kernel_kmeans.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "kernel_kmeans.ipynb",
      "version": "0.3.2",
      "provenance": []
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 2
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython2",
      "version": "2.7.14"
    },
    "kernelspec": {
      "display_name": "Python [conda env:anaconda]",
      "language": "python",
      "name": "conda-env-anaconda-py"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZDFW4TaPtFNR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "sns.set(style=\"whitegrid\", palette=\"muted\", color_codes=True)\n",
        "sns.set_style(\"whitegrid\", {'grid.linestyle': '--'})\n",
        "red = sns.xkcd_rgb[\"light red\"]\n",
        "green = sns.xkcd_rgb[\"medium green\"]\n",
        "blue = sns.xkcd_rgb[\"denim blue\"]\n",
        "\n",
        "from pylab import rcParams\n",
        "rcParams['figure.figsize'] = 6, 6\n",
        "rcParams['font.size'] = 20"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TsjJdT_gtFNa",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 420
        },
        "outputId": "57abcdf2-67f8-47c1-95a8-f10c573247f1"
      },
      "source": [
        "theta = np.linspace(-2*np.pi, 2*np.pi, 50)\n",
        "X1 = np.cos(theta)\n",
        "Y1 = np.sin(theta)\n",
        "X2 = 7 * np.cos(theta)\n",
        "Y2 = 7 * np.sin(theta)\n",
        "\n",
        "\n",
        "plt.scatter(X1, Y1, s=20, c='blue', alpha=0.5, marker=\"x\")\n",
        "plt.scatter(X2, Y2, s=20, c='red', alpha=0.5)"
      ],
      "execution_count": 122,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f341aa8d9b0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 122
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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LPxSylU9bWFhoSDB5JLkCsnwluQKyfOnqPpkX8Lu7beXTlpWVGZCbGJJcAVm+klwBWb50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\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UsP6gvZ_tFNh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 74
        },
        "outputId": "297bfa9c-3cf8-4060-8010-ad9bfc281812"
      },
      "source": [
        "data = np.concatenate((np.concatenate((X1.reshape(50,1), Y1.reshape(50,1)), axis = 1),\n",
        "                       np.concatenate((X2.reshape(50,1), Y2.reshape(50,1)), axis = 1)), axis = 0)\n",
        "data.shape"
      ],
      "execution_count": 123,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(100, 2)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 123
