20190930 15일차 a (Linked list, Boolean model, Ranking model, VS model, TF-IDF).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linked-list 형태의 Posting\n",
    "- Inverted Index 사용\n",
    "    - Inverted index의 장점 -> 수정이 쉽다.\n",
    "- Posting 방식\n",
    "    - TDM에서 Document(postings)를 디스크에 따로 둔다. (메모리에 올리지 않아도 됨)\n",
    "        - FILE(각 문서) ----- V(Controled Vocabulary) : 둘을 분리 시킨다.\n",
    "\n",
    "    - **포인터** 개념으로 posting에 **효율적인 액세스** 구조\n",
    "- 아래 예제에서는 포인터의 개념만 이해하기 위해서 postings를 메모리에 올린 채로 실습한다. 디스크에 분리하는 방법은 나중에 또 실습할 것임."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from konlpy.corpus import kobill\n",
    "from konlpy.tag import Kkma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\JINHYO\\Anaconda3\\lib\\site-packages\\jpype\\_core.py:210: UserWarning: \n",
      "-------------------------------------------------------------------------------\n",
      "Deprecated: convertStrings was not specified when starting the JVM. The default\n",
      "behavior in JPype will be False starting in JPype 0.8. The recommended setting\n",
      "for new code is convertStrings=False.  The legacy value of True was assumed for\n",
      "this session. If you are a user of an application that reported this warning,\n",
      "please file a ticket with the developer.\n",
      "-------------------------------------------------------------------------------\n",
      "\n",
      "  \"\"\")\n"
     ]
    }
   ],
   "source": [
    "from collections import defaultdict\n",
    "\n",
    "Documents = list()\n",
    "\n",
    "kkma = Kkma()\n",
    "Lexicon = list() # Vocabulary를 Lexicon으로 바꿈. 동의어.\n",
    "\n",
    "t2i = lambda t:Lexicon.index(t)\n",
    "i2t = lambda t:Lexicon[t]\n",
    "\n",
    "d2i = lambda t:Documents.index(t)\n",
    "i2d = lambda t:Documents[t]\n",
    "\n",
    "Dicts = defaultdict(lambda: -1) # 최신 pointer 저장용\n",
    "Postings = list() # Documents에 대한 link를 저장함\n",
    "\n",
    "for document in [kobill.open(_).read()\n",
    "                 for _ in kobill.fileids()]:\n",
    "    Documents.append(document)\n",
    "    docID = d2i(document)\n",
    "    for term in [_ for _ in kkma.morphs(document)\n",
    "              if 1 < len(_) < 6]:\n",
    "        if term not in Lexicon:\n",
    "            Lexicon.append(term)\n",
    "            \n",
    "        ptr = Dicts[term] # pointer = next\n",
    "                          # term에 대한 최신 pointer를 가져옴.\n",
    "        termID = t2i(term)\n",
    "        postingPtr= len(Postings)\n",
    "        Postings.append((termID, docID, 1, ptr)) \n",
    "            # 원래 1 대신에 들어가야하는 것은 frequency이다.                     \n",
    "            # 지금은 boolean 모델이므로 term이 document에 있냐 없냐만 중요하다.\n",
    "            # Ranking model에서는 frequency가 필요하다.\n",
    "            # frequency 계산하는 실습은 뒤이어서 해볼 것이다.\n",
