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 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 基于单一种群的特征选择方法\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import pyes\n",
    "import pandas as pd\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "from tensorflow.python.framework.errors_impl import InvalidArgumentError\n",
    "from tensorflow.contrib.distributions import MultivariateNormalFullCovariance\n",
    "from loguru import logger\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "tf.logging.set_verbosity(tf.logging.ERROR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.genfromtxt('../exampleData/glass.data', delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "        0        1      2     3     4      5     6     7     8    9    10\n",
       "0      1.0  1.52101  13.64  4.49  1.10  71.78  0.06  8.75  0.00  0.0  1.0\n",
       "1      2.0  1.51761  13.89  3.60  1.36  72.73  0.48  7.83  0.00  0.0  1.0\n",
       "2      3.0  1.51618  13.53  3.55  1.54  72.99  0.39  7.78  0.00  0.0  1.0\n",
       "3      4.0  1.51766  13.21  3.69  1.29  72.61  0.57  8.22  0.00  0.0  1.0\n",
       "4      5.0  1.51742  13.27  3.62  1.24  73.08  0.55  8.07  0.00  0.0  1.0\n",
       "..     ...      ...    ...   ...   ...    ...   ...   ...   ...  ...  ...\n",
       "209  210.0  1.51623  14.14  0.00  2.88  72.61  0.08  9.18  1.06  0.0  7.0\n",
       "210  211.0  1.51685  14.92  0.00  1.99  73.06  0.00  8.40  1.59  0.0  7.0\n",
       "211  212.0  1.52065  14.36  0.00  2.02  73.42  0.00  8.44  1.64  0.0  7.0\n",
       "212  213.0  1.51651  14.38  0.00  1.94  73.61  0.00  8.48  1.57  0.0  7.0\n",
       "213  214.0  1.51711  14.23  0.00  2.08  73.36  0.00  8.62  1.67  0.0  7.0\n",
       "\n",
       "[214 rows x 11 columns]"
      ],
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     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "# 数据概览\n",
    "pd.DataFrame(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "number of rows: 214, number of column: 11\n"
     ]
    }
   ],
   "source": [
    "n_row, n_col = data.shape\n",
    "print('number of rows: {n_row}, number of column: {n_col}'.format(n_row=n_row, n_col=n_col))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def encode(solution):\n",
    "    \"\"\"用于将个体编码成二进制形式，用于选择特征\"\"\"\n",
    "    v_func = lambda x: 1.0 / (1.0 + np.exp(-x*2))\n",
    "    return [True if v_func(x) > 0.5 else False for x in solution]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x25494c0f0b8>]"
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     "metadata": {},
     "execution_count": 51
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    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# 非关键代码，用于验证 v_func 函数图像是否与文章中\"图 4.1\" 一致\n",
    "v_func = lambda x: 1.0 / (1.0 + np.exp(-x*2))\n",
    "x = np.linspace(-4, 4, 300)\n",
    "plt.plot(x, [v_func(v) for v in x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def DR(encoded_x):\n",
    "    \"\"\"计算特征维度缩减率\"\"\"\n",
    "    return 1 - 1.0 * sum([1 for v in encoded_x if v]) / len(encoded_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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       "      0      1      2      3      4      5      6      7      8      9    10\n",
       "0   True   True   True  False  False   True   True   True  False   True  0.3\n",
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       "3  False  False  False  False  False  False   True   True  False  False  0.8\n",
       "4  False  False   True  False  False   True  False  False  False   True  0.7\n",
       "5   True   True  False  False   True  False   True   True   True  False  0.4\n",
       "6  False  False   True   True  False   True   True  False   True   True  0.4\n",
       "7  False   True   True  False   True   True   True  False  False   True  0.4\n",
       "8  False   True   True  False   True  False   True  False  False  False  0.6\n",
       "9  False   True   True   True   True  False  False  False   True   True  0.4"
      ],
