05-logistic_vs_perceptron.ipynb

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   "execution_count": 51,
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     "text": [
      "<main>:6: warning: already initialized constant Variances\n",
      "<main>:6: warning: previous definition of Variances was here\n"
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       "        var id_name = '#vis-1eb1e38f-5882-4b40-9998-06ea68cf73ec';\n",
       "        Nyaplot.core.parse(model, id_name);\n",
       "\n",
       "        require(['downloadable'], function(downloadable){\n",
       "          var svg = d3.select(id_name).select(\"svg\");\n",
       "\t  if(!svg.empty())\n",
       "\t    svg.call(downloadable().filename('fig'));\n",
       "\t});\n",
       "    };\n",
       "    if(window['Nyaplot']==undefined){\n",
       "        window.addEventListener('load_nyaplot', render, false);\n",
       "\treturn;\n",
       "    } else {\n",
       "       render();\n",
       "    }\n",
       "})();\n",
       "</script>\n"
      ],
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   "source": [
    "# ロジスティック回帰とパーセプトロンの比較\n",
    "\n",
    "require 'daru'\n",
    "require 'nyaplot'\n",
    "require 'numo/narray'\n",
    "\n",
    "Variances = [5, 10, 30, 50] # 両クラス共通の分散（4種類の分散で計算を実施）\n",
    "\n",
    "class Array\n",
    "  def mean\n",
    "    self.inject(:+) / self.size.to_f\n",
    "  end\n",
    "end\n",
    "\n",
    "def normal_rand(mu = 0, sigma = 1.0)\n",
    "  random = Random.new\n",
    "  (Math.sqrt(-2 * Math.log(random.rand)) * Math.sin(2 * Math::PI * random.rand) * sigma) + mu\n",
    "end\n",
    "\n",
    "# データセット {x_n,y_n,type_n} を用意\n",
    "def prepare_dataset(variance)\n",
    "  n1 = 10\n",
    "  n2 = 20\n",
    "  mu1 = [7, 7]\n",
    "  mu2 = [-3, -3]\n",
    "\n",
    "  sigma = Math.sqrt(variance)\n",
    "\n",
    "  df1 = n1.times.map do\n",
    "    [normal_rand(mu1[0], sigma), normal_rand(mu1[1], sigma)]\n",
    "  end\n",
    "  df1 = df1.transpose\n",
    "  df1 = Daru::DataFrame.new(x: df1[0], y: df1[1], type: Array.new(n1).fill(1))\n",
    "\n",
    "  df2 = n2.times.map do\n",
    "    [normal_rand(mu2[0], sigma), normal_rand(mu2[1], sigma)]\n",
    "  end\n",
    "  df2 = df2.transpose\n",
    "  df2 = Daru::DataFrame.new(x: df2[0], y: df2[1], type: Array.new(n2).fill(0))\n",
    "\n",
    "  df = df1.concat(df2)\n",
    "  df = df.reindex(Daru::Index.new(df.index.to_a.shuffle))\n",
    "  df[:index] = (n1 + n2).times.to_a\n",
    "  df.set_index(:index)\n",
    "end\n",
    "\n",
    "# ロジスティック回帰\n",
    "def run_logistic(train_set, plot)\n",
    "  w = Numo::NArray[[0], [0.1], [0.1]]\n",
    "  phi = train_set[:x, :y]\n",
    "  phi[:bias] = Array.new(phi.size).fill(1)\n",
    "  t = train_set[:type]\n",
    "  t = t.to_matrix\n",
    "\n",
    "  # 最大30回のIterationを実施\n",
    "  30.times do\n",
    "    # IRLS法によるパラメータの修正\n",
    "    y = []\n",
    "    phi.each_row do |line|\n",
    "      a = Vector[*line.to_a].dot(w)\n",
    "      y << (1.0 / (1.0 + Math.exp(-a)))\n",
    "    end\n",
    "    r = Matrix.diagonal(*(Numo::NArray[*y] * (1 - Numo::NArray[*y]).to_a))\n",
    "    y = Numo::NArray[y].transpose\n",
    "    tmp1 = Matrix[*Numo::NArray[*phi.to_matrix.transpose.to_a].dot(Numo::NArray[*r.to_a]).dot(Numo::NArray[*phi.to_matrix.to_a]).to_a].inverse\n",
    "    tmp2 = Numo::NArray[*phi.to_matrix.transpose.to_a].dot(y - Numo::NArray[*t.transpose.to_a])\n",
    "    w_new = w - Numo::NArray[*tmp1.to_a].dot(tmp2)\n",
    "\n",
    "    # パラメータの変化が 0.1% 未満になったら終了\n",
    "    if (w_new - w).transpose.dot(w_new - w).flatten[0] < (0.001 * (w.transpose.dot(w))).flatten[0]\n",
    "      w = w_new\n",
    "      break\n",
    "    end\n",
    "  end\n",
    "\n",
    "  # 分類誤差の計算\n",
