Matrix completion on graphs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrix completion on graphs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We try and implement a matrix recovery model with a simulated Netflix-like dataset. The aim is to model a simple recommender system on netflix. Given a fixed percentage of observations on the matrix  users/movies, we want to recover all the values i.e the rating on each movie for each user. \n",
    "\n",
    "The original problem lies on the hypothesis -often verified in practixe- that a such users/movies matrix has a low rank.\n",
    "\n",
    "\n",
    "Given a sparse set $\\Omega$ of observations $M_ij : (i,j) \\in \\Omega \\subseteq \\{1,\\cdots,n\\}*\\{1,\\cdots,m\\}$. We want to find:\n",
    "\n",
    "$\\displaystyle \\min_{X \\in \\mathbb{R}^{m*n}} ||X||_{*}$ s.t $. \\mathcal{A}_{\\Omega}(X)=\\mathcal{A}_{\\Omega}(M)$\n",
    "\n",
    "where $||X||_{*}$ is defined as the classical nuclear norm.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By taking advantage of common caracteristics about users and movies, we can improve the original problem of matrix completation. The [paper](https://arxiv.org/pdf/1408.1717.pdf) suggests the use of graph representation to handle this extra information. This notebook follows their experiments and shows the improvements over the original method to some extent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A syntetic example of Netflix problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "import pandas as pd\n",
    "from itertools import *\n",
    "import collections\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from cvxpy import *\n",
    "import networkx as nx\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let assume known information about users and movies, like age or sex, movies categories (War,Comedy, cartoons) or release date.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "genre      Ca          Wa          Co      \n",
      "release >2000 <1980 >2000 <1980 >2000 <1980\n",
      "age sex                                    \n",
      "<20 W       3     2     4     3     1     3\n",
      "    M       2     1     3     2     2     5\n",
      ">50 W       2     5     2     4     1     2\n",
      "    M       1     4     1     2     5     3\n"
     ]
    }
   ],
   "source": [
    "category = {'users' : {'sex' :['W','M'],\n",
    "                     'age' :['<20','>50']},\n",
    "\n",
    "            'movies' : {'genre':['Ca','Wa','Co'],\n",
    "                      'release':['>2000','<1980']}\n",
    "            }\n",
    "            \n",
    "tuplesU = list(product(*category['users'].values()))\n",
    "tuplesM = list(product(*category['movies'].values()))\n",
    "\n",
    "index = pd.MultiIndex.from_tuples(tuplesU, \n",
    "                                    names=category['users'].keys())\n",
    "columns = pd.MultiIndex.from_tuples(tuplesM, \n",
    "                                  names=category['movies'].keys())\n",
    "\n",
    "scores = [[3,2,4,3,1,3],[2,1,3,2,2,5],[2,5,2,4,1,2],[1,4,1,2,5,3]]\n",
    "# buid table of scores by groups\n",
    "scoresGroup = pd.DataFrame(index=index,columns=columns,data = scores)\n",
    "print(scoresGroup)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The table above gives rating for each category. For instance, a young boy is likely to like a recent war movie and dislike a comedy. This table of score is arbitrary and provides a toy example of a more real case."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have to populate the users/movies matrix UM, according to the score matrix\n",
    "- We define 10 to 12 individus in each group, namely the group of old men, old women, young boys and young girls \n",
    "- For movies, there is 6 groups made up 6 to 8 movies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nbU = np.random.randint(10,12,len(tuplesU))\n",
    "nbM = np.random.randint(6,8,len(tuplesM))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code below build the UM matrix, and shuffle rows and columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "genre            Wa          Ca    Wa    Ca    Wa          Co    Ca    Wa  \\\n",
      "release       <1980 >2000 >2000 >2000 >2000 >2000 <1980 >2000 >2000 >2000   \n",
      "movies           20    13    1     15    5     18    21    31    0     19   \n",
      "age sex users                                                               \n",
      "<20 M   13        2     3     2     3     2     3     2     2     2     3   \n",
      ">50 M   41        2     1     1     1     1     1     2     5     1     1   \n",
      "        39        2     1     1     1     1     1     2     5     1     1   \n",
      "        37        2     1     1     1     1     1     2     5     1     1   \n",
      "    W   27        4     2     2     2     2     2     4     1     2     2   \n",
      "\n",
      "genre          ...     Ca       Co       Ca             Co    Ca  \n",
      "release        ...  >2000    <1980    <1980          >2000 <1980  \n",
      "movies         ...     3  4     36 39    7  6  9  8     30    12  \n",
      "age sex users  ...                                                \n",
      "<20 M   13     ...      2  2     5  5     1  1  1  1     2     1  \n",
      ">50 M   41     ...      1  1     3  3     4  4  4  4     5     4  \n",
      "        39     ...      1  1     3  3     4  4  4  4     5     4  \n",
      "        37     ...      1  1     3  3     4  4  4  4     5     4  \n",
      "    W   27     ...      2  2     2  2     5  5  5  5     1     5  \n",
      "\n",
      "[5 rows x 40 columns]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\KD5299\\AppData\\Local\\Continuum\\Anaconda2\\lib\\site-packages\\IPython\\core\\interactiveshell.py:2723: PerformanceWarning: indexing past lexsort depth may impact performance.\n",
      "  interactivity=interactivity, compiler=compiler, result=result)\n"
     ]
    }
   ],
   "source": [
    "# buid columns and index with hierachical level\n",
