longterm_citation.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "807145ed-a1d3-469f-969f-3c405b4c6b7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.optimize import curve_fit\n",
    "from scipy.stats import norm\n",
    "\n",
    "import requests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "485001f6-cecb-4a7a-85b1-2606b5679c95",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import mpl\n",
    "\n",
    "# 对中文字体的支持\n",
    "mpl.rcParams['font.sans-serif'] = ['SimHei'] \n",
    "mpl.rcParams['axes.unicode_minus'] = False "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "191ff660-2ba2-4d61-8021-26d7967afbbf",
   "metadata": {},
   "source": [
    "## 1. rawdata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f9c998d6-3f16-4677-acad-a06d31757bd9",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_excel('data/network_paper_rank.xlsx',index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "57033064-7d0b-4a07-a41b-82269d2d5717",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28, 5)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e8504e63-8e8c-483b-a025-65440f0a5501",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>link</th>\n",
       "      <th>title</th>\n",
       "      <th>abstract</th>\n",
       "      <th>doi</th>\n",
       "      <th>year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>http://www.sciencedirect.com/science/article/a...</td>\n",
       "      <td>Sequential dynamics of complex networks in min...</td>\n",
       "      <td>Today, based on brain imaging analyses, we can...</td>\n",
       "      <td>10.1016/j.physrep.2020.08.003</td>\n",
       "      <td>2020</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 link  \\\n",
       "17  http://www.sciencedirect.com/science/article/a...   \n",
       "\n",
       "                                                title  \\\n",
       "17  Sequential dynamics of complex networks in min...   \n",
       "\n",
       "                                             abstract  \\\n",
       "17  Today, based on brain imaging analyses, we can...   \n",
       "\n",
       "                              doi  year  \n",
       "17  10.1016/j.physrep.2020.08.003  2020  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.sample()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e9a584a-586a-40ca-b04d-88b1dc20ef41",
   "metadata": {},
   "source": [
    "## 2.get citation from semantic scholar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9c5efb22-df7e-4e90-9ab4-3279b3b3c426",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_full_record(doi,offset=0,limit=1000):\n",
    "    url = f'https://api.semanticscholar.org/graph/v1/paper/DOI:{doi}'\\\n",
    "            f'/citations?fields=year,citationCount,fieldsOfStudy&offset={offset}&limit={limit}'\n",
    "    response = requests.get(url)\n",
    "    rst = response.json()\n",
    "    while len(response.json()['data'])==1000:\n",
    "        offset += 1000\n",
    "        url = f'https://api.semanticscholar.org/graph/v1/paper/DOI:{doi}'\\\n",
    "        f'/citations?fields=year,citationCount,fieldsOfStudy&offset={offset}&limit={limit}'\n",
    "        response  = requests.get(url)\n",
    "        rst['data'].extend(response.json()['data'])\n",
    "    return rst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "251d37ea-5ccd-4cba-abf4-52e1e7c7ba3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "lyst1 = []\n",
    "lyst2 = []\n",
    "for i in range(len(df)):\n",
    "    doi = df.loc[i,'doi']\n",
    "    rst = get_full_record(doi)\n",
    "    #print(f\"论文名:{df.loc[i,'title']},被引量{len(rst['data'])}\")\n",
    "    lyst1.append(len(rst['data']))\n",
    "    lyst2.append(rst)\n",
    "    \n",
    "df.loc[:,'citation_ss'] = lyst1\n",
    "df.loc[:,'citation_per_year'] = lyst2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6eab141f-74c4-48ec-baf0-e200beb86ffe",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>link</th>\n",
       "      <th>title</th>\n",
       "      <th>abstract</th>\n",
       "      <th>doi</th>\n",
       "      <th>year</th>\n",
       "      <th>citation_ss</th>\n",
       "      <th>citation_per_year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>http://www.sciencedirect.com/science/article/a...</td>\n",
       "      <td>The structure and dynamics of multilayer networks</td>\n",
       "      <td>In the past years, network theory has successf...</td>\n",
       "      <td>10.1016/j.physrep.2014.07.001</td>\n",
       "      <td>2014</td>\n",
       "      <td>60</td>\n",
