Cartman0 · May 14, 2019 14:45
diff --git a/ホップフィールドネットワーク.ipynb b/ホップフィールドネットワーク.ipynb
 {
  "cells": [
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "# ホップフィールドネットワーク"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## 参考"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "- https://www.tcom242242.net/entry/2016/12/15/184603\n- http://www.sist.ac.jp/~kanakubo/research/neuro/hopfieldnetwork.html\n- http://rishida.hatenablog.com/entry/2014/03/03/174331"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## 概要"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "ボルツマンマシンの前身\n\n画像などのビット列情報を複数記憶でき，\n似たビット列を入力すると，記憶したビット列を復元し想起させる．\n\n想起ネットワークともいう．\n\n通常のニューラルネットワークとは違い，\n重みとバイアス（しきい値）は固定して入力値（状態）を変化させ平衡させていく．\n\n\n以下のエネルギー関数をだんだん小さくしていく（準）最適化問題を解いていることになる．\n$$\nE= -\\frac{1}{2}\\sum_{ij}^{n} w_{ij} x_i x_j + \\sum_{i} \\theta _i x_i \\ \n$$\n\nなので，"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "ネットワークは，完全グラフを考える．\n\n扱う値は以下．\n\n\n- 入力状態は，$\\{1, -1 \\}$のみ\n\n- グラフの辺は，結合係数（重み）を持ち同じ入力値同士だとこの重みが大きくなる．\nこの重みが記憶情報に該当する．\n\n"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## ベクトルと行列おさらい"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "- ベクトルの内積は類似度を表す:スカラーであり，同じようなベクトル同士だと正，逆向き同士だと負，無関係の場合0（直交）となる．つまり類似度に相当する．\n    \n$$\nw = \\vec{x}^T \\cdot \\vec{y} = \\vec{y}^T \\cdot \\vec{x}\n= \\sum_{i=1}^n x_i y_i \n= x_1y_1 + x_2y_2 + \\cdots x_ny_n\n$$\n\n- 自分との内積は大きさを表す．\n\n$$\n\\vec{x}^T \\cdot \\vec{x} = \\sum_{i=1}^n x_i^2= x_1^2 + x_2^2 + \\cdots x_n^2\\\\\n||x|| = \\sqrt{\\vec{x}^T \\cdot \\vec{x}}\n$$\n\n（厳密にはルートをとると大きさになるが2乗のままのほうが都合がいいことが多い．）\n\n- ベクトルの大きさは平方和（分散）を表す：\n\n$(x_1, x_2, \\cdots, x_n)$を標本の大きさ$n$の身長，体重などのデータとする.\n平均$0$になるように差分・変換したデータ$(x_1, x_2, \\cdots, x_n)=(x_1-\\mu, x_2-\\mu, \\cdots, x_n-\\mu)$\nの分散を考えると\n\n$$\nS(\\vec{x}) = \\sum_{i=1}^n (x_i - \\mu)^2\n$$\n\n今，平均0なので\n\n$$\nS(\\vec{x}) = \\sum_{i=1}^n x_i^2\n$$\n\nつまり，ベクトルの大きさ（自分との内積）は平方和になる．\n\n$$\n\\vec{x}^T \\cdot \\vec{x} = \nS(\\vec{x}) = \\sum_{i=1}^n x_i^2\n$$\n\n- 同様にして，ベクトル$y$もデータと考えればその内積は平方和（共分散）になる．\n\n$$\nS(\\vec{x}, \\vec{y}) = \\sum_{i=1}^{n} (x_i - \\mu_x)( y_i - \\mu_y)\n$$\n\n平均0に変換しているとすると，\n\n$$\nS(\\vec{x}, \\vec{y}) = \\sum_{i=1}^{n} x_i y_i \n$$\n\nつまり，異なるベクトルの内積は，共分散（平方和）に該当する（厳密には1/nが必要）．\n\n\n$$\n\\vec{x}^T \\cdot \\vec{y} \n= \\vec{y}^T \\cdot \\vec{x}\n= S(\\vec{x}, \\vec{y}) = \\sum_{i=1}^{n} x_i y_i \n$$\n\n- 共分散は大きさが最大1になるように標準化すれば相関係数になるので，\n内積は相関係数に該当する（厳密には標準化が必要）．\n\n$$\nr_{xy} = \\frac{S(x, y)}{S(x) S(y)}\n$$\n"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## 重みの求め方"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### 訓練データの相関係数行列（分散共分散行列）を置く場合が多い"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "$$\nw_{ij} = x_{i}x_{j} \\\\\nw_{ii} = 0\n$$\n\n訓練データ複数の場合\n\\begin{equation}\nw_{ij} = \\sum_{s} x^{s}_i x^{s}_j \n\\end{equation} \n\n\nこの重みが何を表しているかを考える．\n真理値表のように書くと\n\n|$x_{i}$|$x_{j}$|$w_{ij}$|\n|:-----:|:-----:|:------:|\n|1|1|1|\n|1|-1|-1|\n|-1|1|-1|\n|-1|-1|1|\n\nつまり，\n- $+1$（正）のとき，同じ値を表し，\n- $-1$（負）のとき，反転していることを表している．\n\n\n\n\n"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## 入力状態の更新方法"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "1. まず重み$w_{ij}=x_i x_j$を計算し，しきい値$\\theta$も0などで決めておく．\n\n2. ランダムにノード$i$を選ぶ．\n\n3. ノードiへ入力されたとして，重み結合を使った線形和を計算．\nしきい値と比較して大きければ1, 同じなら0, 小さければ-1を新しい状態$x_i^{new}$に更新する．\n定式化すると以下の値になる．\n\n$$\ny_i = \\sum_j w_{ij}x_j - \\theta_i  \\\\\nx_{i}^{new} \n= \n\\left\\{\n\\begin{array}\n\\\\1 & (y_i > 0)\\\\\nx_{i} & (y_i = 0)\\\\\n-1 & (y_i < 0)\\\\\n\\end{array}\n\\right.