    "  w0 = w[0]\n",
    "  w1 = w[1]\n",
    "  w2 = w[2]\n",
    "  err = 0\n",
    "  train_set.each_row do |point|\n",
    "    x = point.x\n",
    "    y = point.y\n",
    "    type = point[:type]\n",
    "    type = type * 2 - 1\n",
    "    if type * (w0 + w1*x + w2*y) < 0\n",
    "      err += 1\n",
    "    end\n",
    "  end\n",
    "\n",
    "  err_rate = err * 100 / train_set.size\n",
    "\n",
    "  # 結果を表示\n",
    "  xmin = train_set.x.min - 5\n",
    "  xmax = train_set.x.max + 10\n",
    "  linex = Numo::NArray[*(xmin.to_i-5..xmax.to_i+4).to_a]\n",
    "  liney = -linex * w1 / w2 - w0 / w2\n",
    "  label = \"ERR %.2f%%\" % err_rate\n",
    "\n",
    "  line_err = plot.add(:line, linex.cast_to(Numo::Int64).to_a, liney.cast_to(Numo::Int64).to_a)\n",
    "  line_err.title(label)\n",
    "  line_err.color('blue')\n",
    "end\n",
    "\n",
    "# パーセプトロン\n",
    "def run_perceptron(train_set, plot)\n",
    "  w0 = 0.0\n",
    "  w1 = 0.0\n",
    "  w2 = 0.0\n",
    "  bias = 0.5 * (train_set.x.mean + train_set.y.mean)\n",
    "\n",
    "  # Iterationを30回実施\n",
    "  30.times do\n",
    "    # 確率的勾配降下法によるパラメータの修正\n",
    "    train_set.each_row do |point|\n",
    "      x = point.x\n",
    "      y = point.y\n",
    "      type = point[:type]\n",
    "      type = type * 2 - 1\n",
    "      if type * (w0*bias + w1*x + w2*y) <= 0\n",
    "        w0 += type * bias\n",
    "        w1 += type * x\n",
    "        w2 += type * y\n",
    "      end\n",
    "    end\n",
    "  end\n",
    "\n",
    "  # 分類誤差の計算\n",
    "  err = 0\n",
    "  train_set.each_row do |point|\n",
    "    x = point.x\n",
    "    y = point.y\n",
    "    type = point[:type]\n",
    "    type = type * 2 - 1\n",
    "    if type * (w0*bias + w1*x + w2*y) <= 0\n",
    "      err += 1\n",
    "    end\n",
    "  end\n",
    "\n",
    "  err_rate = err * 100 / train_set.size\n",
    "\n",
    "  # 結果を表示\n",
    "  xmin = train_set.x.min - 5\n",
    "  xmax = train_set.x.max + 10\n",
    "  linex = Numo::NArray[*(xmin.to_i-5..xmax.to_i+4).to_a]\n",
    "  liney = -linex * w1 / w2 - bias * w0 / w2\n",
    "  label = \"ERR %.2f%%\" % err_rate\n",
    "\n",
    "  line_err = plot.add(:line, linex.cast_to(Numo::Int64).to_a, liney.cast_to(Numo::Int64).to_a)\n",
    "  line_err.title(label)\n",
    "  line_err.color('red')\n",
    "end\n",
    "\n",
    "def run_simulation(variance, plot)\n",
    "  train_set = prepare_dataset(variance)\n",
    "  train_set1 = train_set.filter_rows {|row| row[:type] == 1 }\n",
    "  train_set2 = train_set.filter_rows {|row| row[:type] == 0 }\n",
    "  ymin = train_set.y.min - 5\n",
    "  xmin = train_set.x.min - 5\n",
    "  ymax = train_set.y.max + 10\n",
    "  xmax = train_set.x.max + 10\n",
    "  plot.configure do\n",
    "    x_label(\"Variance: #{variance}\")\n",
    "    y_label('')\n",
    "    xrange([xmin, xmax])\n",
    "    yrange([ymin, ymax])\n",
    "    legend(true)\n",
    "    height(300)\n",
    "    width(490)\n",
    "  end\n",
    "\n",
    "  scatter_true = plot.add_with_df(train_set1.to_nyaplotdf, :scatter, :x, :y)\n",
    "  scatter_true.color('green')\n",
    "  scatter_true.title('1')\n",
    "  scatter_false = plot.add_with_df(train_set2.to_nyaplotdf, :scatter, :x, :y)\n",
    "  scatter_false.color('orange')\n",
    "  scatter_false.title('0')\n",
    "\n",
    "  run_logistic(train_set, plot)\n",
    "  run_perceptron(train_set, plot)\n",
    "end\n",
    "\n",
    "fig = Nyaplot::Frame.new\n",
    "\n",
    "Variances.each do |variance|\n",
    "  plot = Nyaplot::Plot.new\n",
    "  run_simulation(variance, plot)\n",
    "  fig.add(plot)\n",
    "end\n",
    "\n",
    "fig.show\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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