    "def build_individus(name,nbInd):\n",
    "    tuplesInd = list(product(*category[name].values()))\n",
    "    u = []\n",
    "    it=0\n",
    "    for g,n in zip(tuplesInd,nbInd):\n",
    "        u+=[g+ (i,) for i in range(it,it+n)]\n",
    "        it +=n\n",
    "    index =  pd.MultiIndex.from_tuples(u, \n",
    "                                        names=list(category[name].keys())+[name])\n",
    "    return index\n",
    "\n",
    "# Mtrice Users/Movies creation  \n",
    "def build_matriceUM(nbU,nbM):\n",
    "    A = pd.DataFrame(index=    build_individus('users',nbU),\n",
    "                 columns = build_individus('movies',nbM))\n",
    "    # fill the matrix according to scoresGroup\n",
    "    for blockM,blockU in product(tuplesM,tuplesU):\n",
    "        A.loc[blockU,blockM] = scoresGroup.ix[blockU].ix[blockM]\n",
    "    # shuffle lign and columns\n",
    "    A = A.sample(frac=1,axis=0)\n",
    "    A = A.sample(frac=1,axis=1)\n",
    "    return A\n",
    "    \n",
    "UM = build_matriceUM(nbU,nbM)\n",
    "print(UM.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The matrix of weights, for movies and users have to be created, according to group caracteristics.\n",
    "\n",
    "By instance, two young girls are linked in users matrix of weight by a 1. \n",
    "\n",
    "A recent war movie and old one do not belong to the same group and a 0 will be add in the movies matrix weight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "genre                   Wa          Ca    Wa    Ca    Wa          Co    Ca  \\\n",
      "release              <1980 >2000 >2000 >2000 >2000 >2000 <1980 >2000 >2000   \n",
      "movies                  20    13    1     15    5     18    21    31    0    \n",
      "genre release movies                                                         \n",
      "Wa    <1980   20         1     0     0     0     0     0     1     0     0   \n",
      "      >2000   13         0     1     0     1     0     1     0     0     0   \n",
      "Ca    >2000   1          0     0     1     0     1     0     0     0     1   \n",
      "Wa    >2000   15         0     1     0     1     0     1     0     0     0   \n",
      "Ca    >2000   5          0     0     1     0     1     0     0     0     1   \n",
      "\n",
      "genre                   Wa  ...     Ca       Co       Ca             Co    Ca  \n",
      "release              >2000  ...  >2000    <1980    <1980          >2000 <1980  \n",
      "movies                  19  ...     3  4     36 39    7  6  9  8     30    12  \n",
      "genre release movies        ...                                                \n",
      "Wa    <1980   20         0  ...      0  0     0  0     0  0  0  0     0     0  \n",
      "      >2000   13         1  ...      0  0     0  0     0  0  0  0     0     0  \n",
      "Ca    >2000   1          0  ...      1  1     0  0     0  0  0  0     0     0  \n",
      "Wa    >2000   15         1  ...      0  0     0  0     0  0  0  0     0     0  \n",
      "Ca    >2000   5          0  ...      1  1     0  0     0  0  0  0     0     0  \n",
      "\n",
      "[5 rows x 40 columns]\n"
     ]
    }
   ],
   "source": [
    "# Create matrix of weigths\n",
    "def build_weight(index,group):\n",
    "    Weight = pd.DataFrame(index = index,columns=index,data=0)\n",
    "    for row,col in zip(group,group):\n",
    "        Weight.loc[row,col]= 1 #nbOfCommonFeature\n",
    "    return Weight\n",
    "\n",
    "WeightU = build_weight(UM.index,tuplesU)\n",
    "WeightM = build_weight(UM.columns,tuplesM)\n",
    "print(WeightM.head())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize graph of individus for instance with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_graph(Weight,level='users'):\n",
    "    G=nx.Graph()\n",
    "    # for all combinations between users, update weight graphs\n",
    "    for tupleEdge in combinations(Weight.index.get_level_values(level),2):\n",
    "        weight = Weight.xs(tupleEdge[0], level='users', axis=0).xs(tupleEdge[1], level=level, axis=1).values\n",
    "        G.add_edge(*tupleEdge,weight=weight)\n",
    "    # \n",
    "    elarge=[(a,b) for (a,b,d) in G.edges(data=True) if d['weight'] ==1]\n",
    "    pos=nx.spring_layout(G) # positions for all nodes\n",
    "    # nodes\n",
    "    nx.draw_networkx_nodes(G,pos,node_size=700)\n",
    "    # edges\n",
    "    nx.draw_networkx_edges(G,pos,edgelist=elarge,\n",
    "                        width=1)\n",
    "    nx.draw_networkx_labels(G,pos,font_size=20,font_family='sans-serif')\n",
    "    plt.axis('off')\n",
    "    plt.show() # display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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T7nsSmawKqiJZrrVQvggwtj00Fkkgih1Cy1wnYVkN9lv46R6mItGQZyLpIP7s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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x28d683c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_graph(WeightU,'users')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let assume that we have partial measurements of $UM$. Some users have scored some movies, but UM entries has a lot of empty spaces. Let us observe **5%** for the next examples of the $UM$ matrix. The goal is now to rebuild it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We observe 5.11904761905 per cent of the entries of a 42*40 matrix\n"
     ]
    }
   ],
   "source": [
    "def mask(u, v, proportion = 0.3):\n",
    "    mat_mask = np.random.binomial(1, proportion, size =  (u, v))\n",
    "    print(\"We observe {} per cent of the entries of a {}*{} matrix\".format(100 * mat_mask.mean(),u, v))\n",
    "    return mat_mask\n",
    "\n",
    "mat_mask = mask(*UM.shape,proportion=0.05)\n",
    "UM_mask = mat_mask*UM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let us recall the original problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The matrix of weights are not used here, so we want to find : \n",
    "$\\displaystyle \\min_{X \\in \\mathbb{R}^{m*n}} ||X||_{*}$ s.t $. \\mathcal{A}_{\\Omega}(X)=\\mathcal{A}_{\\Omega}(M)$\n",
