newtSNE.ipynb

newtsne.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "newtSNE.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "[View in Colaboratory](https://colab.research.google.com/gist/NTT123/4027fe14797374fb76d166559057905c/newtsne.ipynb)"
      ]
    },
    {
      "metadata": {
        "id": "nfAoW9ifHJAO",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# t-distributed stochastic neighbor embedding\n"
      ]
    },
    {
      "metadata": {
        "id": "tM_L5VlzHMrX",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Introduction\n"
      ]
    },
    {
      "metadata": {
        "id": "3roVr-qMHO-0",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "t-SNE is an algorithm for visualizing data developed by Laurens van der Maaten and Geoffrey Hinton.\n",
        "\n",
        "At its core, t-SNE learns a function mapping a high-dimensional space to a low-dimensional space such that the distances between data points are preserved as much as possible.  \n",
        "\n",
        "This is essentially the same as Principal Component Analysis (PCA), except that t-SNE learns a complex and non-linear function.\n",
        "\n",
        "Let $x_1, x_2, \\dots, x_n$ be the set of $n$ points in a high dimensional space $X$, and $y_1, y_2, \\dots, y_n$ be the corresponding points in a low dimensional space $Y$.\n",
        "\n",
        "t-SNE defines two probability distributions which model the closeness between of points in  $X$ and $Y$.\n",
        "\n",
        "For space $X$, it defines a joint distribution of two points $x_i$ and $x_j$ as follows:\n",
        "\n",
        "$$\n",
        "P(j \\mid i) = \\frac{\\exp\\left(-\\frac{\\|x_i - x_j\\|^2}{2\\sigma_i^2}\\right)}{\\sum_{k \\neq i}{\\exp\\left(-\\frac{\\|x_i - x_j\\|^2}{2\\sigma_i^2}\\right)}}\n",
        "$$\n",
        "\n",
        "So,  the conditional probability of $x_j$ given $x_i$ is also depened on the distance between $x_i$ and all other points.\n",
        "\n",
        "The joint distribution is then defined:\n",
        "\n",
        "$$\n",
        "P(i, j) = \\frac{P(i\\mid j) + P(j \\mid i)}{2n}\n",
        "$$\n",
        "\n",
        "For space Y, it defined a joint distribution of $y_i$ and $y_j$ as follows:\n",
        "\n",
        "$$\n",
        "Q(i, j) = \\frac{\\left(1 + \\| y_i - y_j\\|^2\\right)^{-1}}{\\sum_{k \\neq l}\\left(1 + \\| y_k - y_l\\|^2\\right)^{-1}  }\n",
        "$$\n",
        "\n",
        "Then, to determine $y_i$, we need to minimize the $KL$ distance:\n",
        "$$\n",
        "D_{KL} (P \\| Q) = \\sum_{i \\neq j} P(i, j) \\cdot \\log \\frac{P(i, j)}{Q(i,j)} \n",
        "$$\n",
        "\n",
        "The gradient of the loss function is \n",
        "\n",
        "$$\n",
        "\\frac{\\partial D_{KL}}{\\partial y_i} = 4\\sum_j (\\tau  \\times P(i, j) - Q(i, j) ) (y_i - y_j)  (1 + \\| y_i - y_j\\|^2)^{-1}\n",
        "$$\n",
