},
   "source": [
    "# 20-1. PCA를 통한 이미지 잡음 제거\n",
    "\n",
    "- https://jakevdp.github.io/PythonDataScienceHandbook/05.09-principal-component-analysis.html\n",
    "- 위의 Github 실습을 참고했음"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2d219b0d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "손글씨 이미지의 크기는 64 픽셀 입니다.\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "from sklearn.datasets import load_digits\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "digits = load_digits()\n",
    "print(\"손글씨 이미지의 크기는\",digits.data.shape[1],\"픽셀 입니다.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ab72057e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'data': array([[ 0.,  0.,  5., ...,  0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0., ..., 10.,  0.,  0.],\n",
       "        [ 0.,  0.,  0., ..., 16.,  9.,  0.],\n",
       "        ...,\n",
       "        [ 0.,  0.,  1., ...,  6.,  0.,  0.],\n",
       "        [ 0.,  0.,  2., ..., 12.,  0.,  0.],\n",
       "        [ 0.,  0., 10., ..., 12.,  1.,  0.]]),\n",
       " 'target': array([0, 1, 2, ..., 8, 9, 8]),\n",
       " 'frame': None,\n",
       " 'feature_names': ['pixel_0_0',\n",
       "  'pixel_0_1',\n",
       "  'pixel_0_2',\n",
       "  'pixel_0_3',\n",
       "  'pixel_0_4',\n",
       "  'pixel_0_5',\n",
       "  'pixel_0_6',\n",
       "  'pixel_0_7',\n",
       "  'pixel_1_0',\n",
       "  'pixel_1_1',\n",
       "  'pixel_1_2',\n",
       "  'pixel_1_3',\n",
       "  'pixel_1_4',\n",
       "  'pixel_1_5',\n",
       "  'pixel_1_6',\n",
       "  'pixel_1_7',\n",
       "  'pixel_2_0',\n",
       "  'pixel_2_1',\n",
       "  'pixel_2_2',\n",
       "  'pixel_2_3',\n",
       "  'pixel_2_4',\n",
       "  'pixel_2_5',\n",
       "  'pixel_2_6',\n",
       "  'pixel_2_7',\n",
       "  'pixel_3_0',\n",
       "  'pixel_3_1',\n",
       "  'pixel_3_2',\n",
       "  'pixel_3_3',\n",
       "  'pixel_3_4',\n",
       "  'pixel_3_5',\n",
       "  'pixel_3_6',\n",
       "  'pixel_3_7',\n",
       "  'pixel_4_0',\n",
       "  'pixel_4_1',\n",
       "  'pixel_4_2',\n",
       "  'pixel_4_3',\n",
       "  'pixel_4_4',\n",
       "  'pixel_4_5',\n",
       "  'pixel_4_6',\n",
       "  'pixel_4_7',\n",
       "  'pixel_5_0',\n",
       "  'pixel_5_1',\n",
       "  'pixel_5_2',\n",
       "  'pixel_5_3',\n",
       "  'pixel_5_4',\n",
       "  'pixel_5_5',\n",
       "  'pixel_5_6',\n",
       "  'pixel_5_7',\n",
       "  'pixel_6_0',\n",
       "  'pixel_6_1',\n",
       "  'pixel_6_2',\n",
       "  'pixel_6_3',\n",
       "  'pixel_6_4',\n",
       "  'pixel_6_5',\n",
       "  'pixel_6_6',\n",
       "  'pixel_6_7',\n",
       "  'pixel_7_0',\n",
       "  'pixel_7_1',\n",
       "  'pixel_7_2',\n",
       "  'pixel_7_3',\n",
       "  'pixel_7_4',\n",
       "  'pixel_7_5',\n",
       "  'pixel_7_6',\n",
       "  'pixel_7_7'],\n",
       " 'target_names': array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]),\n",
       " 'images': array([[[ 0.,  0.,  5., ...,  1.,  0.,  0.],\n",
       "         [ 0.,  0., 13., ..., 15.,  5.,  0.],\n",
       "         [ 0.,  3., 15., ..., 11.,  8.,  0.],\n",
       "         ...,\n",
       "         [ 0.,  4., 11., ..., 12.,  7.,  0.],\n",
       "         [ 0.,  2., 14., ..., 12.,  0.,  0.],\n",
       "         [ 0.,  0.,  6., ...,  0.,  0.,  0.]],\n",
       " \n",
       "        [[ 0.,  0.,  0., ...,  5.,  0.,  0.],\n",
       "         [ 0.,  0.,  0., ...,  9.,  0.,  0.],\n",
       "         [ 0.,  0.,  3., ...,  6.,  0.,  0.],\n",
       "         ...,\n",
       "         [ 0.,  0.,  1., ...,  6.,  0.,  0.],\n",
       "         [ 0.,  0.,  1., ...,  6.,  0.,  0.],\n",
       "         [ 0.,  0.,  0., ..., 10.,  0.,  0.]],\n",
       " \n",
       "        [[ 0.,  0.,  0., ..., 12.,  0.,  0.],\n",
       "         [ 0.,  0.,  3., ..., 14.,  0.,  0.],\n",
       "         [ 0.,  0.,  8., ..., 16.,  0.,  0.],\n",
       "         ...,\n",
       "         [ 0.,  9., 16., ...,  0.,  0.,  0.],\n",
       "         [ 0.,  3., 13., ..., 11.,  5.,  0.],\n",
       "         [ 0.,  0.,  0., ..., 16.,  9.,  0.]],\n",
       " \n",
       "        ...,\n",
       " \n",
       "        [[ 0.,  0.,  1., ...,  1.,  0.,  0.],\n",
       "         [ 0.,  0., 13., ...,  2.,  1.,  0.],\n",
       "         [ 0.,  0., 16., ..., 16.,  5.,  0.],\n",
       "         ...,\n",
       "         [ 0.,  0., 16., ..., 15.,  0.,  0.],\n",
       "         [ 0.,  0., 15., ..., 16.,  0.,  0.],\n",
       "         [ 0.,  0.,  2., ...,  6.,  0.,  0.]],\n",
       " \n",
       "        [[ 0.,  0.,  2., ...,  0.,  0.,  0.],\n",
       "         [ 0.,  0., 14., ..., 15.,  1.,  0.],\n",
       "         [ 0.,  4., 16., ..., 16.,  7.,  0.],\n",
       "         ...,\n",
       "         [ 0.,  0.,  0., ..., 16.,  2.,  0.],\n",
       "         [ 0.,  0.,  4., ..., 16.,  2.,  0.],\n",
       "         [ 0.,  0.,  5., ..., 12.,  0.,  0.]],\n",
       " \n",
       "        [[ 0.,  0., 10., ...,  1.,  0.,  0.],\n",
       "         [ 0.,  2., 16., ...,  1.,  0.,  0.],\n",
       "         [ 0.,  0., 15., ..., 15.,  0.,  0.],\n",
       "         ...,\n",
       "         [ 0.,  4., 16., ..., 16.,  6.,  0.],\n",
       "         [ 0.,  8., 16., ..., 16.,  8.,  0.],\n",
       "         [ 0.,  1.,  8., ..., 12.,  1.,  0.]]]),\n",