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>0</th>\n      <th>1</th>\n      <th>2</th>\n      <th>3</th>\n      <th>4</th>\n      <th>5</th>\n      <th>6</th>\n      <th>7</th>\n      <th>8</th>\n      <th>9</th>\n      <th>10</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>0.3</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>0.4</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>False</td>\n      <td>0.4</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>0.8</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>0.7</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>0.4</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>0.4</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>0.4</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>0.6</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>0.4</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "# 非关键代码，用于测试 DR 函数\n",
    "test_encoded_xs = np.ones((10, 10), dtype=bool)\n",
    "mask = np.random.normal(0, 1, (10, 10)) > 0\n",
    "test_encoded_xs[mask] = False\n",
    "df = pd.DataFrame(test_encoded_xs)\n",
    "df[10] = [DR(x) for x in test_encoded_xs]\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def CA(encode_x, data_X, data_y):\n",
    "    \"\"\"计算分类准确率\"\"\"\n",
    "    clf = make_pipeline(StandardScaler(), SVC(gamma='auto'))\n",
    "    clf.fit(data_X[:,encode_x], data_y)\n",
    "    return clf.score(data_X[:,encode_x], data_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "准确率为: 0.9345794392523364, 选中的特征下标: 0-1-3-6-7-8-9\n"
     ]
    }
   ],
   "source": [
    "# 非关键代码，用于测试 CA 函数\n",
    "encode_x = np.ones(n_col-1, dtype=bool)\n",
    "encode_x[np.random.normal(0, 1, n_col-1) > 0] = False\n",
    "\n",
    "ca = CA(encode_x, data[:,:10], data[:,10])\n",
    "print('准确率为: {ca}, 选中的特征下标: {idxs_feature}'.format(ca=ca, idxs_feature='-'.join([str(i) for i, v in enumerate(encode_x) if v])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 目标函数包含 CA 和 DR 两部分内容，如果需要修改分类器，请修改 CA 函数\n",
    "# 说明：文章中\"图 4.2\" 曲线与给定的公式 4.2 是对不上的，所以按最曲线重新定义了个 rho 函数\n",
    "def rho(l):\n",
    "    return 0.90 + 0.099 / (l/2000 + 1)\n",
    "\n",
    "def objective(encode_x, data_X, data_y):\n",
    "    l = len(encode_x)\n",
    "    return rho(l) * CA(encode_x, data_X, data_y) + (1 - rho(l)) * DR(encode_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Value of Rho')"
      ]
     },
     "metadata": {},
     "execution_count": 12
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# rho 函数的图示\n",
    "x = np.linspace(0, 100000, 10000)\n",
    "plt.plot(x, rho(x))\n",
    "plt.xlabel('Number of feature')\n",
    "plt.ylabel('Value of Rho')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "       0     1      2      3      4      5      6      7      8      9\n",
       "0  False  True   True   True  False  False   True  False   True   True\n",
       "1  False  True  False   True   True   True  False  False  False  False\n",
       "2  False  True   True  False  False  False   True   True   True  False\n",
       "3  False  True   True  False  False   True   True   True   True   True\n",
       "4   True  True  False   True   True  False  False   True   True   True"
      ],
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>0</th>\n      <th>1</th>\n      <th>2</th>\n      <th>3</th>\n      <th>4</th>\n      <th>5</th>\n      <th>6</th>\n      <th>7</th>\n      <th>8</th>\n      <th>9</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>False</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "source": [
    "# 非关键代码，目标函数的测试 1\n",
    "p = np.random.normal(0, 1, (20, 10)) # 测试种群\n",
    "encoded_p = [encode(x) for x in p]\n",
    "pd.DataFrame(encoded_p).head(5) # 编码后种群(前 5 个)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "       0     1      2      3      4      5      6      7      8      9  \\\n",
       "0  False  True   True   True  False  False   True  False   True   True   \n",
       "1  False  True  False   True   True   True  False  False  False  False   \n",
       "2  False  True   True  False  False  False   True   True   True  False   \n",
       "3  False  True   True  False  False   True   True   True   True   True   \n",