    "        Dicts[term] = postingPtr # 최신 pointer 업데이트"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1139, 10, 6438)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(Lexicon), len(Documents), Dicts[\"국민\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 8, 1, 6660)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Postings[Dicts[i2t(0)]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "인덱스, (termID, docID, freq, ptr)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[(5, (5, 0, 1, -1)),\n",
       " (14, (5, 0, 1, 5)),\n",
       " (560, (5, 0, 1, 14)),\n",
       " (888, (5, 1, 1, 560)),\n",
       " (897, (5, 1, 1, 888)),\n",
       " (1443, (5, 1, 1, 897)),\n",
       " (1771, (5, 2, 1, 1443)),\n",
       " (1780, (5, 2, 1, 1771)),\n",
       " (2482, (5, 2, 1, 1780)),\n",
       " (2816, (5, 3, 1, 2482)),\n",
       " (2825, (5, 3, 1, 2816)),\n",
       " (3375, (5, 3, 1, 2825)),\n",
       " (5143, (5, 6, 1, 3375)),\n",
       " (5146, (5, 6, 1, 5143)),\n",
       " (5157, (5, 6, 1, 5146))]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ptr는 Postings에서 자기 앞에 있는 자기와 같은 term의 위치를 나타낸다.\n",
    "# 아래 출력을 보면, 아래에서부터 ptr은 바로 위의 인덱스와 같다.\n",
    "\n",
    "print(\"인덱스, (termID, docID, freq, ptr)\")\n",
    "[(i, _) for i, _ in enumerate(Postings) if _[0]==5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Query: 지방 docID: 8 next: 6660\n",
      "Query: 지방 docID: 7 next: 3627\n",
      "Query: 지방 docID: 3 next: 3233\n",
      "Query: 지방 docID: 3 next: 3197\n",
      "Query: 지방 docID: 3 next: 3124\n",
      "Query: 지방 docID: 3 next: 3121\n",
      "Query: 지방 docID: 3 next: 2734\n",
      "Query: 지방 docID: 2 next: 2340\n",
      "Query: 지방 docID: 2 next: 2304\n",
      "Query: 지방 docID: 2 next: 2231\n",
      "Query: 지방 docID: 2 next: 2228\n",
      "Query: 지방 docID: 2 next: 1695\n",
      "Query: 지방 docID: 1 next: 1301\n",
      "Query: 지방 docID: 1 next: 1265\n",
      "Query: 지방 docID: 1 next: 1192\n",
      "Query: 지방 docID: 1 next: 1189\n",
      "Query: 지방 docID: 1 next: 812\n",
      "Query: 지방 docID: 0 next: 418\n",
      "Query: 지방 docID: 0 next: 382\n",
      "Query: 지방 docID: 0 next: 309\n",
      "Query: 지방 docID: 0 next: 306\n",
      "Query: 지방 docID: 0 next: 279\n",
      "Query: 지방 docID: 0 next: 78\n",
      "Query: 지방 docID: 0 next: 73\n",
      "Query: 지방 docID: 0 next: 0\n",
      "Query: 지방 docID: 0 next: -1\n"
     ]
    }
   ],
   "source": [
    "ptr = Dicts[i2t(0)] # 첫번째 pointer가 필요함.\n",
    "                    # Dicts는 가장 마지막 ptr를 가지고 있음.\n",
    "while ptr != -1: # ptr가 -1이면 마지막이다. \n",
    "    _struct = Postings[ptr]\n",
    "    print(\"Query:\", i2t(_struct[0]), \"docID:\", _struct[1], \"next:\", _struct[-1])\n",
    "    ptr = _struct[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 9, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 0, 0]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Query = \"법안 의원\"\n",
    "Result = list()\n",
    "for q in [_ for _ in kkma.morphs(Query)\n",
    "         if 1 < len(_) < 6]:\n",
    "    candidates = list()\n",
    "    ptr = Dicts[q]\n",
    "    while ptr != -1:\n",
    "        _struct = Postings[ptr]\n",
    "        candidates.append(_struct[1])\n",
    "        ptr = _struct[-1]\n",
    "    Result.append(candidates)\n",