       " 'DESCR': \".. _digits_dataset:\\n\\nOptical recognition of handwritten digits dataset\\n--------------------------------------------------\\n\\n**Data Set Characteristics:**\\n\\n    :Number of Instances: 1797\\n    :Number of Attributes: 64\\n    :Attribute Information: 8x8 image of integer pixels in the range 0..16.\\n    :Missing Attribute Values: None\\n    :Creator: E. Alpaydin (alpaydin '@' boun.edu.tr)\\n    :Date: July; 1998\\n\\nThis is a copy of the test set of the UCI ML hand-written digits datasets\\nhttps://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+Handwritten+Digits\\n\\nThe data set contains images of hand-written digits: 10 classes where\\neach class refers to a digit.\\n\\nPreprocessing programs made available by NIST were used to extract\\nnormalized bitmaps of handwritten digits from a preprinted form. From a\\ntotal of 43 people, 30 contributed to the training set and different 13\\nto the test set. 32x32 bitmaps are divided into nonoverlapping blocks of\\n4x4 and the number of on pixels are counted in each block. This generates\\nan input matrix of 8x8 where each element is an integer in the range\\n0..16. This reduces dimensionality and gives invariance to small\\ndistortions.\\n\\nFor info on NIST preprocessing routines, see M. D. Garris, J. L. Blue, G.\\nT. Candela, D. L. Dimmick, J. Geist, P. J. Grother, S. A. Janet, and C.\\nL. Wilson, NIST Form-Based Handprint Recognition System, NISTIR 5469,\\n1994.\\n\\n.. topic:: References\\n\\n  - C. Kaynak (1995) Methods of Combining Multiple Classifiers and Their\\n    Applications to Handwritten Digit Recognition, MSc Thesis, Institute of\\n    Graduate Studies in Science and Engineering, Bogazici University.\\n  - E. Alpaydin, C. Kaynak (1998) Cascading Classifiers, Kybernetika.\\n  - Ken Tang and Ponnuthurai N. Suganthan and Xi Yao and A. Kai Qin.\\n    Linear dimensionalityreduction using relevance weighted LDA. School of\\n    Electrical and Electronic Engineering Nanyang Technological University.\\n    2005.\\n  - Claudio Gentile. A New Approximate Maximal Margin Classification\\n    Algorithm. NIPS. 2000.\\n\"}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "930a513f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efc07272",
   "metadata": {},
   "source": [
    "#### 이미지를 출력하는 함수 정의 및 원본 데이터 출력해보기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "504daa87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot_digits(data):\n",
    "    fig, axes = plt.subplots(4, 10, figsize=(10, 4),\n",
    "                             subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                             gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8, 8),\n",
    "                  cmap='binary', interpolation='nearest',\n",
    "                  clim=(0, 16))\n",
    "plot_digits(digits.data) # 원본 손글씨 이미지 출력"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "064ac5eb",
   "metadata": {},
   "source": [
    "### --------------------- DJ's practice -----------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e0b280c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(4, 10, figsize=(10,4),\n",
    "            subplot_kw={'yticks':[], 'xticks':[]},\n",
    "             gridspec_kw=dict(hspace=0.1, wspace=0.1)\n",
    "            )\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4fdaa1ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i: 0\n",
      "ax: [<AxesSubplot:> <AxesSubplot:> <AxesSubplot:> <AxesSubplot:>\n",
      " <AxesSubplot:> <AxesSubplot:> <AxesSubplot:> <AxesSubplot:>\n",
      " <AxesSubplot:> <AxesSubplot:>]\n",
      "i: 1\n",
      "ax: [<AxesSubplot:> <AxesSubplot:> <AxesSubplot:> <AxesSubplot:>\n",
      " <AxesSubplot:> <AxesSubplot:> <AxesSubplot:> <AxesSubplot:>\n",
      " <AxesSubplot:> <AxesSubplot:>]\n",
      "i: 2\n",
      "ax: [<AxesSubplot:> <AxesSubplot:> <AxesSubplot:> <AxesSubplot:>\n",
      " <AxesSubplot:> <AxesSubplot:> <AxesSubplot:> <AxesSubplot:>\n",
      " <AxesSubplot:> <AxesSubplot:>]\n",
      "i: 3\n",
      "ax: [<AxesSubplot:> <AxesSubplot:> <AxesSubplot:> <AxesSubplot:>\n",
      " <AxesSubplot:> <AxesSubplot:> <AxesSubplot:> <AxesSubplot:>\n",
      " <AxesSubplot:> <AxesSubplot:>]\n"
     ]
    }
   ],
   "source": [
    "for i, ax in enumerate(axes):\n",
    "    print('i:', i)\n",
    "    print('ax:', ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "640a664c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<numpy.flatiter at 0x7fd4f7f90a00>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "axes.flat"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7707e15c",
   "metadata": {},
   "source": [
    "### --------------------- end -----------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "157e3bef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 잡음넣기\n",
    "\n",
    "np.random.seed(42)\n",
    "noisy = np.random.normal(digits.data, 4)\n",
    "plot_digits(noisy) # 잡음이 섞인 손글씨 이미지 출력"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "e8bcef5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.65982387, -1.13204668,  5.29854771, ..., -0.80666376,\n",
       "        -0.54443667, -0.19111626],\n",
       "       [-0.60023847, -1.63693137, -0.56605958, ...,  7.05055444,\n",
       "         0.72210269, -0.72050353],\n",
       "       [-0.5210966 , -0.54933487,  0.28433324, ..., 17.60813154,\n",
       "         8.00907083,  0.32330646],\n",
       "       ...,\n",
       "       [-0.25448018, -0.52692731,  1.61112827, ...,  6.73631267,\n",
       "        -2.01681528, -0.79049598],\n",
       "       [ 1.09956505, -1.33732041,  1.85770983, ...,  9.1332841 ,\n",
       "         0.24829357, -0.36997637],\n",
       "       [ 0.13585366, -0.87801192, 10.16015333, ..., 11.37967634,\n",
       "         2.25988686, -0.48567626]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal(digits.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "29f23f28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.07911454e+00, -1.40891544e+00,  8.54480823e-01, ...,\n",
       "         4.31560677e+00, -4.50816707e+00,  2.30673580e-03],\n",
       "       [ 7.21714015e+00, -3.91890245e+00,  3.39029502e+00, ...,\n",
       "         1.26952118e+01,  5.14574065e+00,  2.04321678e+00],\n",
       "       [ 2.86028155e+00,  3.51223617e-01,  7.72335418e+00, ...,\n",
