{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 無限関係モデルによる共クラスタリングの実験用のトイデータ生成\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "クラスタ数は『続・わかりやすいパターン認識』の13章P.279のデータと揃えてある.\n",
    "ただし,関係行列の行数・列数は比率はそのままで数を10倍に増やしてる."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Distributions\n",
    "using Plots\n",
    "\n",
    "using DelimitedFiles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "行(顧客)と列(商品)のクラスタ数$c_1$, $c_2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = 4;\n",
    "c2 = 3;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "行(顧客)と列(商品)のデータ数$K$, $L$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 15 * 10;\n",
    "L = 10 * 10;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "行(顧客)と列(商品)の混合比率$\\pi^1$, $\\pi^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "π1 = [4/15; 3/15; 5/15; 3/15];\n",
    "π2 = [4/10; 3/10; 3/10];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "行列$\\Theta = \\{\\theta_ij\\}$の各成分は,\n",
    "顧客クラスタ$i$に属する顧客が商品クラスタ$j$に属する商品を購入する確率を表す."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "Θ = [0.2 0.9 0.1;\n",
    "     1.0 0.8 0.0;\n",
    "     0.1 0.1 0.9;\n",
    "     0.2 0.7 0.1];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "顧客と商品の所属クラスを表す潜在変数$\\mathbf s^1$, $\\mathbf s^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "s1 = rand(Categorical(π1), K);\n",
    "s2 = rand(Categorical(π2), L);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "顧客$k$が商品$l$を購入してたら1,そうでなければ0を成分にもつ\n",
    "関係行列$\\mathbf R = \\{R_{kl}\\}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "R = zeros(K, L);\n",
    "\n",
    "for k in 1:K\n",
    "    for l in 1:L\n",
    "        R[k, l] = rand(Bernoulli(Θ[s1[k], s2[l]]))\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "顧客と商品の関係行列$\\mathbf R$をプロット"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heatmap(R, yflip=true, c=ColorGradient([:white, :black]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "顧客と商品の関係行列$\\mathbf R$を真のラベルを用いて並べ替えて表示する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_idxs = sort(collect(1:K), by=i->s1[i]);\n",
    "col_idxs = sort(collect(1:L), by=i->s2[i]);\n",
    "\n",
    "heatmap(R[row_idxs, col_idxs], yflip=true, c=ColorGradient([:white, :black]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# データの出力"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://stackoverflow.com/questions/52900232/export-an-array-to-csv-file-in-julia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "writedlm(\"IRM_toydata_R_200402.csv\", R, ',')\n",
    "writedlm(\"IRM_toydata_s1_200402.csv\", s1, ',')\n",
    "writedlm(\"IRM_toydata_s2_200402.csv\", s2, ',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以下,出力したデータを読み込むテスト"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "R_gt = readdlm(\"IRM_toydata_R_200402.csv\", ',');\n",
    "s1_gt = readdlm(\"IRM_toydata_s1_200402.csv\", ',');\n",
    "s2_gt = readdlm(\"IRM_toydata_s2_200402.csv\", ',');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "row_idxs = sort(collect(1:K), by=i->s1_gt[i]);\n",
    "col_idxs = sort(collect(1:L), by=i->s2_gt[i]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
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     "execution_count": 15,
     "metadata": {},
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