    "candidates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### term frequency 포함해서 Posting하기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "Documents = list()\n",
    "\n",
    "kkma = Kkma()\n",
    "Lexicon = list()\n",
    "\n",
    "t2i = lambda t:Lexicon.index(t)\n",
    "i2t = lambda t:Lexicon[t]\n",
    "\n",
    "d2i = lambda t:Documents.index(t)\n",
    "i2d = lambda t:Documents[t]\n",
    "\n",
    "Dicts = defaultdict(lambda: -1)\n",
    "Postings = list()\n",
    "\n",
    "for docName in kobill.fileids():\n",
    "    document = kobill.open(docName).read()\n",
    "    Documents.append(docName)\n",
    "    docID = d2i(docName)\n",
    "    localPostings = defaultdict(int)\n",
    "    for term in [_ for _ in kkma.morphs(document)\n",
    "              if 1 < len(_) < 6]:\n",
    "        if term not in Lexicon:\n",
    "            Lexicon.append(term)\n",
    "        localPostings[term] += 1\n",
    "            \n",
    "    for term, freq in localPostings.items():\n",
    "        ptr = Dicts[term]\n",
    "        termID = t2i(term)\n",
    "        postingPtr= len(Postings)\n",
    "        Postings.append((termID, docID, freq, ptr)) # frequency 넣음\n",
    "        Dicts[term] = postingPtr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2390, (236, 9, 2, 1343))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Dicts[\"행정\"], Postings[2390]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 오늘 공부 내용\n",
    "- Day 1: Boolean and vector space model\n",
    "- http://www.cs.virginia.edu/~hw5x/Course/IR2015/_site/docs/PDFs/Boolean&VS%20model.pdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Boolean model\n",
    "- 문서 내에 query가 있냐 없냐로만 검색함. -> 모든 검색 결과를 제공한다.(순위가 없다)\n",
    "- 논리 연산자에 따라서 query 검색결과를 조합한다.\n",
    "    - AND: 교집합\n",
    "    - OR: 합집합\n",
    "    - NOT: 차집합\n",
    "- 단점: \n",
    "    - query가 너무 특이해서 검색결과가 없는 경우\n",
    "    - query가 너무 흔해서 검색결과가 너무 많은 경우\n",
    "    - 사용자가 query를 잘 써야함.(일반인에게 난이도가 높을 수 있음)\n",
    "    - 문서 중에 어느게 더 중요한지 순위를 매길 수 없음.\n",
    "- 전문적으로 해야하는 검색에서 사용함 \n",
    "    - 예) 법령 검색, 헌법 검색, 유사특허검색, 도서관 사서 등\n",
    "    \n",
    "- 한계:\n",
    "    - 사용자의 needs에 따라서 query는 다른 중요성을 갖는다.\n",
    "    - 모든 문서는 동등하게 중요할 수 없다.  \n",
    "        => 중요성은 정도의 문제이므로 0과 1로 구분할 수 없다. \n",
    "        \n",
    "        \n",
    "- 지금까지 실습했던 내용들은  Boolean model이었다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ranking model\n",
    "- Relevance\n",
    "    - 정도를 표현할 수 있다. -> 비교할 수 있다. -> 순위를 매길 수 있다.\n",
    "- Relevance 종류\n",
    "    - **Similarity** \\* 가장 사랑받는 녀석!\n",
    "        - Bag of Words 를 쓸 수 있다.(벡터로 표현 가능)\n",
    "    - Probability of Relevance\n",
    "        - Bag of Words를 쓸 수 없다(모든 문서는 동등하지 않다고 가정함.)\n",
    "    - Probabilistic inferenced\n",
    "        - Bag of Words를 쓸 수 없다(모든 문서는 동등하지 않다고 가정함.)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 벡터 공간 모델(VS Model, Vector Space Model)\n",
    "- Ranking model의 relevance를 similarity로 구한다.\n",
    "- Query와 documents는 같은 형식으로 표현할 수 있음을 가정한다.\n",