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H9-gBX_atFNw",
        "colab_type": "text"
      },
      "source": [
        "### Kernel Kmeans\n",
        "- Seperate E-step and M-step"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AMg71QBktFNw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class Kernel_Kmeans(object):\n",
        "    \n",
        "    def __init__(self, n_clusters=3, max_iter=500, kernel=\"linear\",\n",
        "                gamma=None, degree=3, coef0=1, kernel_params=None):\n",
        "      \n",
        "        self.n_clusters = n_clusters\n",
        "        self.max_iter = max_iter\n",
        "        self.kernel = kernel\n",
        "        self.gamma = gamma\n",
        "        self.degree = degree\n",
        "        self.coef0 = coef0\n",
        "        self.kernel_params = kernel_params\n",
        "    \n",
        "    \n",
        "    def kernel_matrix(self, X, Y = None):\n",
        "        if callable(self.kernel):\n",
        "            prams = self.kernel_params or {}\n",
        "        else:\n",
        "            params = {\"gamma\": self.gamma,\n",
        "                      \"degree\": self.degree,\n",
        "                      \"coef0\": self.coef0}\n",
        "            \n",
        "        return pairwise_kernels(X, Y, metric = self.kernel,\n",
        "                                filter_params = True, **params)\n",
        "        \n",
        "        \n",
        "    def initialize_cluster(self):\n",
        "        self.labels = np.random.choice(range(self.n_clusters), self.num)\n",
        "        self.cluster_size = np.bincount(self.labels)\n",
        "        \n",
        "    \n",
        "    def distance(self):\n",
        "        self.distance_box = np.zeros((self.num, self.n_clusters))\n",
        "        for i in range(self.num):\n",
        "            for j in range(self.n_clusters):\n",
        "                tmp_data = self.X[self.labels == j]\n",
        "                tmp_xm = np.sum(self.kernel_matrix(tmp_data, Y = self.X[i].reshape(1, self.X.shape[1])))/self.cluster_size[j]\n",
        "                tmp_mm = np.sum(self.kernel_matrix(tmp_data))/(self.cluster_size[j]**2)\n",
        "                self.distance_box[i,j] = tmp_mm - 2*tmp_xm\n",
        "    \n",
        "    \n",
        "    def assign(self):\n",
        "        self.labels = np.argmin(self.distance_box, axis = 1)\n",
        "        self.cluster_size = np.bincount(self.labels)\n",