       "         9.82848952e+00,  3.29607516e+00, -2.05595685e+00],\n",
       "       ...,\n",
       "       [-6.56325899e+00, -6.94842116e-01,  7.54294235e+00, ...,\n",
       "         3.32911436e+00, -4.02529731e+00,  2.55033746e+00],\n",
       "       [ 3.43872945e-01,  4.31381350e+00,  1.99819326e+00, ...,\n",
       "         1.28646265e+01, -7.06282474e+00,  6.61459029e+00],\n",
       "       [ 2.77060689e+00, -3.41679953e+00,  7.51082220e+00, ...,\n",
       "         6.33305788e+00,  2.70115720e+00,  9.50307007e-01]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal(digits.data, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "92bc8780",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-3.53285043, -2.32903794,  3.65407272, ..., -4.3642161 ,\n",
       "         3.19311063, -2.437692  ],\n",
       "       [ 0.70536268,  1.39194156, -2.9866904 , ..., 11.5827146 ,\n",
       "        -2.63653517, -0.23015631],\n",
       "       [-5.47998776,  4.19855202, -2.66906556, ..., 16.05260663,\n",
       "        18.27413151,  1.99171913],\n",
       "       ...,\n",
       "       [-0.59972217, -3.49711458, -6.48724495, ...,  1.6160254 ,\n",
       "         4.6773366 , -3.92462307],\n",
       "       [-0.25381756,  4.97289382,  0.89059292, ..., 11.25675867,\n",
       "         4.91405233, -0.64212257],\n",
       "       [-7.10705788,  2.48784838,  7.97322253, ..., 16.55178662,\n",
       "         1.44772687,  7.06827414]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal(digits.data, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "7f710ff4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  5., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ..., 10.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ..., 16.,  9.,  0.],\n",
       "       ...,\n",
       "       [ 0.,  0.,  1., ...,  6.,  0.,  0.],\n",
       "       [ 0.,  0.,  2., ..., 12.,  0.,  0.],\n",
       "       [ 0.,  0., 10., ..., 12.,  1.,  0.]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "3d9d1322",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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V1ydic/FDRERE9FfH//YiIiIiR+Hih4iIiByFix8iIiJyFFvtLUJDQ92RkZG2HgDdAv3KlStqnpWVBeeqV6+emgcGBsIxHh7W9V18fLykpKRY7scfEhLijoiIsOxvuo07uv068ttvv9naX0TE9J4XFxer+fnz51NKX+hVls8vNzdXzVNTU9W8Vq1acK5Lly6peUBAAByD2lvExsZaXp8Ifo3oFusifxwPmkqVKql5Xl4enAsdD6Zb32vvcXp6uuTk5FiOUfT6EhMT4fzosc+ePavm6Lb+IiItWrRQc09PTzgGiY6OtnyGAQEBbu35FhYWwnlQe4nLly/bfk6I6RwTFRWl5trrE8GfoalNRoUK+qk6OTlZzXNycuBcYWFhao5aqojoxzU6j5blPIMcOnRIzZs3bw7HoO9zw4YN4Zhr165ZsgsXLkhqamq5vD507tNauYiInDlzxtb8IiKtW7eG29A569ixY7aO0bKIjo5Wc3Qciohov8Mi+HdHRKRKlSqWDB2jIjYXP5GRkXLw4EFLjn6ARUR++OEHNZ81a5aab9u2Dc6F+tv07t0bjtF+wNq0aaPuGxERoT7+1q1b4fxdunRRc3QheY0aNeBcyLRp0+A2dFCPHj3acqU++vxM0MkH9WuaM2cOnAv1hdH65JRAi6moqCi1EgG9xjVr1sDHGDp0qJo3atRIzWNiYuBc6NgaP348HKPN995776n7otdn6jeGehoNGjRIzbU+RyW2b9+u5kFBQXAM4nK5LJ9htWrVZO7cuZZ9TQsZtPCbOnWq7eeEdO7cGW7bvHmzmmuvTwR/hmghIyJStapasCJLly5V8z179sC5nnnmGTVPS0uDY7p27WrJ0LFelvMMgvruffHFF3DM8OHD1dz026L9Y7xnz57qvuj1mRaPr776qprfcccdao767pmY3vNff/1VzVu2bGnrGC0L9A+jxx9/HI7RzgEiIh988AEco53P0DEqwv/2IiIiIofh4oeIiIgchYsfIiIichQufoiIiMhRbF3wXFBQIHFxcZYcVWGJ4CvQY2Nj1dzlUi/MFhGR/v37q7mpSqI8DBw4EG5DV7J/++23ao6qZUREjhw5oubodZsev7ygzw9Vv6DKFxGR6dOnl8tzKouCggK47dixY2qOKsRMF3WjCzF79eoFx0ycONGSbdy4Ud337Nmz6oV9L7/8MpwfQRfLp6enwzHowmp0UbWIyIEDB274OQUGBsr9999vyU3nBQRV66EKRhFc2WmqSERVc0hRUZH6HqOLmkVEduzYoebovT13DncmQEUXq1atgmO07+7JkyfVffPy8tSqVtNxhS5+RcfoihUr4FyLFi1Sc7sXy3p5ean75ufnq6/dx8cHzt+kSRM1Rxc2t23bFs6FPnN0gbaIuWhHk5qaqr5fgwcPtjWPyUcffQS3vfnmm2qOijRERJYvX27JUlJS4P78yw8RERE5Chc/RERE5Chc/BAREZGjcPFDREREjsLFDxERETkKFz9ERETkKLZL3U+dOmXJTaXuY8eOVXPUswX1xBIRGT16tJr//vvvcEzTpk3httIqVKigNkczQaXgY8aMUXNUzi4iUrduXVuPLSLSsWNH22NKQ033RETWr1+v5qj83tQX6pZbblFz03tiOh402dnZsmvXLktuKnn09/dX87L0FUKfu6khn/adQqX5Xl5eaqPS0NBQOD8qm0W9e06cOAHnev7559Xc9Ph2ymMLCwvl4sWLao6sXbtWzTt16qTmCxYsgHOh85WJ3e+t2+22fXsOVN5cv359NV+yZAmcS2v2LCIyf/58OEa7BcDdd9+t7lupUiVp1qyZJTf1ikLfwdmzZ6t5zZo14Vz33nuvmj/99NNwjHZMJCUlqft6eXmptyVADVVFcP/Ao0ePqrnpdhroGO3RowccY/d4q1KlilpWbjo3oMcfMWKEmmvnvRKPPPKImn/22WdwjPY4ixcvhvvzLz9ERETkKFz8EBERkaNw8UNERESOwsUPEREROQoXP0REROQotqq9AgIC1OZppkaB69atU3NU/RIcHAznmjBhgpoPGDAAjtEqf4qKiuD+dqFGpajCZu/evXAu1CiwQgVbH5NtpsqJ9u3b25pLa0pZ4vjx47Yfv1+/frYe38fHRxo3bmzJV69eDcdERESoedeuXW09tgiuaEHNFkVEGjRoYMm8vb3VfWvVqiVvvfWWJT9z5gyc/9ChQ2reu3dvNdfev//EVNGlNRxEEhMT1QqfPXv2wDGmKiJNq1at4Lbhw4eruami9PLly7YeX0SvYkTffxFc/bdw4UI1N1UkPvPMM2puOo9qjV09PT3VfS9evKieq7t06QLnR8coak5rapL85JNPqvmLL74Ix2jQOcPT01P9nTL9dm3btk3NUVVXnz594FzvvPMO3IZcuXLF9hiN6X1HjWPXrFmj5h06dIBzmaq6EO0ckZOTA/fnX36IiIjIUbj4ISIiIkfh4oeIiIgchYsfIiIichQufoiIiMhRyqWMaMWKFbbHPPfcc2qOqi1E8JXxpmoLrRIEVacVFBTI6dOnLXlUVBScX+tDJKJX8PwnX375pZrn5eXBMY899pjtxynt3XffhdtQ1VqdOnVsP054eLiaV65cGY6ZNGmSmm/atEnNK1SooPaZWrZs2Q08w3+Hehdt374djhk3bpyat2zZ0vbja1JTU9WqCtPnERYWpuaoDxvqs2Ryzz33wG3Jyck3PE9ERIRazWKq/kDVkOfPn1dzVO0kIuLn56fmqM+TCK6aQwoLC9XnhqplRETS09PVPCEhwVYugvsz3XXXXXCMqSKztODgYHn00Uctebt27eAYrVeWyB/VmxrUn0xE5Pbbb7c1l4hIfn4+3FYe7Fbsop5tIn9URGpeeeUVOAZV05WnyMhINUfnH1PfRlQ1nJaWBsdoawpTT0D+5YeIiIgchYsfIiIichQufoiIiMhRuPghIiIiR+Hih4iIiByFix8iIiJyFFv1d0lJSTJ//nxLjsp7RXCZa40aNdS8U6dOcK5Ro0apeXR0NByjlal7eXnB/bUSyn379sH9tSaTIrhcGJVoi+AmsJ988gkcY0d2drb8/PPPlnzMmDFwTExMjJqjhq6oXF9E5OOPP1bzp556Co4xNaHU5Ofnq6W8U6dOhWPWr1+v5uhzR/uLiAwZMkTNtYbAJc6dO2fJ0O0Y/Pz85I477rDk9erVg/O3bt1azdEtBtDnJIKbU27duhWOmTlzppofOXIEjintoYceuuF9S6DPwgTdNsPUINEuX19f9TNp1qwZHIMafKIGpqaybtQk1VRq/9JLL8FtpSUnJ8vixYstuen1tWnTRs1RA+z9+/fDuT799FM1N90O4rvvvrNkmZmZ6r4ZGRnyzTffWPKdO3fC+dF3AJV7m875qMnu2bNn4Rh0Hne5XHCMXR07dlTzzZs3q/nRo0fhXOhWOKZbamjfUdMtH/iXHyIiInIULn6IiIjIUbj4ISIiIkfh4oeIiIgchYsfIiIichRb1V6VK1eWzp07W3JUcSCCr8rfsmWLml+7dg3O9cILL6i53SaiqBLC5XKpDejat28P51q4cKGtxw4ODobbNmzYoOZLliyBY1AFnMbf31+tptuxYwcco33eIiKxsbFqjhrSieAr+E2NVVFVGeLj4yONGze25N7e3nAMak47dOhQNdeaNv4n8+bNg9u0RpsVK1ZU9/Xw8DC+Fg1qYIqYqr1Q00hT5Ua3bt3UfPLkyZbswoUL6vuhVbiVGDBggJqvXbtWzU1VZlevXlVzU7WeXVlZWfLTTz9ZctRIV0TkjTfeUPM+ffqoOaq8EcFVSabvrvZ9R9VFPj4+0qRJE0uOmsaK4Aot1JB45MiRcC5U4WOqatWqc319fdV9PT091UpJ03M6fvy4mq9Zs0bN0blHBDfsNVVCDRs2DG7TJCQkyD//+U9Lbqq+RQ1+UVNe0/FQFgsWLLBkI0aMgPvzLz9ERETkKFz8EBERkaNw8UNERESOwsUPEREROQoXP0REROQoXPwQERGRo9gqdS8sLFQb/6FySxFcPvn111+ruanMFjXARGWEIiKvv/66JUMlmpcuXZJJkyZZclSOKIIbLqKGdb/99hucKy0tTc1N5ewbN26E20rLyclRbz0QEhJyw3OUQOWWERERcAxq7odK/MsTKocWEenVq5eav/baa2q+dOlSOFd+fr6ah4eHwzHa+6/dckHkj6a8NWvWhHNpMjIy1LxHjx5q3qhRIzgXut2EqYGgndL8ihUrqg0og4KC4Bh0CwVU5tq8efMbfj4lTI1NV6xYYWsul8slnp6etsZ07dpVzefOnavmqElyyeNrJkyYAMfMmjXLkqFmpB4eHrARK4LKngsLC9Xc9H06fPiwmpt+pz7//HNLlp2dre5bXFysfs9r1apla35Tjj5XEfx91n67/pNVq1apuZ+fn3qLF1Nz2JUrV6r58OHDbT8vBD1fEf32DqjBuAj/8kNEREQOw8UPEREROQoXP0REROQoXPwQERGRo3DxQ0RERI7iQlVJ6s4uV7KInPvzns5/TR232121dHgTvT4R5TXe7K9P5KZ6jTf76xPhMfpXx9f313ezv0b19YnYXPwQERER/dXxv72IiIjIUbj4ISIiIkfh4oeIiIgcxVZ7Cz8/P3dwcLAlN936vXLlymp+4cIFNTfdWj83N1fNq1SpAsckJiZasoyMDMnNzbXc4z00NNQdGRkJ57KjqKhIzWNiYmzP1bhxY7gNtUGIjY1NKX2hF3p9WsuSEuiasCtXrqg5unW+iEirVq3UHLWEEBHx8fFR8+joaMvrExGpVKmSOzAw0LK/6dbz0dHRao7aSFy6dAnOhTRo0ABu097jpKQkycjI+FOPUeTo0aNwG2pDkJeXB8eEhYWpeXx8vOUzrFKlilt7300tMux+fto5rAQ6l5nOMYbnpR6jgYGBbq09AzpXiuDvqK+vr5qj1gwi+LMyHaNxcXGWLCcnRwoKCtRjtHbt2pb90TlDBJ/HENPxVrFiRTWvVq0aHOPhYf07QHx8vKSkpNzwd/DMmTNwfvQ5oTYn6DWImFu9IOfO6dcup6SkqMdoaGioW2tlYTq/x8bGqnlBQcGNPs3/0bp1a9tjNOgzFLG5+AkODpaxY8dacq1fVIlOnTqp+bPPPqvmpj45Bw4cUPNBgwbBMW+99ZYlQz1IIiMj5eDBg3AuO9LT09XcdOJFVq9eDbehvlxRUVGWox29PtTDSgSfZLRePyJ/9J5C0Ht77NgxOKZp06Zq7nK51G9zYGCgPP7445ZcOw7+11xqPmbMGDV/5ZVX4FzIggUL4DZtoTxu3Dh13/I8RouLi9X81ltvhWPQAtbUX087Z4iIDBkyxPIZ1qxZUzZv3mzZt379+nB+9Pn94x//UHNTn7dffvlFzU3nGMPzUo/R8PBwWbJkiSXv3LkznAt9R1u2bKnmP//8M5wLLW63bNkCxzz66KOW7Pvvv1f3rV27tuzcudOSv/nmm3B+uz/opgW6tvASwb85IqL2ItN6W4ng7+CDDz4I50c/5mjBa+qR2K9fP7gNGTlypJovX75cPUbr1KmjfhfQP0ZF8OL59OnTN/IU/015neNQ/zkR/rcXEREROQwXP0REROQoXPwQERGRo3DxQ0RERI5i64Ln8PBweemll2w9ALqavW7dump+5513wrmmTJmi5qYLdt955x1L9t1336n7pqeny6ZNmyx5nz594Pzo9aEL+IYPHw7nQhd7m6pATBeClnbx4kX180MXL4uIPPLIIzc8v4hIYWEh3PbVV1+puXZxZAnTc9PUqlVLvbh58uTJcAy6EHLp0qVqbrr4tWfPnmp+7733wjF2FBQUqBcQXr9+HY5B25o3b67mc+fOhXOhqpwuXbrAMTNmzIDbSvP29laP6Q4dOsAxM2fOVPNVq1apuamiFH22pos2o6Ki4DaNp6enen4wXZSPnhd67F9//RXOVaNGDfMTVKxfv96SoYtJr1y5on4mo0aNgvObqjE1pqqjtm3bqvmnn34Kx9ipws3Pz1cv8Nd+O0qg8z4qvjFBVYwXL16EY5YtW6bmy5cvV/O4uDgZOHCgJTddtG6qwNNoFXb/TfzLDxERETkKFz9ERETkKFz8EBERkaNw8UNERESOwsUPEREROQoXP0REROQo9rrJAVevXoXbUP+gffv2qblWml7ixIkTan7ffffBMSkpKZYMlf56eHiIv7+/JUfl7Kbn1KRJEzU39X9BXnjhBbht/PjxNzxPrVq1bJeOP/bYY2q+YcMGNTeVEaNSyKlTp9p6TmWh9SYqgcpAUam0qRfZpEmT1NzU2+v222+3ZEOGDFH3LS4uVhvBmprTou9nixYt1Bw1sxXBtyswQb2WNMnJyWrfq6FDh8Ixo0ePVnPT60C+/fZbNe/VqxccY7fENz8/Xz1vmHqq2S2nb9iwIdxm6s+EaN8R7dwqIhIaGipPPPGEJbdbzi6iN6YWMX+2qBF0UlISHLN3715Lhprcut1utR+f6TseEBCg5h9++KGam37T0G1Udu/eDcfccccdcJumatWq8vTTT1ty061V7DZ8vvvuu23tX974lx8iIiJyFC5+iIiIyFG4+CEiIiJH4eKHiIiIHIWLHyIiInKUcqn2mj17tu0xqErqX//6FxyjXX0ugitjENScMSAgQLp3727JtcqFEqhqLTw8XM1RU1URkQEDBqj5unXr4Jhdu3bBbaUVFRVJRkaGJf/hhx/gGF9f3xueX0Tk5MmTcBtqknrgwAE4BjVPRE6cOKFWT6EGfiIiDz30kJp36tRJzU3HqPb+ioiMGTMGjtGg971SpUpqQ9LAwEA4Fzp+0Pdg+vTpcC7UINZUfYOacg4ePNiSVa1aVW2AiaoOTbKzs9Vcq+gskZycrOamajpT01ONr6+vtGrVypKbKrSQL774Qs1NFV1apZKIuapVqyRC7++RI0fUxtVnzpyB83fs2FHNu3btquaoSsqkWbNmcNuhQ4csWW5urrpvYmKi2vzXVHk7duxYNQ8JCVHzCRMmwLkiIyPV3G5Fl0l+fr78/vvvllz7fSyBqqjReWb79u1wLvRbMXHiRDhGq85Dx6gI//JDREREDsPFDxERETkKFz9ERETkKFz8EBERkaNw8UNERESOUi7VXp988gnc5nK51Pyuu+5Sc1PfJNTfp7Cw0PDsrFBlSkJCglrJ8/7778O5nn32WTVHfW9Mva9++eUXNUfVGSLmSqnSPD091aogVO0kgquXVq5cqeb333//DT+fEm3btoXb0OMgjRs3Vvv0LFq0CI556aWX1Bz1/Lpw4QKca9OmTf/hGVpt3brVkmVmZtqao127dnDblStX1FyrthIRqVOnDpwL9ZhC1ZsiuNeSpqCgQK0Kmj9/PhyDqtmmTJmi5lqlTglU2YmOBRGRv//973CbxsfHR63sQn3FRHA1VJ8+fdQcVcuImM/XyNKlSy2ZVlUpIhIREaFWK61duxbOn5CQoOZxcXE3+Az/L/SbY6r20iqJV6xYoe4bFBQkDzzwgCVHlYIiIs8995yao56DpvNVWlqampsqiXv06AG3adxuN6zeQlavXg3n0qDeaSK4IhP1lLQ7jwj/8kNEREQOw8UPEREROQoXP0REROQoXPwQERGRo3DxQ0RERI7CxQ8RERE5SrmUup89exZu++mnn9Rca14oIrJkyRI4FyoXRCWJaD5UClm9enXYuBFBJft5eXlqjsqLRXBJoKnsGb0nzz//PBxT2scffwy3NW3aVM3R+9SzZ88bftwbMWzYMDUfPny4mp8+fVr69u1ryatXrw4fA5WCo1srvPbaa3AuVPb8xhtvwDHae+zl5aXue+zYMbn11lstOSoVFhFp2bKlmqMScVNJMlK1alW47fvvv7/heXJzc+XgwYO25jc1VdXcdtttcBtqzBsdHQ3H2GkubGJq4tu/f381X7NmjZrPmzcPzoXOf19++SUcozVQPX/+vLpvWFiY2sjX1GxVa5wqItKhQwc1R69BBB8r69evh2O03xB0u5LMzEz19hQLFy6E83fu3FnNf/zxRzU3lboHBQWpud1ydpNq1arB27gg6HvepUsXNU9KSoJzoebRpttwmNYhGv7lh4iIiByFix8iIiJyFC5+iIiIyFG4+CEiIiJH4eKHiIiIHKVcqr1M1RMxMTFqjio0TJUhqILh8OHDcIwdxcXFapVW8+bN4RhUjYSaz2kN/0qgyq23334bjjE1h7tRAwYMgNtQ09EqVaqoube3N5zr8uXLal6jRg3Ds7MnKipKNm/ebGvM8uXL1XzSpElqPmLECDjXuXPn1HzgwIFwjFY5cu3aNXXfpk2bqtVQJug7uHjxYjU3NUkdN26cmvv5+cExdpq0ZmVlqRWiWiPJ/6RBgwZqbmoUXLduXTU3Naw1NQbWxMXFqY1H58yZY2seEfzd3b9/v+0xTz31FBwTHx9vyUwVcBpTFSFqkmpqmIug7yCq5BMR2bdvnyVD59batWsbK7vs6Nq1a7nMI2I+ftD7i1y7dk2tIDVVVqLvzquvvqrmO3bsgHMVFBSoeWpqKhzz8ssvW7KLFy/C/fmXHyIiInIULn6IiIjIUbj4ISIiIkfh4oeIiIgchYsfIiIichQufoiIiMhRbJW6Z2VlqeVpplJzVJqGmsz9+uuvcC5UZmdqcmen6WF8fLzamPLMmTNwDGqKGRsbq+bdu3e/4edTAjU1FDHfZqC0rKws2bZtmyUPCwuzPT+6JYGpBDQ8PFzNUTNQEZGZM2fCbZrc3Fz1eKxWrRocc+HCBTUfOXKkrccWwcfbqVOn4JiIiAhLVrFiRVuPu3fvXrgNlbmi4+rhhx+Gc6Emnqbv4GeffQa3lVaWMmJUun369Gk137BhA5wLnX9MjYJRE2OkXr16xuegQWX76JYTqJmkCG5kbCo9rlDB+lOBPvOioiJJT0+35O+//z6c/+rVq2qOyunRbUFEcAPV+vXrwzFPP/20JUPH+tGjR6VJkyaW/MEHH4Tza99xEXzrE7vNekVEXnzxRbgNlf8jXl5eajNo7ZYAJcaOHavm6Dxjuj0GOu+/9dZbcMzs2bMtmfZ7V4J/+SEiIiJH4eKHiIiIHIWLHyIiInIULn6IiIjIUbj4ISIiIkdx2bmq3OVyJYuIvcvG//9Ux+12Vy0d3kSvT0R5jTf76xO5qV7jzf76RHiM/tXx9f313eyvUX19IjYXP0RERER/dfxvLyIiInIULn6IiIjIUbj4ISIiIkex1d4iJCTErd2mG91GXuSP29Vrzp49q+aenp5wrsaNG6t5UlISHKO1boiPj5eUlBTLvdlDQ0PdkZGRcC47Ll26pObabd9LNGvWzNZcIiIhISFqfvTo0ZTSF3qV5fUlJiaq+cWLF23NU1atW7dW8+joaMvrE/njNWrHXFFREXwM1IqkcuXKao7ecxGR4OBguM0OdIwGBQW5tdvOV6pUCc7l4aH/Gwcdi6bvE2oTEhgYCMcg2meIjtHk5GQ4D7pNPmqZcO3aNTiXt7e3mtesWROOQUzHqN3vIXr958+fV/N69erBuf7sYzQwMNCtHScJCQlwruzsbDVHny36XRER8fX1hdvsML0+7XfF9B1An5PpuLarTp06cFtxcbGaX7hwwdYxGhcXBx8D/XanpKSoeVBQEJwrICBAzatWVa9dFhG9lVZycrJkZWWpfVhsLX4iIiLUnk6mnibvvPOOmg8aNEjNTQfQnj171Hz+/PlwzLhx4yxZmzZt1H0jIyPl4MGDcC47Xn75ZTX//PPP4Rj02BMnToRjBg8erOZNmza1XKlflteHeqmMHz/e1jwien8gEZHr16/DMej5ulwutRKhdu3a8vPPP1tydHIVEWnUqJGad+7cWc0HDhwI53r00UfhNjvQMVq9enVZs2aNJUcLZxH8Y7Bx40Y1f/fdd+FcqH9Qr1694BhE+wzRMbpkyRI4T7t27dR81apVam76EUaLBrs95kTwMVqW7+HixYvVfPTo0Wo+a9YsOJepd5sd6BitVq2avPfee5Z8+vTpcC7tOysi0rx5czU3HaPoedmF5gkLC1N/10zfAfQ5oc+1LKZOnQq3ofPfM888Y+sYRX30RPBiBn13Tf3nunXrpuZaD7YSH3zwgSWbMmUK3J//7UVERESOwsUPEREROQoXP0REROQotq75qVChgnrBEboOQARfsIp8+OGHcNukSZPU3PR/yX+2rl27qvnYsWPV3PR/8eh1zJgxA4558803Dc/u3xUUFMiZM2csuenCs927d6s5+ix69OgB57rrrrvMT7AceHh4iL+/vyXv168fHJOZmanm+/fvV3PTdVvo/8Tj4+PhGO0C3IKCAnVfPz8/adu2rSU3XUiPrvk5dOiQmm/fvh3OtW3bNrgNQceKHaNGjYLb0DGnXZ8oIhIVFQXn2rBhg5r//vvvcMymTZvgNk16ero6pkWLFnAMKnp49dVX1Vy7/qHEI488oubHjx+HY06ePGnJ0DEXEBAg3bt3t+Smi2XHjBmj5v3791dz7TtQ4s++cW9gYKB6fQ+6sFcEX3+GHDlyBG5DxwkqRhARGTZsmJo/88wzcIx2kXRMTAzcf+7cuWpeluuaXC71GmXjNT9aQZSPjw/cn3/5ISIiIkfh4oeIiIgchYsfIiIichQufoiIiMhRuPghIiIiR+Hih4iIiBzFVqk78sADD9geg8okP/nkEzjmq6++UvNbbrkFjrn11lstWX5+vrpvdna27Nq1y5J37NgRzo9aHaDSalPJ7sqVK9XcVCo8fPhwNdduP+B2u6WwsNCST548Gc6P2ltUqVJFzVGpsAgudT93Tr3DuoiI5Obmwm12XL582faYpUuXqvnf/vY3OAb10TL57rvvLBkqdUdMtytIS0tT8/Xr16u5qd/QiRMn1Pzjjz+GY9AtHF5//XVLdvnyZZk2bZol17ISqCwWlQSbbqdhKjcvL0FBQWpLIFO/PPQeon5Optt/oFs1mNoN/PLLL5bM1E9Os3r1argtPDxczV977TU1R333/huSkpLU9hamsnH0m4PK8tExLYJvb4J+H0Xs9xBzu93qLThMrxG18EC/IeiWCyIiX3/9tZpv3rwZjunbt68lM/V5419+iIiIyFG4+CEiIiJH4eKHiIiIHIWLHyIiInIULn6IiIjIUcql2mvOnDm2xwQGBqp5q1at4Bhvb281N1UEaVUEXl5e6r7+/v7Gyi4NamT5+OOPq/mSJUvgXKZtCKq60vj4+EiTJk0seWJiIhxTt25dW88HNSgUwVf9v/DCC7YeoyzmzZsHt2lNGEVERowYoeamiodnn33WztMSEb0xZ0BAgO15kODgYDU/ffq0moeGhsK5UJXNuHHj4JgnnnjC8Oz+XY0aNYyVXRqtWk5E5OGHH1ZzrXKpRFmqvUyVbnaYjitk/Pjxaj5o0CA4ZvDgwbZyEZF69epZMnQ+RkzVSCEhIWqOmsZqjUVLeHp6qnlZ3l9N1apV5amnnrLkpsambdq0UfMGDRqouakJdFnOl8uWLbO1v8vlUj9f0zGCmmBrDVJFRBYtWgTnysrKUvNHH30Ujtm7d68ly8nJgfvzLz9ERETkKFz8EBERkaNw8UNERESOwsUPEREROQoXP0REROQo5VLt9dFHH5XHNCIi0rp1a7hNu5pbxNy3RKsqQ9UAyPbt2+G2+Ph4NR82bJiaP/fcc3Cu559/3tbzKi+m3mwffPCBmu/fv1/NtZ5FJe6++241/29Ue5l6Xz355JNqjqoUXn31VTgX2maqqNP6eBUVFan75ubmSkxMjCVH/X5EcC8rVClo6isUFxen5nPnzoVj3n//fTVfsWKFJcvKypIdO3ZY8s6dO8P5tfdDRO/rJ4J7EIngCiZTrzU7FZcmGzduhNt+/vlnNUd9uuz2hhMR6datm+0xmtzcXDl8+LAlv+222+AY1OMKVVBpx04J9J6Yqr1SU1Mt2fXr19V9XS6XVKxY0ZKbqo4PHjwIt2lOnTpla38RkYkTJ8JtM2bMUHN07kNMfRjRb0VZoHPQ7bffDsdolV3oHC7Cv/wQERGRw3DxQ0RERI7CxQ8RERE5Chc/RERE5Chc/BAREZGjcPFDREREjmKr1D0+Pl5tUqiVNZaYPXu2mi9evFjNtYZxJTw89LUaKpO0Kz09XTZv3mzJ+/btC8dcunSpXB5bxFwu/Gdq37493DZp0iQ1Rw1d09LS4FzaeyuCy+ZFcCNNu1BjQRFc0oqa4i1fvhzONWTIEDUPCwszPDsrdDuGzMxM2bp1qyUfOXIknKtr165qfuTIETU3HYdff/21mpuaoa5duxZuK61y5cpqWTsq9RYR6dSpk5qjRpqo7FdEpLCw0PwEFSdPnrS1f0JCgkyfPt2So++aCD4HocafpteBbhkSGxsLx9jh6+trLGvXoPewYcOGav7000/DubQmrCIivXv3hmO0Y6VCBf3nMTs7Wz0ef/jhBzi/j4+PmqPPCTXrFcG3VzEd12fOnIHb7DCVjqPzeLt27Ww/Dmpc269fPzhGu8WBqfku//JDREREjsLFDxERETkKFz9ERETkKFz8EBERkaNw8UNERESOYqvaKzg4WB566CFLbrryHjU9TUhIsPPQRu+++y7cVqtWLUuWnp6u7utyueAV/sisWbPUfOjQoWpuqjhAV+ub3l/ULNSOyMhIuA1V/pSlme3ly5fVvHr16rbnQoqLiyUvL8+SV6pUCY4ZO3asmqOGuaaKgylTpqh5ZmYmHBMQEAC3lRYWFiZjxoyx5KaKS1SdtmfPHjU3NdhE1SmjRo2CY1q2bAm33ShU0SWCGwK//fbbth/njTfeUHPTOUY7J4rg46pSpUrStGlTS46axorgaq958+apOfpsRURWrVql5qZKnj8baq6MKlE7dOgA50JNMVGlol3+/v7q8XjgwAE4Bv1OjBs3Ts1XrlwJ51q3bp2amx6/bdu2cJvm9OnT6jFn+t3OyMhQ8549e6q5dh4r8e2336r5N998A8ecP3/ekpmqHvmXHyIiInIULn6IiIjIUbj4ISIiIkfh4oeIiIgchYsfIiIichQufoiIiMhRbNV1u1wuqVixoiU3NW1EjSl9fX3VvE+fPnCuDRs2qPnDDz8Mx3zyySeWDDVCvXLlilqSGBMTA+efNm2amqMmhR07doRzoeZ+H3zwARyzcOFCNUeNRzXff/893IbKFLXmmiIi48ePh3N99tlnam4qtY+OjobbNAUFBWoTP1OzzoMHD9p6jB07dsBtqLnfnXfeCcfMnDnTkqGGuYmJieprmTx5Mpx/9+7dao5K4E1NUlHpsalxbKNGjeC20vLz89XvQXh4OByjNTQ0Ka9GyCVMjXk1QUFB6u0S7rnnHjgGvYdbtmxR8w8//BDOpd0KQkSkS5cucIxWeoxKm3NyctRSe1N5+rJly9R84MCBar569Wo41/8rpsawfn5+tuZC74eJ9ttcVlFRUWoj6l27dsExZ8+eVfMJEyaouVaaXgLdwgU1PEX8/f3hNv7lh4iIiByFix8iIiJyFC5+iIiIyFG4+CEiIiJH4eKHiIiIHMVlp/LB5XIli8i5P+/p/NfUcbvdVUuHN9HrE1Fe483++kRuqtd4s78+ER6jf3V8fX99N/trVF+fiM3FDxEREdFfHf/bi4iIiByFix8iIiJyFC5+iIiIyFG4+CEiIiJH4eKHiIiIHIWLHyIiInIULn6IiIjIUbj4ISIiIkfh4oeIiIgc5f8AYSPCb7LPob0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    plot_digits(np.random.normal(digits.data, i))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "3c20f324",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "데이터의 50% 수준(분산 기준)까지 복원 가능한 PCA 기저벡터의 수는 12 개 입니다\n"
     ]
    }
   ],
   "source": [
    "pca = PCA(0.50).fit(noisy) #데이터의 50% 수준(분산 기준)를 표현할 수 있는PCA 기저벡터의 수는?\n",
    "print(\"데이터의 50% 수준(분산 기준)까지 복원 가능한 PCA 기저벡터의 수는\",pca.n_components_,\"개 입니다\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "9286d372",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NirePsm386aefYM5al5jxVhmh2D5qFrj4SafTNmfOnKzc26kLCwthftVVV8F8/vz5dK6OHTvCvF+/fnQM6snTvn17+NxUKmWzZs3Kyr2TJfsBWb9+PcybNm1K52J9wp5//nk6hu3wiUQi60r9dDpt8+bNy3rujh076PysL8urr74K81tvvZXOxfrbsIWwmVmNGjVgfvDBB8NKhHQ6bXPnzs3KvW28//77YT5hwgSYb968mc7FvsORI0fSMa1atcrKWrZsCZ+bSqVs5syZWXloDzQzs3feeQfmXu+y0aNHw9zbrxm2j6JzDDuBmpn17NkT5l988QXMvR9B9g+QK664go7p06cPzKtWrUr3UXQcFsfNN98Mc2+xzc693j880QKd9VmqV6+effrpp1m5tyBji/fu3bvD/IMPPqBzXXfddTAfMmQIHYMWfm3btoXPTaVSsP+d94+4YcOGwXzr1q0wnzhxIp2LLbJYH0Yzsx49esAcHYNmfB/1/hHCfis++eQTmHt9Lvv37w/z0AW61wtM/+0lIiIisaLFj4iIiMSKFj8iIiISK1r8iIiISKwEXfAcRRG84Mi74PmWW26BObuga+jQoXQudpGgdzEkukCLXTAWRRGs0vIu8mKVHg8//DDMd+7cSediF9Lm5/O7jHtX+O+tjz76iD42Y8aMoPeELsYtwi54rlChAh3jXVwcYs2aNfQxdJG7Gb8wnj3fzODFuma8KsfMLDc3lz62p0QiEXxx84IFC2B+7733wtyrnnz77bdhXrNmTTompMqGHYPsokkzXhHE9h3vIkh2UWypUqXomNKlS9PHkCiK7Ndff83KWWWjGa+6ZBfr33fffUHvyQxf1FwEnWPZxafJZDK4+o9d/Lp8+XKYs4ouM7NRo0bB/IwzzqBjUGVTaJUvu8Dem6t58+YwX7hwIZ2LFQWxqsfiyGQy8AJ4di4x48db7dq1Yc7WBmb8gmdvrYGqzdBx9v/noo+IiIiI7Ie0+BEREZFY0eJHREREYkWLHxEREYkVLX5EREQkVrT4ERERkVgJKnU3w2XiS5cupc8fN24czFmvHFZ+a8bLIb2+TaiMmpWtFqdEk5XSeX1WmBNPPBHmTZo0oWNY88YQXpNA1qCVlQR7JagMa7pn5t9mgEFlpQ0bNqTPZ7ddWLJkCcxZI1Qzs2bNmsH8lFNOoWNKAvuezMyGDx8Oc9azrkOHDnQuVsrvjWG3g0ASiQTsAeXtB6zUnH3mXbp0oXP16tUL5t7n6/X+KymTJk2CObstASsvLi50XgxtVMr6WJnxc9DTTz8N88cff5zO9cYbb8C8OM13EXa7Ce/cd+2118J8ypQpMPeafrJbNbRr146OCf2dSCQS8NYL3u0QOnfuDPMHHngA5t55dMWKFTD3mnyjfnbe7SP0lx8RERGJFS1+REREJFa0+BEREZFY0eJHREREYkWLHxEREYmVoDKFRCIBr/BnVTGejh07Bo9BjdbM/GahITKZDKw6OOSQQ+iYRx55BOasyZvXNLJVq1Yw9xonhlYwoGaExxxzDH3+3XffDfNdu3bBfNGiRXQuVpVXtmxZOoY1ofWe/8svv2TlXjPQKlWqwPydd96B+fTp0+lcY8eOhbm3jWi/Zk0jzfBnMm3aNPr8d999F+assaDXxJNVjaxbt46OQdVbobyKMVZlw74/1iTUzOyGG26AuVfR5TVPZEL3a3bssCo71vzSzOzMM8+EuXee8faJveU13mRVOazKj1VomuEmpWa48WWRkOa7rOmnV+3FzoujR4+G+VFHHUXnuuyyy37nHWYL/Z1gVZdNmzalY9g5jv1up1IpOtf48eNhfv3119MxXiUaor/8iIiISKxo8SMiIiKxosWPiIiIxIoWPyIiIhIrWvyIiIhIrARVe0VR5FahILm5uTDv169f0DxmvBfIl19+Scegnjys0iKZTMLKro0bN9L5WTXCscceC/MtW7bQuVhVGepP9nuvz6C+V40aNaLPZ4/961//gjnrVWNm1rNnT5gfd9xxdExoVQzru1McrD+S1ydnxIgRMD/jjDPomJycnKzM65uEvsPZs2fT57NKj4ULF8J8+fLldC5W0VKvXj06JhQ6x7Rv354+n/VNQlV/Zn7V0QcffADzrl270jGhWCWNZ/369TD/6KOPYP7666/TucqXLw/zgQMH0jF169bNykKPzfz8fPoYq4Zi/Q49K1euhLlXFRzyu5ZMJoMri1j176mnngpzb7v79u0b9Nolyav6O/LII2HOfp+9npKDBg2C+eTJk+mY8847jz6G6C8/IiIiEita/IiIiEisaPEjIiIisaLFj4iIiMSKFj8iIiISK1r8iIiISKwENzZFDehq1KhBxyxduhTmy5Ytg3mDBg3oXKzMzis7RGXJXokmesxriMca8vXp0wfmw4cPp3M9/fTTMPfKpEMbDqIy6eJ48cUXYe59F+y1vWaoXtPVEN53XlBQAPPBgwfDnJXAm5n17t0b5u+//z4dM2DAAPrYnqIogo00GzduTMe0aNEC5uwWA16ZNCvZPfroo+mYUF6ZP8KOtS+++ALmjz32GJ2L7Qsedg5gMpkMPC+xZsFmZosXL4Y5+z6eeOIJOhf73m+//XY6ZsKECVkZO55Zc2HvuGH7KLstAdtuM7MePXrAvEmTJnRM6D6HbNiwgT72zTffwLxZs2Ywf/LJJ+lc7FjzmqH+X2LnXq9hePfu3WH+3HPP0TEqdRcRERFxaPEjIiIisaLFj4iIiMSKFj8iIiISK1r8iIiISKwEVXsxRxxxBH2sevXqMD///PNhfvLJJwfP1blzZzqmJKqhWDNHM7MuXbrAnF3hPmbMGDpXtWrVfufd/e9EUQSb+3mNQN966y2Ys6vua9asSediFWKrVq2iY0aNGkUfQ1glDWvuaWb27LPPwpx9Hx9++GHQezLzmzqi98saLbKKy169etH5a9WqBXPU9NfMr0hs3bo1zEuqmWwURfB9HXAAP1Xl5eXB/KWXXoL5unXr6FypVOp33mG2HTt2BI8JbQp6yimnwJxVEbLqKTO+/3pNiVHFK6o6NOPNhVmTazNeqcQat6bTaToXq570GkSXhO3bt9PHPvnkE5i3atUK5l4FYXH2t1CsYo81Fzcze/zxx4Neo2XLlvSxkSNHwtw7z2zatCkr8xp/6y8/IiIiEita/IiIiEisaPEjIiIisaLFj4iIiMSKFj8iIiISK1r8iIiISKwElbpnMhlYZlelShU6hpUqsgaQrGzVzOzqq6+GOSs3Z0Kb2JUtW5Y+VrFiRZhv2bIl6DXMeCm/xyvl21MURfD5Xukkaw6JyiDN/Mapc+fOhXnp0qXpmO+//54+hiSTSVjWjsrJi7AS1QceeADmrETczKxNmzYwP/XUU4Nen5W6M94tHdh7Qs0qzfyGg6effnrQ+zLzP689JRIJWNa+detWOuaKK66A+ZIlS2A+duxYOteJJ574O+8wm1eGj7DbMVStWpWOueaaa2DOyvbbtWtH52LHQrdu3eiY0FuGhGIlzKwE3jvnn3POOSXynkJ5TZ1Z09NZs2bB/Nhjj6Vz1alTJ+yNWfj5ZPfu3fC8xH7vzPjvJLsdAytn91x66aX0MXSOUKm7iIiIyL9p8SMiIiKxosWPiIiIxIoWPyIiIhIrWvyIiIhIrCRCGuwlEon1ZsY7NO47UlEUZXWt3I+2zwxs4/6+fWb71Tbu79tnpn10X6ft2/ft79sIt88scPEjIiIisq/Tf3uJiIhIrGjxIyIiIrGixY+IiIjEStB92XNycqJUKpWVey0N2G21Fy9eDHOv1UGDBg1g7rWrQK9fUFBghYWFWW86JycnSqfTdK4Qu3btgvmiRYvoGHbr8IYNGwa/fl5eXuGeF3qx7fNuAV5QUADzjRs3wtxrdcI+W2//YdD2mfF91Lu2bfXq1TBnbQBYOwzvdbz9qlKlSllZfn7+H76PMuzYNOOtL2rWrEnHHHTQQTBn+yj6/rzb8+fn4+syf/3116D3Y2ZWuXJlmLP2C2b8nDV//ny6j5bUd7hy5UqYe+116tatC3Pv2GWvzfbR0N8JprCwEOZr1qyhY9j3W6NGDTqmQoUKWVno74S3j7JzDNs+9PkVYfuodx5nn/2CBQtKbB9lLWjYd8W2w4y3enLbVYB1ADuPmgUuflKpFOxFcuCBB9Ix7AeE9Ww5+uij6VyvvPIKzL3eW+j1Wd+bdDpts2fPzsqL09eGnZTq169Px3Tq1AnmU6ZMCX79RCKR9YuQTqdt3rx5Wc/1+iZdfvnlMH/hhRdg7vWwevLJJ2Hu/bAwaPvM+D66c+dOOtddd90Fc9bXbM6cOXQudnD+5S9/oWN69eqVlbF+XCW5jzJNmjShj7F99IYbbqBjnEVv1neYSqXg9v300090/ssuuwzm7KRbu3ZtOlf//v1hfthhh9Ex7B8nZcqUgftoOp2Gfe6Kszi44IILYP7mm2/SMSNGjID5gAEDgl67RYsWME+lUvbZZ59l5d6ik3n66adhfuedd9Ix7Bx73XXX0TGop1v79u3hc9l51PtH0e233w7zp556Cub3338/natv374w37RpEx3DzrHlypWj+yjaRs97770H83vvvRfmZ555Jp3ryiuvhPnmzZvpGNTTsW3btvT5+m8vERERiRUtfkRERCRWtPgRERGRWNHiR0RERGIl6ILnRCLhXtyMNG3aFOasisir3CpfvjzMv/vuOzqmTp06WRm7sDCKIlghsnz5cjp/uXLlYP7111/D/IAD+Ec+f/58+tgf6YMPPqCPsQub2UWs7EJvM7PRo0fD/JZbbqFjQrF99Ntvv6VjPv74Y5h7FzwyTzzxBMyXLFlCx/Tr1y8rY/toJpOBF2+z/dDDLrb0LkxFVTFm/Hg28z8vBFXNfP755/T57ELT4lTenXbaaTBfu3YtHeNVoDChFzezi0afeeYZmHfs2JHO5R0LJSV0+6ZPnw5zdGG4mdm5555L52Lnma+++oqOQYUaodvgHYMrVqyAOSsuYNXCZmajRo2CebNmzegYb39AoiiC5xmvinDChAkwZ79r3jF18cUXwxxVxhZB5yBW8Wmmv/yIiIhIzGjxIyIiIrGixY+IiIjEihY/IiIiEita/IiIiEisaPEjIiIisRJU6s7K31atWkXHsDL0s846C+Ze/5XWrVsHvYYZ7snjlbqjMluvJO+3336D+dSpU4Oeb2Z27LHH0scYr2EngrbP6wt1/vnnw/yOO+6Auff9eWWHfzSvvPmSSy6BOesB9+mnn9K5WD8cr9QUfS7se00mk8Uqa0eGDBkC8x49etAx7FYX3nfr9ePZUyKRgKX23nHD+rax3lO9e/emc7FjwSvxrVWrFn0MiaIIbo9Xij1s2DCYswaYw4cPp3Oh23+UpOLcEoXdTuSII46AuXeuHDlyJMy9WziEHIPFwfpY5eXlwXzdunV0LnY7Da8fWHHOvei2M6xk38xgTz4z3gzZO27YLQ5yc3PpmHr16mVl3neuv/yIiIhIrGjxIyIiIrGixY+IiIjEihY/IiIiEita/IiIiEisBDc2LV26dFa+ceNGOoY1WxszZgzMvcqqgw8+GObelfElAW1zkZtvvhnm06ZNC36dzp07w/yXX36hY9hnEqJLly70sV69esGcNTBF1WRF+vTpE/S+fm8+JIoi2BSwbNmydEzbtm1hzpq6fvbZZ3SuE088EeaNGjWiY1DlD6s02b17t23dujUr9xohXnnllTBn1VBeZdqMGTNg3rx5czrGa0a4t/Lz8+ljrDKEVfh5xwxrSLx69Wo6pnHjxvQxJIoi+/nnn7Ny7zusUqUKzNnxWa1aNToXq6D6o3nn6VdeeQXmbLsnTZoU/PpeA9oyZcpkZV6T7VAdOnSA+fjx42HOmoSa8f2afVZm4U1aWdUlay5uZtaqVSuYz5o1C+as0s2MVyu+/vrrdExohaH+8iMiIiKxosWPiIiIxIoWPyIiIhIrWvyIiIhIrGjxIyIiIrESVO2VyWRs+/btWbl3FX/Lli1hXrt27aDczOyCCy6A+eLFi+mYkEqaZDIJq4JycnLo/KxSiPV/8io6vv/+e5h71SmhPVtQBQPrvWJmsCrFzOzxxx+HuVf5V7duXZh71Wxe3zGEVSl4GjRoAPOKFSvC/IsvvqBzHXrooTD3qm8QVmlSqlQpq1ChQlb+8ssv07l++uknmLMeXl4VBqu68nqnlUSPJO87Pfzww2HOelh9++23dC702Zrxfbc4kskkPOYOOICfjlmVzeTJk2E+Z84cOtdzzz0H8/r169MxaB/yqqcQb7/asWMHzFml7aZNm4Je2wz3fiouVIXqvadx48bB/N1334U5qj4rctlll8H8yCOPpGO8alcGHbdNmjShz2f7FcMq3czMBg4cCHPW18zM7yuJ6C8/IiIiEita/IiIiEisaPEjIiIisaLFj4iIiMSKFj8iIiISK1r8iIiISKwElbonk0krV65cVs5Kgs14iR8rQ7388svpXKy0MpVK0TGbN2/e63kymUxww8H27dvDfNWqVTBftGgRnYs1dV22bBkdw8q0GbTtXtM71tzz+eefh/mgQYPoXKxk32tm6936IIT3HbIyalY6+d5779G5Jk6cCPOnn37aeXd7jzVu9b5DVgrepk0bmD/22GN0roKCAph7pbmhTRUR1iDZzGzw4MEwZ2Xr7DYNZmZ9+/aF+UknnUTHhDbfZbxbPrDPnfGaCN90000wHzBgAB1z2mmnZWWh32uNGjXoY71794Y5a7rMGkqb4dubmPFzdagoiuB37p1j2Hn/7rvvhvnMmTPpXOw2GDVr1qRjQm9LYFYyx60ZP7+ff/75dMz06dNh7pXHq9RdRERExKHFj4iIiMSKFj8iIiISK1r8iIiISKxo8SMiIiKxElTtxeTm5gaPueOOO2A+Y8YMOoY1juvfvz8dgyo+WLPMZDIJq1a8hnismRxr9Pj666/Tub7++muYl0RjSI/XHJVVxrAmrNu2baNzjR49GuZe08orrriCPsagz8t7jSlTpsC8cePGMP/888