    "    - concept vector로 표현한다.\n",
    "    - 각 concept는 하나의 dimension을 정의한다.\n",
    "    - vector의 요소는 weight(가중치)이다.\n",
    "- concept space 내에서 query vector와 document vector 간의 거리로 유사도(similarity)를 구할 수 있다.\n"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 개념도\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 모든 vector는 Orthogonal해야한다.\n",
    "    - 모든 term은 independent해야 한다. \n",
    "    - N-gram, BOW(bag-of-words)를 쓸 수 있다.\n",
    "- weight를 산출하는 것은 중요하다.\n",
    "    - Query 측면: 모든 query term이 동일한 가치를 지니고 있지 않으므로 가중치가 필요\n",
    "    - Doc 측면: 어떠한 term은 콘텐츠에 대해서 더 많은 정보를 가지고 있으므로 가중치가 필요"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TF-IDF\n",
    "1. VS model의 heuristic한 concepts\n",
    "1. TF와 IDF를 결합하여 단어의 중요도를 수치로 표현한 것.\n",
    "2. **TF-IDF**는 모든 문서에서 자주 등장하는 단어는 중요도가 낮다고 판단하며, 특정 문서에서만 자주 등장하는 단어는 중요도가 높다고 판단합니다. 단어에 가중치를 매기는 방법입니다.\n",
    "\n",
    "3. TF-IDF는 zipf's law에 기반합니다.\n",
    "    - 빈도가 너무 많거나, 너무 적으면 가중치를 낮게 준다. => 중간 단어가 가중치가 높다.\n",
    "\n",
    "\n",
    "### TF(Term Frequecny)\n",
    "- 한 document 내에서 term이 등장하는 빈도\n",
    "- TF가 높다 => term의 중요도가 높다\n",
    "- 왜냐? 여러번 등장한다는 것은 해당 document의 main topic일 확률이 높기 때문이다.\n",
    "- 예시: (경제기사에서) 시황, 주가, 호황, 영업이익 / (의료분야에서) 간암, 메스, 수술, 회복\n",
    "- 다음과 같이 표현한다.\n",
    "$$\n",
    "tf(t,d)\n",
    "$$\n",
    "    \n",
    "    \n",
    "### IDF(Inverted Document Frequency)\n",
    "- 전체 document 중에서 term이 1번이라도 등장했던 document의 빈도(=DF) 의 역\n",
    "- DF가 높다 => term의 중요도가 낮다\n",
    "- IDF가 높다 => term의 중요도가 높다 (DF의 역이므로)\n",
    "- 왜냐? 많은 document에서 자주 쓰이는 term은 불용어일 확률이 높기 때문이다.\n",
    "- 예시: 나는, 습니다, 읍니다, I, am, a, the 등\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- IDF의 계산식 설명\n",
    "    - 단순히 Document Frequency의 역이라면 N/df(t)이어야하는데 아래와 같은 식이 나온 이유\n",
    "$$\n",
    "IDF(t) = log(\\frac{N}{df(t) + 1})\n",
    "$$\n",
    "    - log를 사용하는 이유: 전체 document의 갯수인 N이 커질수록 IDF의 값이 너무 커지는 것을 방지하기 위해서 사용함.\n",
    "    - df(t)에 1을 더하는 이유: t가 모든 document에서 등장하지 않아 0일때 나눗셈 에러를 대비한 스무딩 기법."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### tf-idf 실습 해봅시다!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TF(Term-Frequency)\n",
    "from math import log\n",
    "\n",
    "tf1 = lambda t: 1\n",
    "tf2 = lambda _struct: _struct[1]\n",
    "tf3 = lambda t:0\n",
    "tf4 = lambda _struct, t: log(1 + _struct[1])\n",
    "tf6 = lambda tf, maxtf, a:a+(1-a)*(tf/maxtf)\n",
    "tf5 = lambda tf, maxtf: tf6(tf, maxtf, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "_Collections = [\n",
    "    [\"A\", \"A\", \"A\",  \"A\", \"A\"],\n",
    "    [\"A\", \"A\", \"A\",  \"A\", \"B\"],\n",
    "    [\"A\", \"A\", \"A\",  \"A\", \"C\"],\n",
    "]\n",
    "\n",
    "_Vocabulary = [\"A\", \"B\", \"C\"]\n",
    "_Lexicon = defaultdict(lambda: -1)\n",
    "_Document = defaultdict(int)\n",
    "_Posting = list()\n",
    "\n",
    "for d in _Collections:\n",
    "    _localPosting = defaultdict(int)\n",
    "    for t in d:\n",
    "        if t not in _Vocabulary:\n",
    "            _Vocabulary.append(t)\n",