       "      <td>{'offset': 0, 'data': [{'citingPaper': {'paper...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                 link  \\\n",
       "15  http://www.sciencedirect.com/science/article/a...   \n",
       "\n",
       "                                                title  \\\n",
       "15  The structure and dynamics of multilayer networks   \n",
       "\n",
       "                                             abstract  \\\n",
       "15  In the past years, network theory has successf...   \n",
       "\n",
       "                              doi  year  citation_ss  \\\n",
       "15  10.1016/j.physrep.2014.07.001  2014           60   \n",
       "\n",
       "                                    citation_per_year  \n",
       "15  {'offset': 0, 'data': [{'citingPaper': {'paper...  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.sample()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "5c6aad3f-61ca-4241-af05-0a1e7ae2845a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# #an offline version due 2020.03.16\n",
    "# df = pd.read_json('data/PR_network_science_paper.json',lines=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fbeeeb3-e173-4eef-9338-e2b5d8c1a7f0",
   "metadata": {},
   "source": [
    "## 3. longterm citation prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2ef39034-15c2-4d30-93a9-13f3d27bbf23",
   "metadata": {},
   "outputs": [],
   "source": [
    "# fit function\n",
    "\n",
    "# M measures the average number of references each new paper contains\n",
    "M = 20\n",
    "def fi(x):\n",
    "    return norm.cdf(x)\n",
    "\n",
    "def func(x,lam,u,sigma):\n",
    "    return M*(np.exp(lam*fi((np.log(x) - u)/sigma))-1)\n",
    "\n",
    "def infinite_citation(lam):\n",
    "    return M*(np.exp(lam) - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "45cacbcc-758d-4b31-86e0-34119083d159",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>link</th>\n",
       "      <th>title</th>\n",
       "      <th>abstract</th>\n",
       "      <th>doi</th>\n",
       "      <th>year</th>\n",
       "      <th>citation_ss</th>\n",
       "      <th>citation_per_year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>http://www.sciencedirect.com/science/article/a...</td>\n",
       "      <td>Complex systems: Features, similarity and conn...</td>\n",
       "      <td>The increasing interest in complex networks re...</td>\n",
       "      <td>10.1016/j.physrep.2020.03.002</td>\n",
       "      <td>2020</td>\n",
       "      <td>24</td>\n",
       "      <td>{'offset': 0, 'data': [{'citingPaper': {'paper...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                link  \\\n",
       "9  http://www.sciencedirect.com/science/article/a...   \n",
       "\n",
       "                                               title  \\\n",
       "9  Complex systems: Features, similarity and conn...   \n",
       "\n",
       "                                            abstract  \\\n",
       "9  The increasing interest in complex networks re...   \n",
       "\n",
       "                             doi  year  citation_ss  \\\n",
       "9  10.1016/j.physrep.2020.03.002  2020           24   \n",
       "\n",
       "                                   citation_per_year  \n",
       "9  {'offset': 0, 'data': [{'citingPaper': {'paper...  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.sample()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c9967784-676d-454d-bcfb-c44206282dfc",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>The Kuramoto model in complex networks</td>\n",
       "      <td>2015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Fundamentals of spreading processes in single ...</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Vital nodes identification in complex networks</td>\n",
       "      <td>2016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Nestedness in complex networks: Observation, e...</td>\n",
       "      <td>2019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Network dynamics of coupled oscillators and ph...</td>\n",
       "      <td>2019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Networks beyond pairwise interactions: Structu...</td>\n",
       "      <td>2020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Computational network biology: Data, models, a...</td>\n",
       "      <td>2019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Ranking in evolving complex networks</td>\n",
       "      <td>2017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Community detection in networks: A user guide</td>\n",
