{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compute Co-Occurence Matrix \n",
    "I always forget this trick that allow to compute a co-occurence matrix in every language easily. \n",
    "\n",
    "if we have a matrix in the shape `n_classes * m_examples` you can compute the co-occurence matrix for the classes my multiplying it by it's transpose."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example\n",
    "We have a matrix w with 3 classes and 5 examples ( each one validate a class or not ), the classes can be word and the examples can be texts where the column indicate for each of the 5 texts if they contain a given word or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "w = np.array([[0,1,0,0,0],[0,1,1,1,0],[1,0,0,0,0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 0, 0, 0],\n",
       "       [0, 1, 1, 1, 0],\n",
       "       [1, 0, 0, 0, 0]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "dot-multyplying by the transpose will give us the co-occurence matrix for each word, so the first row 2nd column number indicate the number of time `word 1` and `word 2` are in the same text. The diagonal is a simple count of the word in all the text ( here `word 2` appears 3 times in all the text ) and the matrix is obviously symetric by the diagonal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 0],\n",
       "       [1, 3, 0],\n",
       "       [0, 0, 1]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(w,w.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can also compute that for the examples, in this case we can see how many common words 2 texts share"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0, 0],\n",
       "       [0, 2, 1, 1, 0],\n",
       "       [0, 1, 1, 1, 0],\n",
       "       [0, 1, 1, 1, 0],\n",
       "       [0, 0, 0, 0, 0]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(w.T,w)"
   ]
  }
 ],
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