    "        _localPosting[t] += 1\n",
    "    docID = len(_Document)\n",
    "    _Document[docID] = max(_localPosting.values())\n",
    "    for t, f in _localPosting.items():\n",
    "        ptr = _Lexicon[t]\n",
    "        nextPtr = len(_Posting)\n",
    "        _Posting.append((docID, f, ptr)) \n",
    "        # 이번 실습에서는 termID를 빼고 _Posting에 저장하므로 헷갈리지 않도록 주의!\n",
    "        _Lexicon[t] = nextPtr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(defaultdict(<function __main__.<lambda>()>, {'A': 3, 'B': 2, 'C': 4}),\n",
       " defaultdict(int, {0: 5, 1: 4, 2: 4}),\n",
       " ['A', 'B', 'C'])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_Lexicon, _Document, _Vocabulary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 5, -1), (1, 4, 0), (1, 1, -1), (2, 4, 1), (2, 1, -1)]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_Posting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "단어:A, 문서:2, 빈도:4, 최고빈도:4\n",
      "단어:A, 문서:1, 빈도:4, 최고빈도:4\n",
      "단어:A, 문서:0, 빈도:5, 최고빈도:5\n",
      "단어:B, 문서:1, 빈도:1, 최고빈도:4\n",
      "단어:C, 문서:2, 빈도:1, 최고빈도:4\n"
     ]
    }
   ],
   "source": [
    "for t, ptr in _Lexicon.items():\n",
    "    while ptr != -1:\n",
    "        _struct = _Posting[ptr]\n",
    "        print(\"단어:{0}, 문서:{1}, 빈도:{2}, 최고빈도:{3}\"\n",
    "              .format(\n",
    "                  t, _struct[0], _struct[1],\n",
    "                  _Document[_struct[0]]))\n",
    "        ptr = _struct[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "단어:A, 문서:2, 빈도:4, 최고빈도:4\n",
      "TF1=1\n",
      "TF2=4\n",
      "TF4=1.6094379124341003\n",
      "TF5=1.0\n",
      "TF6=1.0\n",
      "\n",
      "단어:A, 문서:1, 빈도:4, 최고빈도:4\n",
      "TF1=1\n",
      "TF2=4\n",
      "TF4=1.6094379124341003\n",
      "TF5=1.0\n",
      "TF6=1.0\n",
      "\n",
      "단어:A, 문서:0, 빈도:5, 최고빈도:5\n",
      "TF1=1\n",
      "TF2=5\n",
      "TF4=1.791759469228055\n",
      "TF5=1.0\n",
      "TF6=1.0\n",
      "\n",
      "단어:B, 문서:1, 빈도:1, 최고빈도:4\n",
      "TF1=1\n",
      "TF2=1\n",
      "TF4=0.6931471805599453\n",
      "TF5=0.625\n",
      "TF6=0.25\n",
      "\n",
      "단어:C, 문서:2, 빈도:1, 최고빈도:4\n",
      "TF1=1\n",
      "TF2=1\n",
      "TF4=0.6931471805599453\n",
      "TF5=0.625\n",
      "TF6=0.25\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for t, ptr in _Lexicon.items():\n",
    "    while ptr != -1:\n",
    "        _struct = _Posting[ptr]\n",
    "        tf = _struct[1]\n",
    "        maxtf = _Document[_struct[0]]\n",
    "        print(\"단어:{0}, 문서:{1}, 빈도:{2}, 최고빈도:{3}\"\n",
    "              .format(\n",
    "                  t, _struct[0], tf, maxtf))\n",
    "        print(\"TF1={}\".format(tf1(t)))\n",
    "        print(\"TF2={}\".format(tf2(_struct)))\n",
    "        print(\"TF4={}\".format(tf4(_struct, t)))\n",
    "        print(\"TF5={}\".format(tf5(tf, maxtf)))\n",
    "        print(\"TF6={}\".format(tf6(tf, maxtf, 0)))\n",
    "        print()\n",
    "        ptr = _struct[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# IDF(Inversed Document Frequency)\n",