       "      <td>2016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Complex systems: Features, similarity and conn...</td>\n",
       "      <td>2020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Coevolution spreading in complex networks</td>\n",
       "      <td>2019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Recent advances in percolation theory and its ...</td>\n",
       "      <td>2015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>The physics of communicability in complex netw...</td>\n",
       "      <td>2012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Complex network approaches to nonlinear time s...</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Markovian dynamics on complex reaction networks</td>\n",
       "      <td>2013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>The structure and dynamics of multilayer networks</td>\n",
       "      <td>2014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Reconstruction methods for networks: The case ...</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Sequential dynamics of complex networks in min...</td>\n",
       "      <td>2020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Clustering and community detection in directed...</td>\n",
       "      <td>2013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Spatial networks</td>\n",
       "      <td>2010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Structure-oriented prediction in complex networks</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>Explosive transitions in complex networks’ str...</td>\n",
       "      <td>2016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>Dynamics of information diffusion and its appl...</td>\n",
       "      <td>2016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>The science of science: From the perspective o...</td>\n",
       "      <td>2017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Random walks and diffusion on networks</td>\n",
       "      <td>2017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>Combining complex networks and data mining: Wh...</td>\n",
       "      <td>2016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>Continuous-time quantum walks: Models for cohe...</td>\n",
       "      <td>2011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>Temporal networks</td>\n",
       "      <td>2012</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                title  year\n",
       "0              The Kuramoto model in complex networks  2015\n",
       "1   Fundamentals of spreading processes in single ...  2018\n",
       "2      Vital nodes identification in complex networks  2016\n",
       "3   Nestedness in complex networks: Observation, e...  2019\n",
       "4   Network dynamics of coupled oscillators and ph...  2019\n",
       "5   Networks beyond pairwise interactions: Structu...  2020\n",
       "6   Computational network biology: Data, models, a...  2019\n",
       "7                Ranking in evolving complex networks  2017\n",
       "8       Community detection in networks: A user guide  2016\n",
       "9   Complex systems: Features, similarity and conn...  2020\n",
       "10          Coevolution spreading in complex networks  2019\n",
       "11  Recent advances in percolation theory and its ...  2015\n",
       "12  The physics of communicability in complex netw...  2012\n",
       "13  Complex network approaches to nonlinear time s...  2018\n",
       "14    Markovian dynamics on complex reaction networks  2013\n",
       "15  The structure and dynamics of multilayer networks  2014\n",
       "16  Reconstruction methods for networks: The case ...  2018\n",
       "17  Sequential dynamics of complex networks in min...  2020\n",
       "18  Clustering and community detection in directed...  2013\n",
       "19                                   Spatial networks  2010\n",
       "20  Structure-oriented prediction in complex networks  2018\n",
       "21  Explosive transitions in complex networks’ str...  2016\n",
       "22  Dynamics of information diffusion and its appl...  2016\n",
       "23  The science of science: From the perspective o...  2017\n",
       "24             Random walks and diffusion on networks  2017\n",
       "25  Combining complex networks and data mining: Wh...  2016\n",
       "26  Continuous-time quantum walks: Models for cohe...  2011\n",
       "27                                  Temporal networks  2012"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.reset_index(drop=True)\n",
    "df[['title','year']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "15b46c91-9643-44a2-998f-fd5f9dfe3876",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "F:\\Anaconda\\envs\\AI\\lib\\site-packages\\scipy\\optimize\\minpack.py:828: OptimizeWarning: Covariance of the parameters could not be estimated\n",
      "  warnings.warn('Covariance of the parameters could not be estimated',\n"
     ]
    }
   ],
   "source": [
    "for idx,row in df.iterrows():\n",
    "    nums = {}\n",
    "    for item in  df.loc[idx,'citation_per_year']['data']:\n",
    "        if item['citingPaper']['year']:\n",
    "            nums[item['citingPaper']['year']] = nums.setdefault(item['citingPaper']['year'],0) + 1\n",
    "    \n",
    "    nums = {k:v for k,v in nums.items() if k >= df.loc[idx,'year']}\n",
    "    x = np.arange(min(nums),2022)\n",
    "    y = [nums[l] if l in nums else 0 for l in x]\n",
    "    \n",
    "    x = np.arange(1,2022-min(nums)+1)\n",
    "    y_cumsum = np.cumsum(y)\n",
    "#     print('title:',df.loc[idx,'title'])\n",
    "#     print('citation per year:',nums)\n",
    "#     print('x:',x)\n",
    "#     print('y:',y)\n",
    "#     print('y_cumsum:',y_cumsum)\n",
    "    \n",
    "    # at least 3 data points needed\n",
    "    if len(x)>2:\n",
    "        coes,cov = curve_fit(func,x,y_cumsum)\n",
    "        #print('lambda,u,sigma:',coes)\n",
    "        lam = coes[0]\n",
    "        final = infinite_citation(lam)\n",
    "        #print('final:',final)\n",
    "        df.loc[idx,'infinite_citation'] = final\n",
    "    df.loc[idx,'first_two_year_citation'] = y[0]+y[1]\n",
    "    #print('\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "46021426-e4d7-470b-a7e8-dcbda0cec6fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "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>link</th>\n",
       "      <th>title</th>\n",
       "      <th>abstract</th>\n",
       "      <th>doi</th>\n",
       "      <th>year</th>\n",
       "      <th>citation_ss</th>\n",
       "      <th>citation_per_year</th>\n",
       "      <th>infinite_citation</th>\n",
       "      <th>first_two_year_citation</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>http://www.sciencedirect.com/science/article/p...</td>\n",
       "      <td>Nestedness in complex networks: Observation, e...</td>\n",
       "      <td>The observed architecture of ecological and so...</td>\n",
       "      <td>10.1016/j.physrep.2019.04.001</td>\n",
       "      <td>2019</td>\n",
       "      <td>64</td>\n",
       "      <td>{'offset': 0, 'data': [{'citingPaper': {'paper...</td>\n",
       "      <td>100.121944</td>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                link  \\\n",
       "3  http://www.sciencedirect.com/science/article/p...   \n",
       "\n",
       "                                               title  \\\n",
       "3  Nestedness in complex networks: Observation, e...   \n",
       "\n",
       "                                            abstract  \\\n",
       "3  The observed architecture of ecological and so...   \n",
       "\n",
       "                             doi  year  citation_ss  \\\n",
       "3  10.1016/j.physrep.2019.04.001  2019           64   \n",
       "\n",
       "                                   citation_per_year  infinite_citation  \\\n",
       "3  {'offset': 0, 'data': [{'citingPaper': {'paper...         100.121944   \n",
       "\n",
       "   first_two_year_citation  \n",
       "3                     31.0  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# infinite_citation column added\n",
    "df.sample()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3b337973-c153-4819-a6e9-3674e19fdcee",
   "metadata": {},
   "outputs": [],
   "source": [
    "# paper with num of data points < 3\n",
    "ratio = 0\n",
    "i = 0\n",
    "for idx,row in df.iterrows():\n",
    "    if not np.isnan(row['infinite_citation']):\n",
    "        ratio += row['infinite_citation']/row['first_two_year_citation']\n",
    "        i += 1\n",
    "        \n",
    "ave_ratio =  ratio/i\n",
    "\n",
    "for idx,row in df.iterrows():\n",
    "    if np.isnan(row['infinite_citation']):\n",
    "        df.loc[idx,'infinite_citation'] = df.loc[idx,'first_two_year_citation']*ave_ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "83220b75-b7b7-439d-98e7-c16f77b5513f",
   "metadata": {},
   "outputs": [],
   "source": [
    "df[['title','year','infinite_citation']].to_csv('rst.csv',index=0,encoding='utf-8')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ded4b132-d0a0-4220-8d7c-b128f63d8fe5",