    "\n",
    "The library CVXPY provide user-friendly tools to define this problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = Variable(*UM.shape)\n",
    "obj = Minimize(norm(X, 'nuc') )  # norm nuclear: hypotesis of low rank\n",
    "constraints = [mul_elemwise(mat_mask, X) == mul_elemwise(mat_mask, np.array(UM))]\n",
    "prob = Problem(obj, constraints)\n",
    "prob.solve(solver=SCS)\n",
    "UM_rebuild = pd.DataFrame(index = UM.index,columns=UM.columns,data=X.value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def rmse(A,B):\n",
    "    rmse = ((A-B).values**2).mean()\n",
    "    print(\"RMSE: %.2f\" %rmse)\n",
    "    return rmse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The RMSE of the recovered solution can be find:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE: 6.68\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "6.680457170479519"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rmse(UM,UM_rebuild)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### With the information of similar rating over groups:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, by putting aside low rank hypothesis, the intuition is to force two different vectors of users noted $x_{i}$ and $x_{i'}$ to be closed when their respective link $w_{ii'}^{u}$ are not zero. $w_{ii'}^{u}$ is the entries of the matrix of weight for users $W^{c}$.  Namely, we want to find $X \\in \\mathbb{R}^{m*n}$ minimizing ;\n",
    "\n",
    "$\\sum\\limits_{i,i'} w_{ii'}^{u}||x_{i}-x_{i'}||_{2}^{2} = tr(XL_{u}X^t) =  ||X||^2_{\\mathcal{D},u} $\n",
    "\n",
    "We then define  positive semidefinite matrix $L^{u}$ defined as $D^{u}-W^{u}$ where is defined such that :$(D^{u})_{ij}=diag(\\sum_{j=1}^m W_{ij}^{u})$.\n",
    "\n",
    "The same idea is applied for movies vectors.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, the problem of matrix completion can be formulated as follows :\n",
    "\n",
    "\n",
    "$\\displaystyle \\min_{X} \\frac{\\gamma_u}{2}||X||^2_{\\mathcal{D},u}+\\frac{\\gamma_m}{2}||X||^2_{\\mathcal{D},m}$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def build_L(Weight):\n",
    "    D =  np.diag(Weight.sum(axis=0))\n",
    "    L = (D-Weight).values\n",
    "    return L\n",
    "LM = build_L(WeightM)\n",
    "LU = build_L(WeightU)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since it is not that easy to find a procedure minimizing $||X||^2_{\\mathcal{D},u}$, we have expressed $X$ in other basis, in order to take benefit from the cvxpy toolbox. Indeed, we can use $tr(XX^t) = ||X||^2_{\\mathcal{F}}$, which is the square of the Frobenius norm.\n",
    "\n",
    "More precisions may be found in our report, stored in this Github repository."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def change_basis(L):\n",
    "    V,P = np.linalg.eigh(L) # diagonalise\n",
    "    V1 = np.diag(np.sqrt(np.abs(V))) \n",
    "    P1 = np.dot(P,V1)\n",
    "    return P1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "PM1 = change_basis(LM)\n",
    "PU1 = change_basis(LU)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.78323494167496e-05"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = Variable(*UM.shape)\n",
    "obj = Minimize(norm(X*PM1, 'fro') + norm((PU1.T)*X, 'fro')) # norm frobenius: information from graphs\n",
    "constraints = [mul_elemwise(mat_mask, X) == mul_elemwise(mat_mask, np.array(UM))]\n",
    "prob = Problem(obj, constraints)\n",
    "prob.solve(solver=SCS)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE: 1.04\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.0416666834620083"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "UM_rebuild = pd.DataFrame(index = UM.index,columns=UM.columns,data=X.value)\n",
    "rmse(UM,UM_rebuild)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rmse is here better than the first case. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparision of those methods, under several scenarios"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "To assess the improvement from graphs information, a lot of cases have been simulated. We wanted to compare the performances in term of RMSE for the matrix completion problem with:\n",
    "- Nuclear norm, based on low rank hypothesis\n",
    "- Graph information \n",
    "- The combination of both\n",
    "\n",
    "Under several scenarios:\n",
    "- With noise in the matrix of weight. Some 1 have been added, creating a wrong link, or some 0 have replaced 1, removing a correct link.\n",
    "- With different percentages of $UM$'s observation.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To add noise, we can use a XOR provided by numpy to flip the bits of the matrix of weight. We delete some links inside the communities or create ones between them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We observe 10.0340136054 per cent of the entries of a 42*42 matrix\n"
     ]
    },
    {
     "data": {
      "image/png": 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P5Zh/jsjc/oncKU+h7vVbIBfH+gnnbkB5/WNRF7Ggwfn3nOTDw8BS+PhpWO9c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\nEJCkEjMEJKnE/g91bOaW4IU9oQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x298b8ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "WeightU_noise =  np.logical_xor(WeightU,mask(*WeightU.shape,proportion=0.1))\n",
    "plot_graph(WeightU_noise,'users')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# optimization problem inside a function\n",
    "def rebuild(nuc,fro,PM1,PU1,mat_mask):\n",
    "    X = Variable(*UM.shape)\n",
    "    obj = Minimize(nuc*norm(X, 'nuc') +  # norm nuclear: hypotesis of low rank\n",
    "                   fro*(norm(X*PM1, 'fro') + norm((PU1.T)*X, 'fro'))) # norm frobenius: information from graphs\n",
    "    constraints = [mul_elemwise(mat_mask, X) == mul_elemwise(mat_mask, np.array(UM))]\n",
    "    prob = Problem(obj, constraints)\n",
    "    prob.solve(solver=SCS)\n",
    "    UM_rebuild = pd.DataFrame(index = UM.index,columns=UM.columns,data=X.value)\n",