        "\n",
        "    \n",
        "    def fit(self, data):\n",
        "        self.X = data\n",
        "        self.num = self.X.shape[0]\n",
        "        self.initialize_cluster()\n",
        "        for ite in range(self.max_iter):\n",
        "            # if np.size(self.cluster_size) == 1:\n",
        "            #    break\n",
        "            self.distance()\n",
        "            self.assign()\n",
        "\n",
        "    def plot(self, X):\n",
        "        for i in range(self.n_clusters):\n",
        "            mask = kkm.labels == i\n",
        "            plt.scatter(X[mask][:,0], X[mask][:,1], s=30, alpha=0.5, marker=\"+\")  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sGjLOwF-1ggq",
        "colab_type": "text"
      },
      "source": [
        "### pairwise_kernelsについて\n",
        "\n",
        "kernel-matrixを計算する関数\n",
        "- https://scikit-learn.org/stable/modules/generated/sklearn.metrics.pairwise.pairwise_kernels.html#sklearn.metrics.pairwise.pairwise_kernels\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9Gm00xGm1s4-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 107
        },
        "outputId": "3c593b4b-da55-402b-84ed-48f83368dc0a"
      },
      "source": [
        "X = np.array([[2, 3], [3, 5], [5, 8]])\n",
        "Y = np.array([[1, 0], [2, 1]])\n",
        "\n",
        "pairwise_kernels(X, Y, metric='linear')"
      ],
      "execution_count": 125,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 2.,  7.],\n",
              "       [ 3., 11.],\n",
              "       [ 5., 18.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 125
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eGno_3Or0xbX",
        "colab_type": "text"
      },
      "source": [
        "### Linear\n",
        "\n",
        "$$\n",
        "k(x, y)=x^{\\top} y\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4bMbVCFLtFNz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 403
        },
        "outputId": "d39669f7-7a45-4171-9246-7b1214e942c5"
      },
      "source": [
        "kkm = Kernel_Kmeans(n_clusters=2, kernel=\"linear\")\n",
        "kkm.fit(data)\n",
        "kkm.plot(data)"
      ],