/pXKxJrFfJE9KIlTVu7dixIx3Tr1+/vZ7fzKxSpUr0sUaNGsHca/5bnEqTPXlVf6zaqrCwEOafffYZnWvYsGFhb8x49Q3DKvZYE2gz3hh3/fr1MPeqhVjl0fHHH0/HdO3aNSsLPS81bdqUPsbOo1u2bIG5VznGmmKWVOVoIpGATWi945id21lj7CpVqtC51qxZA3OvatarBEOiKILnLK+ykTXTve+++2DOKvnMzObPnw9zr/kvaqrNKv/M9JcfERERiRktfkRERCRWtPgRERGRWNHiR0RERGJFix8RERGJFS1+REREJFZKpNSdNaw04yW+pUuXhvmOHTvoXLfddhvMmzdvTseg8sPQhm1e00aGlW7edddddAwrqa9atWrw64fwyhdZA9p58+bBnJUXm5kdeOCBMK9cuTId483HoO/XKzX/8MMPYX7llVfCvH79+nSu66+/HubeMYLKlb0STaR69epBz/d4pfxsXwkt9w7FzhdmZlOnToX5kiVLYO418OzUqVPQ+zILb2yaSCTg7Ta8z3DdunUwZw1BvVtqtG7dGubetqNjlN0yhPHKlNljrMmud07s3r170PsqKayRrhm/3cSNN94I827dutG5WNn6Tz/9RMewW5MwrMm3t42swTl77aFDh9K5Dj30UJgPGTKEjgm99YL+8iMiIiKxosWPiIiIxIoWPyIiIhIrWvyIiIhIrGjxIyIiIrGSCLlCOpFIrDez/D/u7fzHpKIoyuoUuB9tnxnYxv19+8z2q23c37fPTPvovk7bt+/b37cRbp9Z4OJHREREZF+n//YSERGRWNHiR0RERGJFix8RERGJlaD2Fjk5ORFrwcCsWbMG5hs2bIC5d4v3dDoN8/Llywe9p5UrV1phYWFWD4ScnJyIvQaDbgFuZrZixQqYe20IcnJyYO61/GCtN+bPn1+454VeOTk5USqVynqud3v+ZcuWwZy1i/Bah7D3WqVKFTqG3U594cKFWdtnxrdx9+7d9DW+++47mG/fvh3mXruTatXgtXXuNqLPrKCgoMT2UeaHH36Aube/1a1bF+Ze+wkmLy+vRPbRpUuXwpzto16rkeLso4cccgjMFyxYELSPesfO5s2bYb5q1SqYs1YyZrxlTdmyZekY9N7y8/Ntw4YNe72Pet8ha4GwceNGmLP2B/9+ffpYiNDfCe/62bVr18KcnWO2bt1K52K/kYcddhgdw86j6Bg0K953yH4r2LZ4v9us5ZF3HKJ2K/n5+fA7NAtc/NSrV88+/fTTrNzrQ3TffffB/Nlnn4W594E8+eSTMD/hhBPoGPSjl5ubC5+bTqdpzyrmyy+/hPnAgQNh7vUmueCCC2A+f/58OqZx48YwL1OmTNaV+qlUymbNmpX1XHYAmvGeNN9++y3MvR/BRo0awfy8886jY7p27QrzSpUqwUqEVCplM2fOzMq9bTzttNNgPmfOHJizvm1mZpdeeinMzzrrLDoGfWbt2rWDzy3OPsrccsstMF+wYAEd89BDD8Hc+0yYRCIB99HZs2dnPdfrW9ShQweY5+fjYhXvR4Lto+eccw4dw3piVahQge6j6DzqHTuvvfYazK+99lqY165dm841YsQImB933HF0DOq91bFjR/hcto96i+qbbroJ5hMnToT5sGHD6FwXXXQRfYxBC5eWLVvC56bTaZs7d25W7v0D695774V5Xl4ezFm/OjO+nzz88MN0zMknnwxzdAyaFe87POOMM2DOtsXrycnOl2effTYdgxZM7LfeTP/tJSIiIjGjxY+IiIjEihY/IiIiEitB1/wkk0l4QSC7mMvM7J577oE5+z90dg2LmdmDDz4Ic/Z/s2b+xY17ymQy8AJm7wJXdH2CGb9ugm2DGf8/UHQhVxF20SoSRRG8Puujjz6iY77++muYs4tuly9fTudi19Z4F4F7/4+OJBIJ+J0/99xzdAy6DsrM7Oijj4b5woUL6Vyff/45zPv370/HoAsY2cWvURTZzp07s3LvehF2Mem7774Lc/Y9mfkX0paEKIrs119/zcrZtRFmZtu2bYM5u7DXu/6rRYsWMPfOAV6RBpJIJIIvEL/66qthzr5b76L4oUOHwvzRRx+lY5o2bZqVeRdoo2toPv74Y/r8N954A+bs3F5YWEjnKg50US4792QyGXjtC7v43IwX/jRr1gzmbdq0oXONHDkS5iX5mbDjkF17Zmb2/vvvw5xd08mulzXjvyPsQmgzXHzkXYSuv/yIiIhIrGjxIyIiIrGixY+IiIjEihY/IiIiEita/IiIiEisaPEjIiIisRJU6s6sX78+eMzYsWNhznojmZm1b98e5tOnT6djunfvvtfvKZFIBJfyNmnSBOY9evSAOeuNZMZLzk866SQ6pkGDBs67+5/YrQpQ6XQRVorJvoslS5bQuU488USYe2W/Xi+XEKxk3zN48GCYjx49mo5hbQUqVqwY9NqsjJiV8ntYCWyNGjVgjsqai9SvXz/otUOxfbRSpUp0DDs+WEm7Nxe7rb5Xzl6uXDn6WIiCggL6GCtpZ210xowZQ+dirVO822agWwB4pe6Id25t2LAhzFkLjR9//JHOxcqbvfeLjk92i5FkMgn7oHll2N26dYM5K4/3blXAWuiwW3OYGSxbLw7vViYMa0mxa9cuOobdpsI7DlGPPe/5+suPiIiIxIoWPyIiIhIrWvyIiIhIrGjxIyIiIrGixY+IiIjESolUe3366afBY1gzVHQVfRF2tf4nn3xCx4RWe3lNRJHc3FyYX3XVVTAfP348nYs1FuzSpQsd4zVu21teFQarZJk2bRrMN2/eTOd6+eWXYd63b186piS2z8zs8MMPp4917twZ5qxJqVc1wj4vrzqFVV0hURTBKgmvAmzy5Mkwr1ChAsxRg8AioRU+JcVrLMoqAlmzzBNOOIHOxc5LqVSKjimpffSrr76ij7GKSNYg2ntPrOIUNfcsLrSfeJ9hhw4dYP7ee+/B3KuMO+WUU2Du/Raghs/sM2THIDuezHgl78MPPwzz6667js41aNAgmKNtKBJaxcwqn4866ig6hlW0scpu75xYq1YtmHvNY739C9FffkRERCRWtPgRERGRWNHiR0RERGJFix8RERGJFS1+REREJFaCq73QFfBz5swJfuFffvkF5gcddBAds3jxYpijvjPFhbavOBUu7Mr38uXL0zGTJk2C+cSJE+kYrw/T3mI9t8z41f27d++GufdeZ86cCfPTTjvNeXfhMplMVsZ6NpmZnX/++TBftmwZzL1+aq1bt4a51/eHfZYI6+2Vl5dHx4wcORLmrN/PggUL6Fysj96FF15Ix7Rs2ZI+hqDvz/vM2fHPqj+8Sqg1a9YEzVUcmUzGduzYkZV7lSzsOGS9r7zqONY3yau+Qd9JKO87vPbaa2HOjhvvPHPrrbfCvHr16nRM8+bNs7LQ/nobN26k87NjilVhse/VzOyYY46BudcrqzjQceKdR73HkNWrV9PH2PnEOzep2ktERETEocWPiIiIxIoWPyIiIhIrWvyIiIhIrGjxIyIiIrGixY+IiIjESnCpOyr/69SpE33+q6++CnNWnuqVv7FSQq/xJ2rW55UWJ5PZ60GvNHb27NkwnzFjBsxvuukmOhcrI77hhhvomJJoqlixYsXgx7755huYL1myhM7VrFkzmDdp0oS/uWJA32HVqlWD5/niiy9g/tRTT9Ex7NYD3i0cQmQyGdu+fXtWvmXLFjqGlbSz8ulx48bRuf72t7/B/Nlnn6Vj2PfOhB6D7DNfvnw5zFmDXTPeHLJnz550TKhkMgkbOHulugsXLoQ5a77rNRhmt5y49NJL6ZjQ82godp7p378/zHv16kXnuvnmm2E+atQoOmbChAnOu9s76PYFRdhtBFhZvvf9LVq0COasBN7Mb1bM/NFNjGvXrk0fY82ev//++xJ7ff3lR0RERGJFix8RERGJFS1+REREJFa0+BEREZFY0eJHREREYiW42gvp06cPfey2226D+dq1a2HOru739OjRI+j5pUqVgnkURbA5nFdJ88Ybb8CcNZNs27YtnWvu3Lkw965wL4mr34tTMcaqfiZPnkzHeNUkDKu+KUmsyu6RRx6BeX5+Pp1r06ZNJfGWqEQiYQcckH3YehVzXbt2hXmFChVg7u0PK1asgLnXtLIkeE0bX3jhBZizqpjXXnuNzjV+/PiwN2Yl0/TTzG9mybAGkKwJtBmvCsrNzQ16bXYezWQywdVFrAKPzcNe25uLVTeaGaygDP1ed+7cSR9j5zHUINWMH5vF5TW6DYE+pyLPPPMMzFkTc6+ym1U3elWXob9j+suPiIiIxIoWPyIiIhIrWvyIiIhIrGjxIyIiIrGixY+IiIjEihY/IiIiEislUupevnx5+ljfvn1hfuSRR8K8Tp06dK6SaOLp+e2332DzVK/skJVvT5kyBea33347nYuVEXslqKxUkkGf4bZt2+jzTz31VJjPmTMH5n/961/pXCeddNLvvLtsqMllcXilt1dffTXMWWPToUOH0rkGDRoU9L7McBND1jQyiiL4WPXq1en8U6dOhfn9998P8w4dOtC5mOHDh9PHUBPPUF4TTVZiW1BQAPO77rqLznXeeeeFvTEruX3UO5ZfeeUVmJ955pkwZ7c3MOP7Q0lCZeJec99ly5bB/IEHHoB5cRp1nnHGGfQxVHbNGgIzNWvWpI+1a9cO5qwxtndrh5JuBI1EUQS3H91mo8ikSZNgzpp8t27dms41ZMgQmLPP0Qx/Zt6aQX/5ERERkVjR4kdERERiRYsfERERiRUtfkRERCRWtPgRERGRWEmEVFAlEon1Zsa7Ou47UlEUVdsz3I+2zwxs4/6+fWb71Tbu79tnpn10X6ft2/ft79sIt88scPEjIiIisq/Tf3uJiIhIrGjxIyIiIrGixY+IiIjEihY/IiIiEita/IiIiEisaPEjIiIisaLFj4iIiMSKFj8iIiISK1r8iIiISKz8N3mHuejbS4zCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "components = pca.transform(noisy)\n",
    "filtered = pca.inverse_transform(components)\n",
    "plot_digits(filtered) # 복원된 손글씨 이미지"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f873d663",
   "metadata": {},
   "source": [
    "## ------------------------------------- DJ's practice ------------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "ca4786bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(n_components=0.5)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_pca = PCA(0.50)\n",
    "\n",
    "test_pca"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "7515a97a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(n_components=0.5)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_pca_fit = test_pca.fit(noisy)\n",