    "    return UM_rebuild"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataframe containing results is now created"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                0    10   20   30   40   50   60   70\n",
      "noise fro nuc                                        \n",
      "0     0   1    NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN\n",
      "      1   0    NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN\n",
      "          1    NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN\n",
      "10    0   1    NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN\n",
      "      1   0    NaN  NaN  NaN  NaN  NaN  NaN  NaN  NaN\n"
     ]
    }
   ],
   "source": [
    "dic_result={'noise':range(0,40,10),\n",
    "            'nuc':[0,1],\n",
    "            'fro':[0,1]}\n",
    "\n",
    "result = pd.DataFrame(index=pd.MultiIndex.from_product(dic_result.values(),\n",
    "                                                       names=dic_result.keys()),\n",
    "        columns=range(0,80,10))\n",
    "result = result.ix[~((result.index.get_level_values('nuc')==0) & (result.index.get_level_values('fro')==0))]\n",
    "print(result.head())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The loops to fill it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We observe 0.0 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 10.5625 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.92063492063 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 9.625 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.58049886621 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 9.3125 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.0907029478 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 19.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.5782312925 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 19.125 per cent of the entries of a 40*40 matrix\n",
      "We observe 21.3151927438 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 19.1875 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.8979591837 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 29.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 31.0090702948 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 28.5625 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.7052154195 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 30.1875 per cent of the entries of a 40*40 matrix\n",
      "We observe 31.9160997732 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 9.16666666667 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 3.33\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 11.125 per cent of the entries of a 40*40 matrix\n",
      "We observe 11.4512471655 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 3.33\n",
      "We observe 9.6875 per cent of the entries of a 40*40 matrix\n",
      "We observe 8.10657596372 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.15\n",
      "We observe 10.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.0907029478 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.08\n",
      "We observe 21.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.2947845805 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 3.33\n",
      "We observe 19.25 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.1814058957 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.43\n",
      "We observe 21.625 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.1814058957 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 3.34\n",
      "We observe 29.9375 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.8752834467 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 3.33\n",
      "We observe 31.625 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.6485260771 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.15\n",
      "We observe 29.125 per cent of the entries of a 40*40 matrix\n",
      "We observe 31.9727891156 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.51\n",
      "We observe 19.2261904762 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.62\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 10.375 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.3741496599 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.62\n",
      "We observe 10.75 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.3741496599 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.11\n",
      "We observe 9.625 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.2970521542 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.16\n",
      "We observe 20.125 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.5011337868 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.62\n",
      "We observe 20.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.5215419501 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.59\n",
      "We observe 21.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.9546485261 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.25\n",
      "We observe 30.0625 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.3650793651 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.62\n",
      "We observe 29.875 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.5918367347 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.50\n",
      "We observe 31.1875 per cent of the entries of a 40*40 matrix\n",
      "We observe 30.2154195011 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.58\n",
      "We observe 31.130952381 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 9.75 per cent of the entries of a 40*40 matrix\n",
      "We observe 8.78684807256 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 10.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.5442176871 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.72\n",
      "We observe 10.75 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.75056689342 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.33\n",