       "4   True  True  False   True   True  False  False   True   True   True   \n",
       "\n",
       "    fitness  \n",
       "0  0.742479  \n",
       "1  0.710116  \n",
       "2  0.695969  \n",
       "3  0.746995  \n",
       "4  0.924300  "
      ],
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>0</th>\n      <th>1</th>\n      <th>2</th>\n      <th>3</th>\n      <th>4</th>\n      <th>5</th>\n      <th>6</th>\n      <th>7</th>\n      <th>8</th>\n      <th>9</th>\n      <th>fitness</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>0.742479</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>False</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>0.710116</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>0.695969</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>0.746995</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>False</td>\n      <td>False</td>\n      <td>True</td>\n      <td>True</td>\n      <td>True</td>\n      <td>0.924300</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "source": [
    "# 非关键代码，目标函数的测试 2\n",
    "df = pd.DataFrame(encoded_p)\n",
    "df['fitness'] = [objective(encoded_x, data[:,:10], data[:,10]) for encoded_x in encoded_p]\n",
    "df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def real_objectives(lam, population, data_X, data_y):\n",
    "    \"\"\"\n",
    "    适应值塑造,对应文章中的公式 4.3, 返回 lam 个塑造后的较优适应值，及各个体下标\n",
    "    \"\"\"\n",
    "    encoded_population = [encode(x) for x in population]\n",
    "    fitness_values = [objective(x, data_X, data_y) for x in encoded_population]\n",
    "    # 取前 lam 个适应值较优的个体下标,再按升序排列\n",
    "    selected = np.argsort(fitness_values)[::-1][:lam][::-1]\n",
    "\n",
    "    temp = 1.0 * (fitness_values[selected[lam-1]] - fitness_values[selected[0]]) / (lam - 1) \n",
    "    \n",
    "    real_fitness_values = [0] * lam\n",
    "\n",
    "    for i, idx in enumerate(selected):\n",
    "        if i == 0:\n",
    "            real_fitness_values[i] = - (fitness_values[selected[lam-1]] - fitness_values[selected[i]]) / 2\n",
    "        else:\n",
    "            real_fitness_values[i] = real_fitness_values[0] + i * temp\n",
    "    \n",
    "    return real_fitness_values, selected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "([-0.21914911424187478,\n",
       "  -0.1793038207433521,\n",
       "  -0.1394585272448294,\n",
       "  -0.09961323374630672,\n",
       "  -0.059767940247784035,\n",
       "  -0.019922646749261363,\n",
       "  0.019922646749261336,\n",
       "  0.059767940247784035,\n",
       "  0.0996132337463067,\n",
       "  0.13945852724482938,\n",
       "  0.17930382074335205,\n",
       "  0.21914911424187478],\n",
       " array([10,  3,  6,  2,  0,  9,  8,  4, 11,  5,  7,  1], dtype=int64))"
      ]
     },
     "metadata": {},
     "execution_count": 16
    }
   ],
   "source": [
    "# 非关键代码，用于测试 real_objective\n",
    "real_objectives(lam=12, population=np.random.normal(0, 1, (12, 10)), data_X=data[:,:10], data_y=data[:,10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def event_on_generation(gen, population, current_best, history_best):\n",
    "    best = history_best\n",
    "    if gen == 0:\n",
    "        best = current_best\n",
    "    print('iter: {gen}, best solution(bool): {best}, best idxs: {idxs}'.format(gen=gen, best=encode(best), idxs='-'.join([str(i) for i, v in enumerate(encode(best)) if v])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def NES(\n",
    "    n_dimension: int, \n",
    "    objective, \n",
    "    n_iter, \n",
    "    learn_rate, \n",
    "    lam,\n",
    "    mean,\n",
    "    cov,\n",
    "    random_state=None, \n",
    "    event_on_genration=event_on_generation):\n",
    "\n",
    "    logger.debug({\n",
    "        'dimension': n_dimension,\n",
    "        'n_iter': n_iter,\n",
    "        'learn_rate': learn_rate,\n",
    "    })\n",
    "\n",
    "    tf.set_random_seed(random_state)\n",
    "    best, best_fitness = None, 1e+10\n",
    "    \n",
    "    def get_fitness(population): \n",