   "metadata": {},
   "source": [
    "## 4. case "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "7405c592-1f33-4fc4-a51e-9a65ad234b39",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_longterm_citation(x,y,func,coes):\n",
    "    X = np.arange(1,50)\n",
    "    plt.figure(figsize=(9,6))\n",
    "    plt.plot(x,y,'*',label='record')\n",
    "    plt.plot(X,func(X,coes[0],coes[1],coes[2]),alpha=0.5,label='predict')\n",
    "    plt.xlabel('year',fontsize=15)\n",
    "    plt.ylabel('citation',fontsize=15)\n",
    "    plt.legend(fontsize=15)\n",
    "    return "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "5215fee2-2b39-4d9b-a94a-3996ec9c8b29",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "title: Random walks and diffusion on networks\n",
      "lambda,mu,sigma: [3.78575064 0.93611564 0.91744462]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = 24\n",
    "nums = {}\n",
    "for item in  df.loc[idx,'citation_per_year']['data']:\n",
    "    if item['citingPaper']['year']:\n",
    "        nums[item['citingPaper']['year']] = nums.setdefault(item['citingPaper']['year'],0) + 1\n",
    "\n",
    "nums = {k:v for k,v in nums.items() if k >= df.loc[idx,'year']}\n",
    "x = np.arange(min(nums),2022)\n",
    "y = [nums[l] if l in nums else 0 for l in x]\n",
    "\n",
    "x = np.arange(1,2022-min(nums)+1)\n",
    "y_cumsum = np.cumsum(y)\n",
    "\n",
    "coes,cov = curve_fit(func,x,y_cumsum)\n",
    "print('title:',df.loc[idx,'title'])\n",
    "print(\"lambda,mu,sigma:\",coes)\n",
    "\n",
    "plot_longterm_citation(x,y_cumsum,func,coes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "75381f24-f3f6-4d2b-a9c1-4b723025fcde",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "title: The physics of communicability in complex networks\n",
      "lambda,mu,sigma: [3.75086062 1.66099763 1.43512322]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# case: longterm citaion is much greater than current citation\n",
    "idx = 12\n",
    "nums = {}\n",
    "for item in  df.loc[idx,'citation_per_year']['data']:\n",
    "    if item['citingPaper']['year']:\n",
    "        nums[item['citingPaper']['year']] = nums.setdefault(item['citingPaper']['year'],0) + 1\n",
    "\n",
    "nums = {k:v for k,v in nums.items() if k >= df.loc[idx,'year']}\n",
    "x = np.arange(min(nums),2022)\n",
    "y = [nums[l] if l in nums else 0 for l in x]\n",
    "\n",
    "x = np.arange(1,2022-min(nums)+1)\n",
    "y_cumsum = np.cumsum(y)\n",
    "\n",
    "coes,cov = curve_fit(func,x,y_cumsum)\n",
    "print('title:',df.loc[idx,'title'])\n",
    "print(\"lambda,mu,sigma:\",coes)\n",
    "\n",
    "plot_longterm_citation(x,y_cumsum,func,coes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "5986e913-95fd-4019-8f87-4d64ccbb59cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "F:\\Anaconda\\envs\\AI\\lib\\site-packages\\scipy\\optimize\\minpack.py:828: OptimizeWarning: Covariance of the parameters could not be estimated\n",
      "  warnings.warn('Covariance of the parameters could not be estimated',\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "title: Complex network approaches to nonlinear time series analysis\n",
      "lambda,mu,sigma: [1.89711999 0.41653215 0.037221  ]\n",
      "cov: [[inf inf inf]\n",
      " [inf inf inf]\n",
      " [inf inf inf]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# in a few cases,scipy can not fit data well\n",
    "# example as below, notice the warnings and cov matrix\n",
    "# some other tool may help, see in longterm_citation_wl.ipynb\n",
    "\n",
    "idx = 13\n",
    "nums = {}\n",
    "for item in  df.loc[idx,'citation_per_year']['data']:\n",
    "    if item['citingPaper']['year']:\n",
    "        nums[item['citingPaper']['year']] = nums.setdefault(item['citingPaper']['year'],0) + 1\n",
    "\n",
    "nums = {k:v for k,v in nums.items() if k >= df.loc[idx,'year']}\n",
    "x = np.arange(min(nums),2022)\n",
    "y = [nums[l] if l in nums else 0 for l in x]\n",
    "\n",
    "x = np.arange(1,2022-min(nums)+1)\n",
    "y_cumsum = np.cumsum(y)\n",
    "\n",
    "coes,cov = curve_fit(func,x,y_cumsum)\n",
    "print('title:',df.loc[idx,'title'])\n",
    "print(\"lambda,mu,sigma:\",coes)\n",
    "print('cov:',cov)\n",
    "\n",
    "plot_longterm_citation(x,y_cumsum,func,coes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "86d21d13-962e-4641-b204-42512c47d478",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "AI",
   "language": "python",
   "name": "ai"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}