      "We observe 20.0625 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.6916099773 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 20.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 18.6507936508 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.02\n",
      "We observe 20.1875 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.5578231293 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.55\n",
      "We observe 30.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.9319727891 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 29.8125 per cent of the entries of a 40*40 matrix\n",
      "We observe 31.0090702948 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.18\n",
      "We observe 30.25 per cent of the entries of a 40*40 matrix\n",
      "We observe 30.4988662132 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.79\n",
      "We observe 39.5833333333 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 9.9375 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.12698412698 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 10.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.7142857143 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.67\n",
      "We observe 9.125 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.6009070295 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.24\n",
      "We observe 21.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.6712018141 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 20.25 per cent of the entries of a 40*40 matrix\n",
      "We observe 21.0884353741 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.94\n",
      "We observe 20.5625 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.6712018141 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.54\n",
      "We observe 30.375 per cent of the entries of a 40*40 matrix\n",
      "We observe 30.4988662132 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 31.1875 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.7619047619 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.05\n",
      "We observe 28.875 per cent of the entries of a 40*40 matrix\n",
      "We observe 31.0657596372 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.62\n",
      "We observe 49.5833333333 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 8.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.3174603175 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 10.0625 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.4308390023 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.48\n",
      "We observe 10.25 per cent of the entries of a 40*40 matrix\n",
      "We observe 11.0544217687 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.11\n",
      "We observe 20.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.8979591837 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 18.75 per cent of the entries of a 40*40 matrix\n",
      "We observe 17.5170068027 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.61\n",
      "We observe 20.1875 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.6712018141 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.21\n",
      "We observe 31.1875 per cent of the entries of a 40*40 matrix\n",
      "We observe 30.7256235828 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 29.5625 per cent of the entries of a 40*40 matrix\n",
      "We observe 30.3854875283 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.72\n",
      "We observe 29.9375 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.8752834467 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.31\n",
      "We observe 60.5952380952 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 10.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.0340136054 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 9.5625 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.2040816327 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.25\n",
      "We observe 9.8125 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.58049886621 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.03\n",
      "We observe 19.3125 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.6916099773 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 20.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 18.1972789116 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.40\n",
      "We observe 19.6875 per cent of the entries of a 40*40 matrix\n",
      "We observe 21.9954648526 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.09\n",
      "We observe 28.625 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.9886621315 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 29.75 per cent of the entries of a 40*40 matrix\n",
      "We observe 28.798185941 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.56\n",
      "We observe 28.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 30.4421768707 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.15\n",
      "We observe 68.2142857143 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 10.1875 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.75056689342 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 8.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.86394557823 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.18\n",
      "We observe 10.125 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.97732426304 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.02\n",
      "We observe 20.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 22.1655328798 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 19.0625 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.2176870748 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.33\n",
      "We observe 19.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.6712018141 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.03\n",
      "We observe 31.625 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.8185941043 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 30.25 per cent of the entries of a 40*40 matrix\n",