      "execution_count": 126,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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m9Pb2Zm5/5vP50N7ejng8Pm91vUI9plgsZusxAdD+mFKplKPfJ5WPCYCW557Kx6Tr5yn7\nMSWTycw23P6Yslvd8H0aHBxErhy9Smfbtm1455138Pjjj6O8vNzW17j9Bij9/f1oamrSnWELW9Vg\nqzqSet3WqvUGKD/96U/R09ODxx57zPZgL0H2rMDt2KoGW9WR1JtPq1vWx3fkkM57772HX/7yl1i3\nbh2uu+46AMCaNWvw2GOPObF5IiJygCMD/rnnnot33nnHiU0RERUNY1Y/PJaa976uVTW5tIKFtrY2\n3Qm2sVUNtqojqVdSqxmuh28hmUyKOSfBVjXYqo6k3qW0uu1OWJzhW8i+bMvt2KoGW9WR1Cup1Qxn\n+EREiume2Rs4wyci8ggO+BYaGxt1J9jGVjXYqo6kXkmtZopuwHf67la1tbWObUs1tqrBVnUk9Upq\nNVN0A77TstfVcDu2qsFWdST1Smo1UzQnbU+/u5XxPu9uRUQ0hzN8IiKPKJoZvjGTd3pmHwgEHNlO\nIbBVDbaqI6lXUqsZzvAtNDc3606wja1qsFUdSb2SWs0U3YC/lPvWLiYWizm2LdXYqgZb1ZHUK6nV\nTNEN+E7LvnOP27HVOdnrl7+6+7gr1jK3w+379XSSeiW1mimaY/hETrAa2E//d7e8ZJ7IDg745HnZ\nKxnuPTgJAAgGfOiLn8Deg5PoHyzB8kAK3ZGj2HtwEheuqzT9eiI7dD1nOOBb6Ojo0J1gG1vtO/0H\nzhjoxydPZf6bOJZCoLIMVVVV6IufwMj4NGKDycznGIxfAm4Y+HXv11xJ6pXUaoYDvoVEIiHmJdVs\ntZZ9SMYY5IfHUhifPJV5P9ywHCPj0whUluHWL67Ff/5XPwZGS3Hhusp5g/2RYynsPTiJ8clTGB5L\nYWR8GoDeAV/ScwCQ1etEq+47YHHAtzAwMCDmCclWa9mHbIxBfnzyFMINy1FfXY69BydRX12O+uoP\nb3QxOjqKC9etO+OH0pjZv753HH3xE5mPZx/6KfTgL+k5AMjqldRqhgM+ecLDfzwEYP4hGwC4cF1l\nZpDPHpyz3/7YujQ6Fhi4jQE9+5cI0WJ03wGLAz55SrhhOQCYHn6x+gFc6N+zT+IavzyCAR+Gx1KZ\nXzS3fnFtXt1ETuCAbyEcDutOsI2tZzIGXGP2bQz02YO01SBv1Xr6rE0nSc8BQFavk626zvNwwLfg\n9/t1J9jGVvty+YGz29rZUZPZ7um/aAo109e9X3MlqVdSqxm+0tbCnj17dCfYxtYP/ev5HfjX8zsQ\nDPgQDPgwMj6NkfFp3PrFtTkPutyv6kjqldRqhgM+kQLGLxbjF41xVdDDfzzkikM/5E1Fc0iHNzwh\nYO55cOrQXpw7NYGy+nOAY/8AAHzsi/9HcxmRfpzhWwgGg7oTbGOrGvm03vrFtbhwXWXmZLFx7b+q\nWb6k/QrI6pXUakb8DF/1rQ2bmpoc2U4heL3V+N6XrqzFbPI4ZicSuHBdXd7PBa/vV5Uk9UpqNcMZ\nvoXe3l7dCbaxFTh1aC9ODfc5us18Wzs7anDhukoEKufmV8aVOypm+ZKeA4CsXkmtZsTP8FXd2tCQ\nTCYd3Z5KXm81vvenDu1F2doLHXsuON1qLMR2+qqbTpD0HABk9UpqNSN+wCcCPjxZO5ucADA36APu\nOYlvXKOvc50doqIZ8FX9YPt8ctZHYeucsvpzUFpV59j2nGo1BntjdU0V66lIeg4AsnoltZopSafT\naZ0BU1NT6Onpwfr161FRUaEzhYTKPnF/argPpf5Vjh7ScUr20rh98RMIVJZxpk9LtpSx07GTtgcO\nHMC1116LjRs34tprr8XBgwed2rRW8Xhcd4JtXm89NdyH2eMJx7frVKtxWKe+ulzZYC/pOQDI6pXU\nasaxAf+uu+7CDTfcgJdeegk33HADfvCDHzi1aa2GhoZ0J9jm1daK9k5UtHfOzez/VxiVV97q6Oze\nyVbjsM6/3juOHX9PzLtZuhMkPQcAWb1Otz78x0OZNZYKxZEBf3R0FPv27UNXVxcAoKurC/v27cPR\no3wJOak3Fe3GVLQbs8kJzCYnMu+71YXrKrHSXzSnz0gQR551Q0NDqK+vx7JlywAAy5YtQ11dHYaG\nhlBTw+OTRAbjZilT07Pz3udxfO8wZvXx0al57xfingmumWb09PRk3m5paQEA7N+/P/OxUCiEhoYG\nRKNRTE/PvUzd7/ejtbUV/f39GBkZyXxuW1sbkskk+vo+fAFOY2MjamtrEYlEMh8LBAJobm5GLBbD\n+Ph45uMdHR1IJBIYGBgAAEQiEYTDYfj9/nkr5gWDQTQ1NaG3tzdzja7P50N7ezvi8fi8PwEL9Zhi\nsZitxwRA+2NKpVLOfJ+m5wbLYDKFVatWoqLl03OP6d/byPcxrV69GgAc+T6NjMz9UX38g1IsK1uG\n8ePjmE5NIxI54sj3qaWlRdtzz+7PU/ZjApDZhht/nrIfU3ZrPt+no0fLUFNTg6mpKaRS0xhJz11K\nPDlZk9NjGhwcRK4cuUpndHQUGzduxJtvvolly5ZhZmYGl1xyCV5++WXLGb7br9KZnJxEZaXzL5BR\nwautxuGbk/98HgBw1sVXAXDuUl0V+/X//XJuAHngG82OblfScwCQ1et0a74ze21X6axevRqtra34\n85//DAD485//jNbW1qI4nJP929btvN5auqoWpaucv8m0k63GSdrk1AySUzOOn7SV9BwAZPVKajXj\n2CGdu+++G7fffjt+/vOfY9WqVdi2bZtTmyayqUR3gC17D06irqo8c39d8iYd9zl2bMAPh8P4wx/+\n4NTmiJZk9viRzFo6bmScnDVuds6TtVRIrjlp61ahUEh3gm1ebc0+Vu/0wmmAc63ZSysAaq7QkfQc\nAGT1Smo1wwHfQkNDg+4E27zc+uHiaceReucNRwd+Ffs13LAc9dXljm9X0nMAkNUrqdVM0ayHr+rF\nNtFo1PFtquL11rK1F6KsPuz4dp1oNU7MGmvhG3fAcvqQjqTnACCrV1KrmaIZ8FUxrn2VwMutxkx+\ndiIBoASlK+eu1nFiEuBU696Dk+iLn3BkW2YkPQcAWb2SWs2IP6Sj+haHJNOp4fdROpFwzcnb7JO1\nXCGTdBE/4KtmvBpQAq+3GouoGcfznTqGn29rd+QoVg/+N3yTpzA+3aF0OQVJzwFAVq+kVjNFsx4+\nZ/YEzD95W1Yf/vchHqDyylu1NRkD/vHJU/if2ssyJ2s5y6d8aF0Pv1j19/frTrCNrXOcPnmbT+vk\nCw/j0sNPobVqErWlx3BB8h/Y4IsoG+wlPQcAWb2SWs0UzYBv/DnvtOwFl9yOrR8+D2YnEpidSKB0\nZS1KV9Zi8oWHMfnCw0vaJverOpJ6JbWa4TF8IgWMXy7G1UKzEwmsWwFUXnmTzizyOA74VJSMY/an\nD7zG+yqO6fM8ErkdB3wLbW1tuhNsY6t9uQzOubSeOrQXwPyZPVC4k8a692uuJPU62Wq8EK/QJ+45\n4FtIJpMoL3f+JfAqsPVMZjN9Y2A2LuM03l7IQq3ZX5O97dnk8X9fJTSBsvpzHH401iQ9BwBZvZJa\nzRTNSVtVsu+I43ZstXZq+H2cGn4fs8njmE0ez1zGaTCW6MheqmP4v5/NvG21hEdZfRhlay9EqX8l\nSqvqUHnlrQW9JFTScwCQ1etEq3H/g+GxFIbHUo7fD8EKZ/jkCQvN9E8N92Vm47PHjsx7wZaZ7EM2\n2V9fVn9O5vDN8g3/V/GjIVoaDvjkKdmDubH0wuyxI5mlGE4d7sNs8jiAksza+pXDh5CaiuPUob04\ndbgPpavq5v5COJ5AqX/Vgv8fnrilhRjH7HkM36UaGxt1J9jGVmvGQDwV7c4svTAV7f5w8E8eP+Nr\nlvs/vDNV6aq6zGy+1L8KlVfemjnE44aZvaTnACCrV1KrGQ74Fmprnb9Hqipste/0GbjZujsV7Z0o\nyzpBawzupVV16iOXQPd+zZWkXidbdS2rwZO2FiKRiO4E29i6NFav0j548MyX1Gd/japXeS+Fm/ar\nHZJ6JbWa4QyfKMtCA/cHZ/9vVLR3mP47kRRFN8NXdecrIiLpim7Ad1ogENCdYBtb1WCrOpJ6JbWa\nKbr18I07Xxkn1fgnOBEVI66Hr0AsFtOdYBtb1WCrOpJ6JbWaKZqTttnXV2e/n6/x8XFHtlMIbFWD\nrepI6pXUaoYzfCIijyiaGb6Bx+yJiBZWNCdtiYi8hCdtFUgkEroTbGOrGmxVR1KvpFYzHPAtDAwM\n6E6wja1qsFUdSb2SWs1wwCciUqzQNzoxwwGfiMgjiu4qHaeFw2HdCbaxVQ22qiOpdymtxqx+eCw1\n731dyyPnPeDfc889eOONN1BeXg6/34/vf//7ou5Eb8Xv9+tOsI2tarBVHUm9klrN5H1IZ8OGDdi5\ncyeef/55fOMb38B3vvMdJ7pcY8+ePboTbGOrGmxVR1LvUlo7O2rQ2VGD+upy1FeXZ97XJe8Z/uWX\nX555+6KLLsLhw4cxOzuL0lKeHiAichNHj+Fv374dn/nMZzjYExFl0Tmrz2Y54F9zzTWIx+ML/tvr\nr7+OZcuWAQBeeOEF7Ny5E9u3b19SSE9PT+btlpYWAMD+/fszHwuFQmhoaEA0GsX09DSAuWNqra2t\n6O/vx8jISOZz29rakEwm0dfXl/lYY2Mjamtr592mLBAIoLm5GbFYbN7CSB0dHUgkEpnrbiORCMLh\nMPx+/7w/64LBIJqamtDb24tkMgkA8Pl8aG9vRzwex9DQUMEfUywWs/WYAGh/TKlUytHvk6rHtHz5\n3E3MdTz3cn1MwWBQ23NvKY8J+PDWgW78ecp+TNmtbvh5GhwcRK4cWVqhu7sb27Ztw5NPPok1a9bk\n9LVcWoGIKHdallZ49dVXcd999+HXv/51zoN9oeRz28Pe3l6Ha9RhqxpsVUdSr6RWM3kfw//e974H\nn8+Hb3/725mPPfnkk6iurs53065g/BkmAVvVYKs6knoltZrJe8D/xz/+4USHEqff9tDpm6MQEUnC\ny2ks+Hw+3Qm2sVUNtqojqVdSqxlPrIfPmT0RFRuuh6+A2SWpbsRWNdiqjqReSa1mPDHgV7R3Lnl2\nn32drNuxVQ22qiOpV1KrGU8M+ERExAGfiMgzOOBbMF7uLAFb1WCrOpJ67bS65c5WZjjgExF5BAd8\nC9kLGbkdW9VgqzqSehdrNWb2w2MpDI+lXDvT54BPROQRvKctEVGejPXudd+z1gpn+BZCoZDuBNvY\nqgZb1ZHUK6nVjCeWViAiKjZcWkGBaDSqO8E2tqrBVnUk9UpqNeP5Ad/q5ijGbcUkYKsabFVHUq+k\nVjOeH/CJiLzCs1fp2L05inGjZQnYqgZb1ZHUK6nVDGf4FlpbW3Un2MZWNdiqjqReSa1mPDvgG0sm\nl1bVobSqznQJ5f7+fg11S8NWNdiqjqReSa1mPDvg2zUyMqI7wTa2qsFWdST1Smo149lj+Abe9pCI\nvIIzfCIij+ArbS2kUimUl5frzrCFrWqwVR1JvW5r5SttFUgmk7oTbGOrGmxVR1JvMpl07bLHdnHA\nt9DX16c7wTa2qsFWdST1Smo14/mTtkREVrojR3HwYAmWB1KZ9wH3LoNshjN8IiKP4AzfQmNjo+4E\n29iqBlvVkdLb2VGDROMM3h5YlnlfIs7wLdTW1upOsI2tarBVHUm9klrNcMC3EIlEdCfYxlY12KqO\npN5IJILOjhqxs3uAAz4RkWdwwLfJ6kYpRERuxwHfQiAQ0J1gG1vVYKs6knoltZpxbMB/88030dra\nimeeecapTbrC2uQBTEW7MXvsCGaPHXH1TL+5uVl3gm1sVUNSKyCrV1KrGUcG/A8++AAPPvggNmzY\n4MTmXOXI8BHdCbbFYjHdCbaxVQ1JrYCsXkmtZhwZ8O+//37ceOONqK6udmJzrnKkpsXWjVLcYHx8\nXHeCbWxVQ1IrIKtXUquZvAf81157DRMTE9i0aZMTPUREpIjlK22vueYaxOPxBf/txRdfxEMPPYQn\nnngi75Cenp7M2y0tLQCA/fv3Zz4WCoXQ0NCAaDSK6elpAHM3FW5tbUV/f/+8u9G0tbUhmUzOW+yo\nsbERtbW18677DQQCaG5uRiwWm/fbu6OjA4lEAgMDAwDmrr8Nhy+G3++f9/XBYBBNTU3o7e3NrPrn\n8/nQ3t6OeDyOoaGhgj+mWCxm6zEBQDgcht/vx549e7Q8plQq5ej3SdVjMuh47uX6mABoe+4t5TEB\nH16L78afp+zHlN3qhp+nwcGDns8CAAANLElEQVRB5Cqv9fB37dqFb33rW1i+fDkAYGxsDOXl5fjK\nV76CrVu32tqG29fDJ6LiZlyE4dZDtWaWMnbmtZbOxz/+cbzxxhuZ92+//XasX78eW7ZsyWezrpJI\nJMS8pJqtarBVHUm9klrN8Dp8C9l/srkdW9Vgqzo6e41LrO1eci1t3y7E0dUy77//fic3R0REDuLy\nyETkScYxe6nH8JeCh3QshMNh3Qm2sVUNtqojqVdSqxnO8C0Yl45JwFY12KqOG3rtzuzd0JovzvAt\nZF9T63ZsVYOt6kjqldRqhgO+Am5eYI2IvIsDPhGRR/AYvoVgMGj7c41Z/eyxI/PeL9TZ/1xadWOr\nGpJaAVm9klrNcIZvoampSXeCbWxVg63qSOqV1GqGA76F3t5e259rLJ2saynlXFp1Y6sakloBWb2S\nWs1wwLdgrHAnAVvVYKs6knoltZrhMXwFvPCKPSKShzN8C8Ya4xKwVQ22qqOiV9Vl0dL27ULyWg/f\nCVwPn4ic5JW1cZYydnKGb8Hsbl9uxFY12KqOk725LnecK2n7diEc8C1k34LM7diqBlvVkdQrqdUM\nT9oSUVHw4nLHueIMn4jIIzjDt2DcSb4Q8p2ZFLI1X2xVQ1IroKZX1cxe2r5dCGf4REQewQHfwv79\n+5X/P5y6uqAQrU5hqxqSWgFZvZJazXDAJyLyCB7DdwFeXUBEhcAZvoVQKKQ7wTa2qsFWdST1Smo1\nw6UViMh1+NeuNS6toEA0GtWdYBtb1WCrOpJ6JbWa4TF8C9PT07oTbGOrGmxV5/Re3bcJXYy0fbsQ\nzvCJiDyCM3wLfr9fd4JtbFWDreqc3uvmK9ak7duF8KQtEbmOGwd8t+FJWwX6+/t1J9gyFe1G/JX/\n0J1hm5T9CrBVJbPeivZO1w320vbtQjjgWxgZGdGdYNvEBx/oTrBN0n5lqzqSeiW1muExfOGyr2rw\nnRjjn8JEZIozfCIij+BJWwupVArl5eW6MyxNRbtx6tQMKj+2SXeKLVL2K8BWlST1uq11KWOnI4d0\nnn76aWzfvh0+nw+lpaV47rnnnNisKySTSVd9kxeTSk2hUneETZL2K1uXxs7hRTf1WpHUaibvQzov\nv/wyXnzxRTz77LPYuXMnfv3rXzvR5Rp9fX26E2ypaO/E+741ujNsk7JfAbaqJKlXUquZvGf4v/nN\nb3DLLbdgxYoVAIBgMJh3FBHJ5eblEbwu7wG/r68Pu3fvxiOPPIJUKoXrrrsOX/7yl3PeTk9PT+Zt\n496R2XeYCYVCaGhoQDQazaxp4ff70draiv7+/nmXTLW1tSGZTM77jdzY2Ija2lpEIpHMxwKBAJqb\nmxGLxTA+Pp75eEdHBxKJBAYGBgAAkUgE4XAYfr8fe/bsyXxeMBhEU1MTent7kUwmAQA+nw/t7e2I\nx+MYGhoq+GOKxWK2HhMA7Y8plUo5+n1S9ZgMOp57uT4mANqee8ZjOjJ8BMkTJ+A7MQYAOLuqDhMT\nE+jJ+lzjMQHIbMONP0/Z36fsVjf8PA0ODiJXlidtr7nmGsTj8QX/7fXXX8fFF1+MzZs346677sLY\n2Biuv/56/OhHP8LFF19sK8DtJ20TiQRqa2t1Z9jCVjXYujR2ZvZu6rXitlYlJ23/9Kc/LfrvDQ0N\n6OrqQmlpKVavXo1LL70U0WjU9oDvdm76BlvJp7XQf3Z7Zb8WmqRWQFavpFYzeZ+07erqwl//+lcA\nc2exI5FI5k+TYpD9553bsVUNti6NneUR3NRrRVKrmbyP4X/1q1/FnXfeiSuvvBIAcPXVV+NTn/pU\n3mFUGDzBRuQdeQ/4Z511Fh544AEnWoiISCGupWMhEAjoTrBtKa261h8v9v2qixOthXwueG3f6sa1\ndCw0NzfrTrCNrWqwVR1JvZJazXDAt2BcfytBPq2FXn/cK/u10PJpnYp2YyrajdljRzB77EjmfZW8\nsm/dggO+hewXxbidG1rtDhJuaLWLrepI6pXUaobH8IkIgLvvJ0vO4IBPjuDlnUTux/XwyRGnD/il\nVXUAOOAXEn/JegtvYq5AIpHQnWCbzlbjpG9pVR1Kq+osTwJzv6oxMTGhOyEnkvatpFYzHPAtZK+G\n53ZsVcPtrdlX1xz/n76CXF3jFLfv22ySWs3wGD45ysnDCTxEQeQsDvhEwmVfXTN97AR/QZIpDvgW\nwuGw7gTbiqXVbVf8qNyvTj+2ujpZS/gWy3NWCg74Foy78kjAVnP5DKynt+r+BWSmor0TJamU7oyc\n8DlbWDxpayH7dmVuVyytuV7xo5qK/apqGQNJzwFAVq+kVjOc4VNRc/LwkNsONRHligM+uVYxD6Rc\nxoB04IBvIRgM6k6wja1ncmJgNVolDNKSngOArF5JrWY44FtoamrSnWAbW9VQ2er0Lw1J+xWQ1Sup\n1QxP2lro7e3VnWAbW83lc+L39FbdJ5EXI+k5AMjqldRqhgO+hWQyqTvBNraqwVZ1JPVKajXDAZ+I\nyCM44Fvw+Xy6E2xjqxpsVUdSr6RWM1wPn4hIIK6Hr0A8HtedYBtb1WCrOpJ6JbWa4YBvYWhoSHeC\nbWxVg63qSOqV1GqGAz4RkUdwwCci8ggO+BZaWlp0J9jGVjXYqo6kXkmtZjjgExF5BAd8C/v379ed\nYBtb1WCrOpJ6JbWa4YBPROQR2lfLNF73lXLxrdmmpqZ0J9jGVjXYqo6kXje1GmNmLq+d1f5K24mJ\nCbz77rs6E4iIxDrvvPOwcuVKW5+rfcCfnZ3F5OQkfD4fSkpKdKYQEYmRTqcxPT2NyspKlJbaOzqv\nfcAnIqLC4ElbIiKP4IBPROQRHPCJiDyCAz4RkUdwwCci8ggO+EREHsEBn4jIIzjg2/T0009j06ZN\n2Lx5M66++mrdOZbefPNNtLa24plnntGdYuqee+7Bpk2bcNVVV+G6667Dnj17dCed4cCBA7j22mux\nceNGXHvttTh48KDupAWNjY3h61//OjZu3IjNmzdj69atOHr0qO4sS48++ijOP/98V7/afmpqCnfd\ndRc+97nPYfPmzbjzzjt1Jy2Z9rV0JHj55Zfx4osv4tlnn8WKFSswMjKiO2lRH3zwAR588EFs2LBB\nd8qiNmzYgDvuuAM+nw+vvvoqvvOd7+Avf/mL7qx57rrrLtxwww24+uqr8dxzz+EHP/gBnnrqKd1Z\nZygpKcFNN92ESy65BACwbds2PPjgg/jxj3+suczc3r178fbbb+Pss8/WnbKoBx54ABUVFXjppZdQ\nUlLi+p//xXCGb8NvfvMbbN26FStWrAAABINBzUWLu//++3HjjTeiurpad8qiLr/8cvh8PgDARRdd\nhMOHD2N2dlZz1YdGR0exb98+dHV1AQC6urqwb98+V86cq6qqMoM9MLc/3XzT7VQqhR/+8Ie4++67\ndacsanJyEjt27MAtt9ySWfrF7T//i+GAb0NfXx92796N6667Dl/4whfw+9//XneSqddeew0TExPY\ntGmT7pScbN++HZ/5zGdsrwlSCENDQ6ivr8eyZcsAAMuWLUNdXZ3rb2Y9OzuL3/3ud7jiiit0p5h6\n5JFHcNVVV2HNmjW6UxZ16NAhVFVV4dFHH8UXvvAFfOUrX8GuXbt0Zy0ZD+kAuOaaa0xnQ6+//jpm\nZmYwNDSE3/72txgbG8P111+Pj3zkI7j44osLXLp464svvoiHHnoITzzxRIGrFma1X42B9IUXXsDO\nnTuxffv2QuYVrXvvvRd+vx9btmzRnbKgt956Cz09Pfjud7+rO8XSzMwMDh06hAsuuAC33XYbdu/e\njW9+85vo7u7O/MUvCQd8AH/6058W/feGhgZ0dXWhtLQUq1evxqWXXopoNKplwF+sddeuXUgkEvjS\nl74EYO5E3quvvopjx45h69athUrMsNqvANDd3Y2f/exnePLJJ133p3IoFMLw8DBmZmawbNkyzMzM\n4MiRIwiFQrrTTG3btg39/f14/PHHXfXXUrZ//vOf6Ovrw2c/+1kAwOHDh3HjjTfivvvuw2WXXaa5\nbr5QKISysrLMYb2PfvSjqK6uxoEDB9DW1qa5bgnSZOkXv/hF+qGHHkqn0+n05ORkuqurK/23v/1N\nc5W12267Lf3000/rzjD1yiuvpC+//PL0wYMHdaeY2rJlS3rHjh3pdDqd3rFjR3rLli2ai8w99NBD\n6S1btqSTyaTulJxcfvnl6XfeeUd3hqmvfe1r6b/+9a/pdDqdfv/999Of+MQn0uPj45qrlobLI9tw\n8uRJ3Hnnndi3bx8A4Oqrr8bNN9+sucra7bffjvXr17v2T/tPfvKT8Pl8qKmpyXzsySefdNXJ5r6+\nPtx+++04fvw4Vq1ahW3btuGcc87RnXWG9957D11dXVi3bh3OOussAMCaNWvw2GOPaS6zdsUVV+Dx\nxx/HeeedpztlQYcOHcIdd9yBY8eOoaysDLfeeis+/elP685aEg74REQe4c6DfERE5DgO+EREHsEB\nn4jIIzjgExF5BAd8IiKP4IBPROQRHPCJiDyCAz4RkUf8f15wdhJonhFTAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Yh8QI6yI1IXz",
        "colab_type": "text"
      },
      "source": [
        "### RBF\n",
        "\n",
        "$$\n",
        "k(x, y)=\\exp \\left(-\\gamma\\|x-y\\|^{2}\\right)\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PSssrVvGtFNx",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 403
        },
        "outputId": "c7dd6209-e803-4ffc-8f58-e71c4115fd10"
      },
      "source": [
        "kkm = Kernel_Kmeans(n_clusters=2, kernel=\"rbf\")\n",
        "kkm.fit(data)\n",
        "kkm.plot(data)"
      ],
      "execution_count": 127,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Wr1IraPUqtYJer5c5V/i33HILAwMDnv/trbfeYsmSJQC8+uqrvPLKK7z00ksL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\nGGNKxP8Hgf6xPNtkq3EAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fi_W14sc1CRQ",
        "colab_type": "text"
      },
      "source": [
        "### Sigmoid\n",
        "\n",
        "$$\n",
        "k(x, y)=\\tanh \\left(\\gamma x^{\\top} y+c_{0}\\right)\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G4nOx7fPtFN0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "outputId": "af419a99-3691-4412-aef9-0b60776ea648"
      },
      "source": [
        "kkm = Kernel_Kmeans(n_clusters=2, kernel=\"sigmoid\")\n",
        "kkm.fit(data)\n",
        "kkm.plot(data)"
      ],
      "execution_count": 128,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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VYKsabNUnpQd8IiL6Cgd8IiKH4IBvwrjrzQ7YqgZb1UjFVqs92coMB3wiIofg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\njgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SZQnhdIltFN_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}