        "where  $\\tau = 1$ in the original formula.\n",
        "\n",
        "**The authors suggest setting $\\tau = 4$ at the first $50$ gradient steps which helps very much in creating seperated clusters of points. \n",
        "Here I propose to gradually decreasing  $\\tau$ from $6$ to $1$. This method seems to be helpful with MNIST dataset.**"
      ]
    },
    {
      "metadata": {
        "id": "pp4qnSffGyKC",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "##  Experiments"
      ]
    },
    {
      "metadata": {
        "id": "uXNXOZE3GXpy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "7b616310-c24f-4e9d-c3b0-7043142c1860"
      },
      "cell_type": "code",
      "source": [
        "#@title\n",
        "!apt install ffmpeg -y > /dev/null 2>&1"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "metadata": {
        "id": "kPoHDGVgItMF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 17
        },
        "outputId": "42a28253-abbd-42aa-b2e7-8118deb2b3dd"
      },
      "cell_type": "code",
      "source": [
        "#@title\n",
        "# http://pytorch.org/\n",
        "from os import path\n",
        "from wheel.pep425tags import get_abbr_impl, get_impl_ver, get_abi_tag\n",
        "platform = '{}{}-{}'.format(get_abbr_impl(), get_impl_ver(), get_abi_tag())\n",
        "\n",
        "accelerator = 'cu80' if path.exists('/opt/bin/nvidia-smi') else 'cpu'\n",
        "\n",
        "!pip install -q http://download.pytorch.org/whl/{accelerator}/torch-0.4.0-{platform}-linux_x86_64.whl torchvision\n",
        "import torch"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "metadata": {
        "id": "ar9Z1Rf7Cq1d",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "db9719f9-e0d6-4fb7-a755-9c01d9f9a375"
      },
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import matplotlib.pyplot as plt\n",
        "from pylab import rcParams\n",
        "plt.style.use('seaborn-white')"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "metadata": {
        "id": "3JX-p0anP1Pa",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Synthetic dataset"
      ]
    },
    {
      "metadata": {
        "id": "MMiagI5iC7Mu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "250461b7-7a5d-40fd-b7f8-64652b7d4d8c"
      },
      "cell_type": "code",
      "source": [
        "#@title\n",
        "def generateData(N, dim=2, group=2):\n",
        "    ss = group*torch.rand(group) * 2\n",
        "    loc = group*torch.rand(group, dim) * 5\n",
        "    sigma = 0.5\n",
        "    \n",
        "    data = torch.empty(group*N, dim)\n",
        "    target = torch.empty(group*N)\n",
        "    for g in range(group):\n",
        "        for i in range(N):\n",
        "            v = torch.randn(dim)\n",
        "            data[i+g*N] = sigma * v /torch.norm(v) * ss[g] + loc[g]\n",
        "            target[i+g*N] = g\n",
        "            \n",
        "    return data, target\n",