      "We observe 31.9160997732 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.47\n",
      "We observe 30.6875 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.9319727891 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.08\n"
     ]
    }
   ],
   "source": [
    "for observation in result.columns:\n",
    "    proportion = observation/100.\n",
    "    mat_mask = mask(*UM.shape,proportion=proportion)\n",
    "    for noise,fro,nuc in product(*result.index.levels):\n",
    "        if ~((nuc==0) & (fro==0)):\n",
    "#            print(noise,fro,nuc)\n",
    "            WeightM_noise = np.logical_xor(WeightM,mask(*WeightM.shape,proportion=noise/100.))\n",
    "            WeightU_noise =  np.logical_xor(WeightU,mask(*WeightU.shape,proportion=noise/100.))\n",
    "            LU_noise = build_L(WeightU_noise)\n",
    "            LM_noise = build_L(WeightM_noise)\n",
    "            UM_rebuild =  rebuild(nuc,fro,\n",
    "                                  change_basis(LM_noise),\n",
    "                                  change_basis(LU_noise),mat_mask)\n",
    "            r = rmse(UM_rebuild,UM)\n",
    "            result.loc[(noise,fro,nuc),observation] = r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It yields to the next graphs, showing the effect of noise, for different percentages of observation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x29143898>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MoGvXrhQVFQEwePDgcvd6QWJiIo0aNcLZ2dlaFhoaSmJiIgDNmjVjw4YNHDlyhNTUVO66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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x200ee550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(20,8))\n",
    "ax = fig.add_subplot(111)\n",
    "color_dic = {(0,1):'b',(1,1):'r',(1,0):'g'}\n",
    "style_dic = {k:v for k,v in zip(dic_result['noise'],[':','-.','--','-'])}\n",
    "result.loc[(slice(None),1,1),:]\n",
    "for noise,fro,nuc in  product(*result.index.levels):\n",
    "    if ~((nuc==0) & (fro==0)):    \n",
    "        label = nuc*'nuclear'+ nuc*fro*'+'+ fro*'graph' +', noise: '+ str(noise)+ '%'\n",
    "        result.loc[(noise,fro,nuc),:].T.plot(color = color_dic[(nuc,fro)],\n",
    "                                            style=style_dic[noise],\n",
    "                                            label=label,\n",
    "                                            alpha = 0.6)\n",
    "ax.legend()\n",
    "ax.set_xlabel('% of observation')\n",
    "ax.set_ylabel('RMSE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "As we can show, information of communities is very strong, and outperforms the original problem if there is no noise. In case of noise for the matrix of weights, 30% of wrong links for instance, the first problem based on nuclear norm minimization gets better result from more than 10% of observations.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To be more realistic, the matrix of weight have been made sparser. The half of links is removed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We observe 52.2675736961 per cent of the entries of a 42*42 matrix\n",
      "We observe 49.125 per cent of the entries of a 40*40 matrix\n"
     ]
    }
   ],
   "source": [
    "WeightU = WeightU*mask(*WeightU.shape,proportion = 0.5)\n",
    "WeightM = WeightM*mask(*WeightM.shape,proportion = 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same fillling is done:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We observe 0.0 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 9.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.2607709751 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 9.75 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.80725623583 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 10.125 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.0340136054 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 19.875 per cent of the entries of a 40*40 matrix\n",
      "We observe 18.820861678 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 20.125 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.6916099773 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 19.3125 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.3514739229 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 30.3125 per cent of the entries of a 40*40 matrix\n",
      "We observe 27.8911564626 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 31.125 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.1383219955 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 30.25 per cent of the entries of a 40*40 matrix\n",
      "We observe 31.2925170068 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 8.57\n",
      "We observe 10.2380952381 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 3.11\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 3.16\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.94\n",
      "We observe 11.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 8.44671201814 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 3.11\n",
      "We observe 10.375 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.3741496599 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.72\n",
      "We observe 10.375 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.8843537415 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 3.13\n",
      "We observe 17.6875 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.5011337868 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 3.11\n",
      "We observe 19.9375 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.5578231293 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 3.14\n",
      "We observe 18.5625 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.5011337868 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.96\n",
      "We observe 30.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.1950113379 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 3.11\n",
      "We observe 30.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.3650793651 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.50\n",