    "test_pca_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "3b4afe98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_pca_fit.n_components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "07590806",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -9.82613291,  19.60311879,  -3.49445446, ...,   7.26107832,\n",
       "          0.58419145,   1.8438046 ],\n",
       "       [ 14.65827166, -15.58079811,  11.61685625, ...,   5.96816258,\n",
       "          1.69008628,  -7.38319027],\n",
       "       [  5.30646513, -14.73205492,   0.26421735, ...,  -4.26313868,\n",
       "         -2.47186264,  -7.46461662],\n",
       "       ...,\n",
       "       [  7.71966027,  -6.95777476,  -6.08565658, ..., -10.8659198 ,\n",
       "          5.73479747,   5.54420925],\n",
       "       [ -8.91737494,  11.35437432, -11.91713483, ..., -11.08482921,\n",
       "          3.23292014,   0.46439398],\n",
       "       [ -6.88599972,   3.56177468,  14.54014659, ..., -12.42281561,\n",
       "          0.88588017,  10.20443299]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.inverse_transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "66036909",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.41042987e-01,  8.44556435e-01,  1.06479115e+01, ...,\n",
       "         3.24790614e+00,  1.81488255e-03, -1.74913633e-01],\n",
       "       [ 1.07473665e-01, -1.96428904e-01,  6.01705313e-01, ...,\n",
       "         9.98670022e+00,  3.98285398e+00,  8.50605231e-01],\n",
       "       [ 3.20231232e-01, -5.21159240e-01, -2.60882866e+00, ...,\n",
       "         9.13162583e+00,  3.28708174e+00, -1.05499403e-01],\n",
       "       ...,\n",
       "       [ 4.39729573e-01,  4.37965521e-02,  2.94366949e+00, ...,\n",
       "         4.40779637e+00, -1.64716424e+00,  3.72674661e-01],\n",
       "       [ 2.15123457e-01,  1.38979729e-01,  3.38129363e+00, ...,\n",
       "         1.03937945e+01,  1.45823909e+00,  6.98451492e-01],\n",
       "       [-1.07487531e-01,  2.94227969e-01,  7.68362973e+00, ...,\n",
       "         1.45826294e+01,  2.02113903e+00,  1.25426720e+00]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filtered"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "532ca2e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(n_components=0.3)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PCA(0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a3bf207",
   "metadata": {},
   "source": [
    "## ------------------------------------- end ------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3c957b0",
   "metadata": {},
   "source": [
    "## 20-2. PCA를 통한 이미지 압축 및 복원"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "b8e29ec2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "손글씨 이미지의 크기는 64 픽셀 입니다.\n"
     ]
    }
   ],
   "source": [
    "# 손글씨 데이터 불러오기\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.datasets import load_digits\n",
    "\n",
    "digits = load_digits()#[YUOR CODE]\n",
    "print(\"손글씨 이미지의 크기는\",digits.data.shape[1],\"픽셀 입니다.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "d1d3f460",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 이미지 출력하는 함수 정의하기\n",
    "\n",
    "def plot_digits(data):\n",
    "    fig, axes = plt.subplots(4, 10, figsize=(10, 4),\n",
    "                             subplot_kw={'xticks':[], 'yticks':[]},\n",
    "                             gridspec_kw=dict(hspace=0.1, wspace=0.1))\n",
    "    for i, ax in enumerate(axes.flat):\n",
    "        ax.imshow(data[i].reshape(8, 8),\n",
    "                  cmap='binary', interpolation='nearest',\n",
    "                  clim=(0, 16))\n",
    "plot_digits(digits.data) # 원본 이미지 출력"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "ab6e0485",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],\n",
       "       [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],\n",
       "       [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],\n",
       "       [0, 9, 5, 5, 6, 5, 0, 9, 8, 9]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.target[:40].reshape(4,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "649c3b8e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "데이터의 90% 수준까지 복원 가능한 PCA 기저벡터의 수는 21 개 입니다\n"
     ]
    }
   ],
   "source": [
    "# 데이터의 90% 수준까지의 주성분을 포함하는 PCA객체를 만들고 손글씨 데이터에 적용합니다.\n",
    "\n",
    "pca = PCA(0.90).fit(digits.data) #데이터의 90% 수준까지 복원 가능한 PCA 기저벡터의 수는?\n",
    "print(\"데이터의 90% 수준까지 복원 가능한 PCA 기저벡터의 수는\",pca.n_components_,\"개 입니다\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "601930f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sklearn.decomposition._pca.PCA"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(pca)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "bce7ec94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(n_components=0.9)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "ed7ed118",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "압축률은 67.1875 % 입니다.\n"
     ]
    }
   ],
   "source": [
    "# PCA를 통해 21차원으로 축소되었으므로 압축률은(64-21)/64 * 100(%) 이 됩니다.\n",
    "\n",
    "\n",
    "compression_ratio= (digits.data.shape[1] - pca.n_components_)/digits.data.shape[1] * 100#[YOUR CODE]\n",
    "print(\"압축률은\",compression_ratio,\"% 입니다.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "afbcf1b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 축소된 주성분을 inverse_transform을 통해 기존 64차원으로 매핑하여 복원합니다. 그리고 plot_digits함수를 통해 이미지를 확인해봅시다\n",
    "\n",
    "components = pca.transform(digits.data)\n",
    "filtered = pca.inverse_transform(components)\n",
    "plot_digits(filtered) #복원된 이미지"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10f3a86c",
   "metadata": {},
   "source": [
    "### 결과 : 원본 이미지와 압축 후 다시 복원된 이미지의 퀄리티가 육안으로는 비슷해 보임"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fe1fc3a1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
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