        "\n",
        "X, target = generateData(100, group=10)\n",
        "\n",
        "rcParams['figure.figsize'] = 4,4\n",
        "\n",
        "_ = plt.scatter(X[:, 0].numpy(), X[:, 1].numpy(), c=target.numpy(), s=5, cmap=\"tab10\")"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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ffPMNGzdubHwviiJxcXFMnDiRbt1OnqNfkWTOjc9BtniIn9YXQ5q5yeebN2+m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\nKFH8guChRPELgof6P5HE0Jm2paftAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fdc46632588>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "MOK1t-dqP7hc",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### MNIST dataset"
      ]
    },
    {
      "metadata": {
        "id": "HVOrHlimYCVx",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 485
        },
        "outputId": "8d6cf84e-020b-4c29-87de-034d41a3440f"
      },
      "cell_type": "code",
      "source": [
        "#@title\n",
        "import torchvision.datasets as dset\n",
        "import torchvision.transforms as transforms\n",
        "trans = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.5,), (1.0,))])\n",
        "train_set = dset.MNIST(root=\"./\", train=True, transform=trans, download=True)\n",
        "\n",
        "\n",
        "N = 6000\n",
        "idx = torch.randint(low=0, high=train_set.train_data.shape[0], size=(N,)).long()\n",
        "data = train_set.train_data[idx].float() / 255\n",
        "data = data.view(N, -1)\n",
        "\n",
        "\n",
        "rcParams['figure.figsize'] = 8,8\n",
        "\n",
        "for i in range(16):\n",
        "    plt.subplot(4,4, i+1)\n",
        "    plt.imshow(data[i].view(28,28).numpy())\n",
        "\n",
        "\n",
        "tt = data.numpy()\n",
        "\n",
        "from sklearn.decomposition import PCA\n",
        "pca = PCA(n_components=64)\n",
        "ttt = pca.fit_transform(tt)\n",
        "\n",
        "data = torch.from_numpy(ttt)\n",
        "X = data\n",
        "\n",
        "target = train_set.train_labels[idx]"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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YyZsSLF68WDnHn8uz2fcaHzx4sIjlFakAvXs9p6aminjp0qUitq+MVZepU6eK\n2Ju55xMuERGRBmxwiYiINGCDS0REpIHxY7iOtGzZUjlOTk4W8e9+9zsR28fj5GP75uTy6jdPPfWU\niLdu3aqUk8c76hqLMp08xvLSSy+5/LlLLrlExJ9++qmI5Q2xAXU6lrzCkLx6DgA88MADIq5rzE+e\nWiRPRQCAb7/91uHn4uLiRCy/H+DO2HFj8s033yjH8nsXdf3fyTmsq5y8k9CuXbuUc/KOQ42Z/Pvu\nkUceUc7JG7/7i/qM28puuukmD9ekdnzCJSIi0oANLhERkQbGdym7OkVAJq9IJcd28rQCAOjcubOI\n3377bRHbu5S3bNki4sbcpSx381ZUVLj8uZkzZ4o4PDxcxPYVnuQu5smTJzssJ6+SY++Wlr9/5PvO\nnz/fYf3kLm9AXe2Mq4yd7cSJEyIeN26ciP/6178q5ezTUhpK3gxB3rAEAHbv3i3i888/36P3DSRf\nf/21iO1TKd1h//4/77zzRCx368rDMIA6Jcz+MxpI+IRLRESkARtcIiIiDdjgEhERaWDcGK59g+OH\nH35YxC+++KKIvb10W4cOHRyemzdvnojvuusu5Vxj2pT85ZdfFnFd0zdat26tHI8YMcKl64eFhYl4\n1apVIj5+/LhSTr63/ftHHreta+qSvMPIa6+9ppyTl58kdToOADzxxBMizsnJceka8pKt8tJ+AHDr\nrbeKWH5fAlA3