\n$$\n\n4. エネルギー関数が変化しなくなるまで2-3を繰り返す．\n\n\n更新を繰り返していくと，エネルギー関数が小さくなっていく．\n\n$$\nE= -\\frac{1}{2}\\sum_{ij}^{n} w_{ij} x_i x_j + \\sum_{i} \\theta _i x_i \\ \n$$\n\n第1項は重みのもつ符号情報と入力情報があっているかを見ている．\n第1項の符号を真理値表のように確認する．\n\n|$w_{ij}$|$x_{i}$|$x_{j}$|$w_{ij}x_{i}x_{j}$|$- w_{ij}x_{i}x_{j}$|\n|:------:|:-----:|:-----:|:----------------:|:-----------------:|\n|+（同じ）|1      |1       |正 |負 |\n|+（同じ）|-1     |-1      |正 |負 |\n|+（同じ）|1      |-1      |負 |正 |\n|+（同じ）|-1     |1       |負 |正 |\n|-（反転）|1      |-1      |正 |負 |\n|-（反転）|-1     |1       |正 |負|\n|-（反転）|1      |1       |負 |正|\n|-（反転）|-1     |-1      |負 |正|\n\n負の時エネルギー関数が小さくなる．\nつまり，重みの符号情報と入力状態が一致しているとき負になる．\n"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### $y_i$の線形和は何を計算しているか？"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "$$\ny_i = \\sum_j w_{ij}x_j - \\theta_i  \\\\\n$$\n\nの線形和が何を計算しているのかを確認する．\n\n- 重みが正（入力が同じだった）の場合：\n    - $x_j=+1$が多いと，和を取ると正に大きくなりしきい値を超えやすく+1になりやすい．\n    - $x_j=-1$が多いと，負の絶対値が大きくなりしきい値を超えにくく-1になりやすい．\n\nつまり，入力の多数決を行っており，出現回数の多い値が新しい入力状態へ更新される．\n\n- 重みが負（入力が反転だった）の場合：\n    - $x_j=+1$が多いと，負の絶対値が大きくなりしきい値を超えにくく-1になりやすい．\n    - $x_j=-1$が多いと，正に大きくなりしきい値を超えやすく+1になりやすい．\n\nつまり，出現回数の多かった値の反転が新しい入力状態へ更新される．\n"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## 更新ごとにエネルギー関数が小さくなる証明"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "http://www.sist.ac.jp/~kanakubo/research/neuro/hopfieldnetwork.html\n"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "### "
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## 例：2ノードの場合"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "- 入力状態：$x_1, x_2$\n- 重み $w_{12}$のみ\n\n重みのパターン\n\n|$x_{1}$|$x_2$|$w_{12}$|\n|:-:|:-:|:-:|\n|1|1|1|\n|-1|-1|1|\n|1|-1|-1|\n|-1|1|-1|\n"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## 例：3ノードの場合"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "重みは$\\{2, 0, -2\\}$の3パターンになる．\n\n"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": ""
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## 実装"
    },
    {
      "metadata": {
        "scrolled": true,
        "trusted": true
      },
      "cell_type": "code",
      "source": "import scipy as sp\nimport matplotlib.pyplot as plt\n\ntrain_vec_x = sp.matrix([[1, -1, -1, -1, -1, -1, -1, -1, -1, -1, \n                          -1, -1, -1]])\nn = train_vec_x.shape[1]\ninitail_state_x = sp.matrix([-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, \n                             -1, -1, -1])\nindex_array = sp.arange(n)\nthreshold = 0\nthreshold_vec = sp.full(initail_state_x.shape, threshold)\niterate_count = 10000\n\ndef train_weights(train_vec_x):\n    '''\n    W = mat 0\n    W_1 = vec_x_1.T dot vec_x_1\n    W += W_1\n    repeat.\n    '''\n    train_num, n = train_vec_x.shape\n    W = sp.zeros((n, n))\n    for i in sp.arange(train_num):\n        W_i = train_vec_x[i].T.dot(train_vec_x[i])\n        sp.fill_diagonal(W_i, 0)\n        W += W_i\n        \n    return W\n\ndef choice_Node(index_array):\n    return sp.random.choice(index_array)\n\ndef calc_ward(state_x, index_array, weight_mat, threshold_vec):\n    '''\n    y_i = sum w_ij x_j - theta_i\n    '''\n    \n    node_idx = choice_Node(index_array)\n#     print(node_idx)\n#     print(\"state_x:\", state_x.T)\n#     print(\"weight_mat[node_idx]:\", weight_mat[node_idx])\n#     print(\"th\", threshold_vec)\n#     print(\"th id\", threshold_vec[node_idx].T)\n    y_i = weight_mat[node_idx].dot(state_x.T) - threshold_vec.T[node_idx]\n#     print(y_i)\n    y_i = sp.asscalar(y_i)\n    