      "We observe 29.75 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.8752834467 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.71\n",
      "We observe 19.2857142857 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.79\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.07\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.42\n",
      "We observe 10.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.52380952381 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.79\n",
      "We observe 9.9375 per cent of the entries of a 40*40 matrix\n",
      "We observe 8.95691609977 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.87\n",
      "We observe 9.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.52380952381 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.86\n",
      "We observe 18.625 per cent of the entries of a 40*40 matrix\n",
      "We observe 22.4489795918 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.79\n",
      "We observe 19.875 per cent of the entries of a 40*40 matrix\n",
      "We observe 18.7074829932 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 2.18\n",
      "We observe 20.125 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.9750566893 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.69\n",
      "We observe 27.375 per cent of the entries of a 40*40 matrix\n",
      "We observe 28.9115646259 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.79\n",
      "We observe 30.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.9886621315 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.81\n",
      "We observe 31.5625 per cent of the entries of a 40*40 matrix\n",
      "We observe 31.4058956916 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.79\n",
      "We observe 28.5714285714 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.08\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.18\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.49\n",
      "We observe 9.1875 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.1473922902 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.08\n",
      "We observe 10.3125 per cent of the entries of a 40*40 matrix\n",
      "We observe 11.0544217687 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.89\n",
      "We observe 9.1875 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.2040816327 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.86\n",
      "We observe 19.875 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.4081632653 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.08\n",
      "We observe 21.75 per cent of the entries of a 40*40 matrix\n",
      "We observe 18.9342403628 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.41\n",
      "We observe 17.875 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.8616780045 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.92\n",
      "We observe 29.625 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.7052154195 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.08\n",
      "We observe 31.875 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.4217687075 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.44\n",
      "We observe 30.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 28.9115646259 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.07\n",
      "We observe 38.3928571429 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.90\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.27\n",
      "We observe 10.8125 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.4308390023 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 9.3125 per cent of the entries of a 40*40 matrix\n",
      "We observe 8.90022675737 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.70\n",
      "We observe 8.9375 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.9977324263 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.64\n",
      "We observe 20.8125 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.3310657596 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 19.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 17.5736961451 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.35\n",
      "We observe 18.0625 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.2947845805 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.79\n",
      "We observe 28.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.3083900227 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 29.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.4217687075 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 1.36\n",
      "We observe 30.25 per cent of the entries of a 40*40 matrix\n",
      "We observe 28.7414965986 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.74\n",
      "We observe 50.7738095238 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.49\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.03\n",
      "We observe 9.5625 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.3741496599 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 10.5625 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.2040816327 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.81\n",
      "We observe 8.875 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.410430839 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.16\n",
      "We observe 20.25 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.2743764172 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 20.375 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.9750566893 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.85\n",
      "We observe 19.9375 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.387755102 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.29\n",
      "We observe 28.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 31.0090702948 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.01\n",
      "We observe 29.9375 per cent of the entries of a 40*40 matrix\n",