    "        return [-objective(solution) for solution in population]\n",
    "\n",
    "    mean = tf.Variable(mean, dtype=tf.float32)\n",
    "    cov = tf.Variable(cov, dtype=tf.float32)\n",
    "    mvn = MultivariateNormalFullCovariance(loc=mean, covariance_matrix=cov)\n",
    "    make_population = mvn.sample(lam)\n",
    "\n",
    "    fitness_input = tf.placeholder(tf.float32, [lam, ])\n",
    "    prob_output = tf.placeholder(tf.float32, [lam, n_dimension])\n",
    "    loss = -tf.reduce_mean(mvn.log_prob(prob_output) * fitness_input)\n",
    "    train_op = tf.train.GradientDescentOptimizer(learn_rate).minimize(loss)\n",
    "\n",
    "    sess = tf.Session()\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "\n",
    "    for g in range(n_iter):\n",
    "        population = sess.run(make_population)\n",
    "\n",
    "        scores = [objective(c) for c in population]\n",
    "        \n",
    "        event_on_genration(g, population, population[np.argsort(scores)[0]], best)\n",
    "\n",
    "        fitness_values = get_fitness(population)\n",
    "        sess.run(train_op, {fitness_input: fitness_values, prob_output: population}) \n",
    "\n",
    "        for i, score in enumerate([objective(x) for x in population]):\n",
    "            if score < best_fitness:\n",
    "                best, best_fitness = population[i], score\n",
    "\n",
    "    return [best, best_fitness]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_dimension = n_col - 1\n",
    "n_iter = 10\n",
    "learn_rate = 0.002\n",
    "mu = 4\n",
    "lam = 12\n",
    "mean = data[:,:n_dimension].mean(axis=0)\n",
    "cov = 10000 * tf.eye(n_dimension)\n",
    "random_state = 1 # 固定输出\n",
    "\n",
    "def es_objective(x):\n",
    "    return -objective(encode(x), data[:,:n_dimension], data[:,n_dimension])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "2021-07-11 16:14:51.616 | DEBUG    | __main__:NES:15 - {'dimension': 10, 'n_iter': 10, 'learn_rate': 0.002}\n",
      "iter: 0, best solution(bool): [True, True, False, True, True, True, False, False, False, True], best idxs: 0-1-3-4-5-9\n",
      "iter: 1, best solution(bool): [True, True, False, True, True, True, False, False, False, True], best idxs: 0-1-3-4-5-9\n",
      "iter: 2, best solution(bool): [True, True, False, True, True, True, False, False, False, True], best idxs: 0-1-3-4-5-9\n",
      "iter: 3, best solution(bool): [True, True, False, True, True, True, False, False, False, True], best idxs: 0-1-3-4-5-9\n",
      "iter: 4, best solution(bool): [True, True, False, True, True, True, False, False, False, True], best idxs: 0-1-3-4-5-9\n",
      "iter: 5, best solution(bool): [True, True, False, True, True, True, False, False, False, True], best idxs: 0-1-3-4-5-9\n",
      "iter: 6, best solution(bool): [True, True, True, True, False, True, True, True, True, False], best idxs: 0-1-2-3-5-6-7-8\n",
      "iter: 7, best solution(bool): [True, True, False, False, False, True, True, True, False, False], best idxs: 0-1-5-6-7\n",
      "iter: 8, best solution(bool): [True, True, False, False, False, True, True, True, False, False], best idxs: 0-1-5-6-7\n",
      "iter: 9, best solution(bool): [True, True, False, False, False, True, True, True, False, False], best idxs: 0-1-5-6-7\n"
     ]
    }
   ],
   "source": [
    "best, best_fitness = NES(n_dimension, es_objective, n_iter, learn_rate, lam, mean, cov, random_state, event_on_generation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "best solution(bool): [True, True, False, False, False, True, True, True, False, False], best idxs: 0-1-5-6-7\n维度缩减率 DR: 0.5\n分类准确率 CA: 0.9532710280373832\n"
     ]
    }
   ],
   "source": [
    "print('best solution(bool): {best}, best idxs: {idxs}'.format(best=encode(best), idxs='-'.join([str(i) for i, v in enumerate(encode(best)) if v])))\n",
    "print('维度缩减率 DR: {dr}'.format(dr=DR(encode(best))))\n",
    "print('分类准确率 CA: {ca}'.format(ca=CA(encode(best), data[:,:n_dimension], data[:,n_dimension])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 结论\n",
    "# 原先 10 个特征，经过基于 NES 的特征选择方法，特征数缩减至 5 个，同时准确率保持在 95% 以上"
   ]
  }
 ]
}