    "\n",
    "idf1 = lambda df, N:log(N/df) # inverse document frequency\n",
    "idf2 = lambda df, N:log(N/(1+df)) # inverse document frequency smooth\n",
    "idf3 = lambda df, N:log((1 + N-df)/df) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "단어:A, 문서:2, 빈도:4, 최고빈도:4\n",
      "TF1=1\n",
      "TF2=4\n",
      "TF4=1.6094379124341003\n",
      "TF5=1.0\n",
      "TF6=1.0\n",
      "IDF1=0.0\n",
      "IDF2=-0.2876820724517809\n",
      "IDF3=-1.0986122886681098\n",
      "0.0\n",
      "0.0\n",
      "\n",
      "단어:A, 문서:1, 빈도:4, 최고빈도:4\n",
      "TF1=1\n",
      "TF2=4\n",
      "TF4=1.6094379124341003\n",
      "TF5=1.0\n",
      "TF6=1.0\n",
      "IDF1=0.0\n",
      "IDF2=-0.2876820724517809\n",
      "IDF3=-1.0986122886681098\n",
      "0.0\n",
      "0.0\n",
      "\n",
      "단어:A, 문서:0, 빈도:5, 최고빈도:4\n",
      "TF1=1\n",
      "TF2=5\n",
      "TF4=1.791759469228055\n",
      "TF5=1.125\n",
      "TF6=1.25\n",
      "IDF1=0.0\n",
      "IDF2=-0.2876820724517809\n",
      "IDF3=-1.0986122886681098\n",
      "0.0\n",
      "0.0\n",
      "\n",
      "단어:B, 문서:1, 빈도:1, 최고빈도:4\n",
      "TF1=1\n",
      "TF2=1\n",
      "TF4=0.6931471805599453\n",
      "TF5=0.625\n",
      "TF6=0.25\n",
      "IDF1=1.0986122886681098\n",
      "IDF2=0.4054651081081644\n",
      "IDF3=1.0986122886681098\n",
      "0.27465307216702745\n",
      "0.6866326804175686\n",
      "\n",
      "단어:C, 문서:2, 빈도:1, 최고빈도:4\n",
      "TF1=1\n",
      "TF2=1\n",
      "TF4=0.6931471805599453\n",
      "TF5=0.625\n",
      "TF6=0.25\n",
      "IDF1=1.0986122886681098\n",
      "IDF2=0.4054651081081644\n",
      "IDF3=1.0986122886681098\n",
      "0.27465307216702745\n",
      "0.6866326804175686\n",
      "\n"
     ]
    }
   ],
   "source": [
    "N = len(_Collections)\n",
    "\n",
    "for t, ptr in _Lexicon.items():\n",
    "    dfPtr = ptr\n",
    "    df = 0\n",
    "    while dfPtr != -1:\n",
    "        _struct = _Posting[dfPtr]\n",
    "        dfPtr = _struct[-1]\n",
    "        df += 1\n",
    "    while ptr != -1:\n",
    "        _struct = _Posting[ptr]\n",
    "        tf = _struct[1]\n",
    "        print(\"단어:{0}, 문서:{1}, 빈도:{2}, 최고빈도:{3}\"\n",
    "              .format(\n",
    "                  t, _struct[0], _struct[1],\n",
    "                  maxtf))\n",
    "        print(\"TF1={}\".format(tf1(t)))\n",
    "        print(\"TF2={}\".format(tf2(_struct)))\n",
    "        print(\"TF4={}\".format(tf4(_struct, t)))\n",
    "        print(\"TF5={}\".format(tf5(tf, maxtf)))\n",
    "        print(\"TF6={}\".format(tf6(tf, maxtf, 0)))\n",
    "        print(\"IDF1={}\".format(idf1(df, N)))\n",
    "        print(\"IDF2={}\".format(idf2(df, N)))\n",
    "        print(\"IDF3={}\".format(idf3(df, N)))\n",
    "        print(tf6(tf, maxtf, 0)*idf1(df, N))\n",
    "        print(tf5(tf, maxtf)*idf1(df, N))\n",
    "        \n",
    "        print()\n",
    "        ptr = _struct[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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