      "We observe 31.3492063492 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.85\n",
      "We observe 29.9375 per cent of the entries of a 40*40 matrix\n",
      "We observe 28.798185941 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.41\n",
      "We observe 60.0595238095 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.36\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 10.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.3741496599 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 9.375 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.63718820862 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.62\n",
      "We observe 10.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.63718820862 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.05\n",
      "We observe 21.625 per cent of the entries of a 40*40 matrix\n",
      "We observe 21.485260771 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 19.6875 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.7845804989 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.64\n",
      "We observe 19.8125 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.2380952381 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.11\n",
      "We observe 29.75 per cent of the entries of a 40*40 matrix\n",
      "We observe 30.2721088435 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 29.375 per cent of the entries of a 40*40 matrix\n",
      "We observe 30.2154195011 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.67\n",
      "We observe 30.25 per cent of the entries of a 40*40 matrix\n",
      "We observe 29.0816326531 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.16\n",
      "We observe 69.7619047619 per cent of the entries of a 42*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.26\n",
      "We observe 0.0 per cent of the entries of a 40*40 matrix\n",
      "We observe 0.0 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 10.1875 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.97732426304 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 9.6875 per cent of the entries of a 40*40 matrix\n",
      "We observe 10.3741496599 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.38\n",
      "We observe 9.8125 per cent of the entries of a 40*40 matrix\n",
      "We observe 9.75056689342 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 19.375 per cent of the entries of a 40*40 matrix\n",
      "We observe 19.7845804989 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 19.4375 per cent of the entries of a 40*40 matrix\n",
      "We observe 20.2380952381 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.43\n",
      "We observe 20.1875 per cent of the entries of a 40*40 matrix\n",
      "We observe 21.1451247166 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.04\n",
      "We observe 30.5 per cent of the entries of a 40*40 matrix\n",
      "We observe 30.3854875283 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.00\n",
      "We observe 30.5625 per cent of the entries of a 40*40 matrix\n",
      "We observe 31.4058956916 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.52\n",
      "We observe 28.3125 per cent of the entries of a 40*40 matrix\n",
      "We observe 30.1020408163 per cent of the entries of a 42*42 matrix\n",
      "RMSE: 0.07\n"
     ]
    }
   ],
   "source": [
    "for observation in result.columns:\n",
    "    proportion = observation/100.\n",
    "    mat_mask = mask(*UM.shape,proportion=proportion)\n",
    "    for noise,fro,nuc in product(*result.index.levels):\n",
    "        if ~((nuc==0) & (fro==0)):\n",
    "#            print(noise,fro,nuc)\n",
    "            WeightM_noise = np.logical_xor(WeightM,mask(*WeightM.shape,proportion=noise/100.))\n",
    "            WeightU_noise =  np.logical_xor(WeightU,mask(*WeightU.shape,proportion=noise/100.))\n",
    "            LU_noise = build_L(WeightU_noise)\n",
    "            LM_noise = build_L(WeightM_noise)\n",
    "            UM_rebuild =  rebuild(nuc,fro,\n",
    "                                  change_basis(LM_noise),\n",
    "                                  change_basis(LU_noise),mat_mask)\n",
    "            r = rmse(UM_rebuild,UM)\n",
    "            result.loc[(noise,fro,nuc),observation] = r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x2b6cf1d0>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IyACgbdu2JCUlcejQIXJycrjrrrsYO3Ysc+fOxd7evtbzl+tzyyaKAPq/1wvXorupzE2m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\nKCIi4k0A8wAMAFAF4H5d118Jsp8IRYIgdHm2lW3DA18+gIWjF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Y3DdYdhsVsQ2SsSl+Zc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ONjRsACCZTxLLxOis7bS1l0tSMAW2bdiGMYbh2WF2j+3GV+Ejlonhq/ARzUTZ2LiR/pb+324P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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x200fd7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(20,8))\n",
    "ax = fig.add_subplot(111)\n",
    "color_dic = {(0,1):'b',(1,1):'r',(1,0):'g'}\n",
    "style_dic = {k:v for k,v in zip(dic_result['noise'],[':','-.','--','-'])}\n",
    "result.loc[(slice(None),1,1),:]\n",
    "for noise,fro,nuc in  product(*result.index.levels):\n",
    "    if ~((nuc==0) & (fro==0)):    \n",
    "        label = nuc*'nuclear'+ nuc*fro*'+'+ fro*'graph' +', noise: '+ str(noise)+ '%'\n",
    "        result.loc[(noise,fro,nuc),:].T.plot(color = color_dic[(nuc,fro)],\n",
    "                                            style=style_dic[noise],\n",
    "                                            label=label,\n",
    "                                            alpha = 0.6)\n",
    "ax.legend()\n",
    "ax.set_xlabel('% of observation')\n",
    "ax.set_ylabel('RMSE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With partial information of communities membership, the results are worse. Basically, for 10% of observation, graph-based resolution is still better, but after, nuclear norm based optimization becomes more accurate.\n"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}