state_x.T[node_idx] = 1 if y_i > 0 else -1 if y_i < 0 else state_x.T[node_idx]\n    return state_x\n\ndef update(initail_state_x, index_array, W, threshold_vec, iterate_count):\n    state_x = initail_state_x\n    for i in sp.arange(iterate_count):\n        state_x = calc_ward(state_x, index_array, W, threshold_vec)\n    return state_x\n\nW = train_weights(train_vec_x)\nW\nindex_array\nthreshold_vec\n# calc_ward(initail_state_x, index_array, W, threshold_vec)\nvec_x = update(initail_state_x, index_array, W, threshold_vec, iterate_count)\nvec_x",
      "execution_count": 235,
      "outputs": [
        {
          "data": {
            "text/plain": "matrix([[ 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1]])"
          },
          "execution_count": 235,
          "metadata": {},
          "output_type": "execute_result"
        }
      ]
    },
    {
      "metadata": {
        "scrolled": true,
        "trusted": true
      },
      "cell_type": "code",
      "source": "fig = plt.figure()\nax = fig.add_subplot(1,1,1) \nax.set_xticks(sp.linspace(0-.5, train_vec_x.shape[1]-.5, train_vec_x.shape[1]+1), minor=True)\nax.set_yticks(sp.linspace(0-.5, train_vec_x.shape[0]-.5, train_vec_x.shape[0]+1), minor=True)\nax.matshow(train_vec_x, vmin=-1, vmax=1)\nax.grid(True, which='minor')\n# plt.colorbar()\nplt.show()",
      "execution_count": 230,
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/plain": "<Figure size 432x288 with 1 Axes>"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "plt.matshow(W, vmin=-1, vmax=1)\nplt.colorbar()",
      "execution_count": 231,
      "outputs": [
        {
          "data": {
            "text/plain": "<matplotlib.colorbar.Colorbar at 0x26036891eb8>"
          },
          "execution_count": 231,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": "<Figure size 288x288 with 2 Axes>"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "fig = plt.figure()\nax = fig.add_subplot(1,1,1) \nax.set_xticks(sp.linspace(0-.5, vec_x.shape[1]-.5, vec_x.shape[1]+1), minor=True)\nax.set_yticks(sp.linspace(0-.5, vec_x.shape[0]-.5, vec_x.shape[0]+1), minor=True)\nax.matshow(vec_x, vmin=-1, vmax=1)\nax.grid(True, which='minor')\n# plt.colorbar()\nplt.show()",
      "execution_count": 236,
      "outputs": [
        {
          "data": {
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            "text/plain": "<Figure size 432x288 with 1 Axes>"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
    }
  ],
  "metadata": {
    "hide_input": false,
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3",
      "language": "python"
    },
    "language_info": {
      "name": "python",
      "version": "3.7.0",
      "mimetype": "text/x-python",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "pygments_lexer": "ipython3",
      "nbconvert_exporter": "python",
      "file_extension": ".py"
    },
    "toc": {
      "nav_menu": {},
      "number_sections": true,
      "sideBar": true,
      "skip_h1_title": false,
      "base_numbering": 1,
      "title_cell": "Table of Contents",
      "title_sidebar": "Contents",
      "toc_cell": false,
      "toc_position": {
        "height": "calc(100% - 180px)",
        "left": "10px",
        "top": "150px",
        "width": "165px"
      },
      "toc_section_display": true,
      "toc_window_display": true
    },
    "gist": {
      "id": "",
      "data": {
        "description": "ホップフィールドネットワーク",
        "public": true
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 2
 }