JZfHhE+ePKmUy8jIELF92UdyTh6rHT58uIgfeughpVxd78jI5Hx7YwxXHqu+6qqr\nPH79GnzCJSIi0oANLhERkQbGdSnbp2vI03Pk7qVBgwZ5tR7y9R9//HGH5YKDg71aDxPIU3MAdfWb\nc889t97Xa968uXJ87NgxEctTeADH3chdunRRjjMzM0XMLuSzyatG2bto16xZ49I1EhMTRfz666+L\nuFmzZg4/065dO+VYHs6Rp/7Y1bXjEzl3xx13iFjeiacu8tRA+y5tffr08Ui9HJG/L2655RYR21ck\nbCg+4RIREWnABpeIiEgD47qU6yK/oSi/tQqcvdJMQ1122WUitndLyCtesUvZuSNHjijH8kLzvXr1\nqvf17G+u3nfffSLeuXOnck5+g/m6664TsbyhPQBERETUux6Nyd///ncRu9qFLG8qAagbRtTVjSy/\nBS139QN1dyOT56xfv17E8kb1dvn5+SKWN3yxdyl7W2FhoYiXL18uYnmWgifwCZeIiEgDl55w09PT\nsX37dlRVVSElJQXdunXD9OnTUV1djejoaCxatMjl+VTke8yneZhTszCfZnLa4G7ZsgV79uxBdnY2\nysrKMGzYMPTp0wdJSUkYPHj+kFUcAAAgAElEQVQwlixZgpycHCQlJemoLzUQ82ke5tQszKe5nDa4\nvXv3Rvfu3QGc2R2noqIC+fn5YrWPhIQErF692m+SP2TIEOVYHquVN4y3r3gir3Ajjw+NHj1aKSdv\nQl7X6khr164VsX0MskePHrXeS4dAy2dDyJtRv//++yK+5557lHJyTu0bj8+ZM0fEEyZM8HQVPcIf\nc2r/nl+2bJlLn8vLyxNxzb+phvzz9tFHH4l43759Sjl5Gl5paalL97300kuVY0+P3dWHP+Xziiuu\nEPGoUaOUc/I4rd22bdtE3LVrV89XzIEbbrhBxG3btlXO1bVSnC5Ox3CDg4PFFmg5OTno378/Kioq\nRHdGVFQUSkpKvFtL8hjm0zzMqVmYT3O5/NLUpk2bkJOTg1mzZilfl58OKHAwn+ZhTs3CfJrHpZem\nNm/ejJUrV+K5555DREQEwsPDUVlZibCwMBQXFyMmJsbb9XSZvUtZXvVnx44dIrYvUi93AcvsKw+5\n2qVcF3nDbU9vqu0Kf8nnO++8I2J5gXNA3Rzc7re//a2I5Sk99i6j8vJyEcur2LRp00YpJ68KJk9N\nAOrehMKf+EtOa9inu8mbO9TFEysKufozev3114s4OztbOdeqVasG16Mh/CWf8kpu8uYvQN1dyt5k\n7yqWVyB7/vnnRWzfkEL+Of/zn/+snJOnoN12220eqWdtnD7hlpeXIz09HatWrRLzSePj45GbmwsA\n2LhxI/r16+e1CpJnMZ/mYU7Nwnyay+mfnRs2bEBZWRmmTJkivrZgwQKkpaUhOzsbsbGxGDp0qFcr\nSZ7DfJqHOTUL82kupw3uyJEjMXLkyLO+7upqMeRfmE/zMKdmYT7NZdzSjvKyiYD6TXr//feLeOvW\nrV6tR81bhgBw5513KucefPBBEbdo0cKr9fBn8ni7vAk5ADz22GMOP3f06FERyxuFX3zxxUq5lJQU\nEctTKGJjY5VyXJbR8+z/p9OmTRPxpEmTtNVDHu8H1GUG5amB9t8bdDb7uPymTZtEbJ8y5Op0LFfJ\nG9q/9957yjlHP7+RkZHKsVxHe3114XcZERGRBmxwiYiINDCuS9lOnhb0ySefiNi+W9CePXtE/NVX\nX4n4448/VspdcMEFIrZvLB8XFyfiCy+8UMT2Lkw62/Tp05XjRx55RMT2KVzy6/5y133Hjh2VctyJ\nyX+MGzdOxPYpYKtXr671M/Pnz1eOmzdvLuKHH37Y4b3kKR72ldyaNGnivLJUK/sUq4SEBBHLvz8B\ndXrOunXrRPzFF18o5eSf+06dOol42LBhSjn557xp06b1qbZf4RMuERGRBmxwiYiINDC+S1kmdzFO\nnDjRhzUhO3t3ldz1Z3/7mAKPvGKRfaUvR2+k1/WmOvkX+xvBU6dOrTVu7PiES0REpAEbXCIiIg3Y\n4BIREWnABpeIiEgDNrhEREQasMElIiLSgA0uERGRBmxwiYiINGCDS0REpAEbXCIiIg3Y4BIREWnA\nBpeIiEgDr29eUF1dDQAoKiry9q3Ipub/vCYHnsKc+gbzaR7m1CzO8un1BrekpAQAkJyc7O1bkQMl\nJSVnbc7e0OsBzKmvMJ/mYU7N4iifQZZlWd68cWVlJQoKChAdHa1sj0feV11djZKSEsTFxSEsLMxj\n12VOfYP5NA9zahZn+fR6g0tERER8aYqIiEgLNrhEREQasMElIiLSgA0uERGRBl6fFlRj3rx52LFj\nB4KCgjBjxgx0795d161RWFiIiRMnYuzYsRg9ejQOHTqE6dOno7q6GtHR0Vi0aBFCQ0O9Xo/09HRs\n374dVVVVSElJQbdu3XxSD09gPs3KJ8CcAmbllPn0w3xaGuTn51sTJkywLMuy9u7da40YMULHbS3L\nsqwTJ05Yo0ePttLS0qy1a9dalmVZqamp1oYNGyzLsqzFixdbWVlZXq9HXl6eNX78eMuyLOvnn3+2\nBgwY4JN6eALzaVY+LYs5tSyzcsp8+mc+tXQp5+XlITExEQDQqVMnHD16FMePH9dxa4SGhiIzMxMx\nMTHia/n5+Rg4cCAAICEhAXl5eV6vR+/evbF06VIAQGRkJCoqKnxSD09gPs3KJ8CcAmbllPn0z3xq\naXBLS0vRqlUrcdy6dWuxEoq3hYSEnDUBuaKiQnQjREVFaalLcHAwwsPDAQA5OTno37+/T+rhCcyn\nWfkEmFPArJwyn/6ZT5+8NGX50VobuuuyadMm5OTkYNasWT6thyf5U92ZT8/wp/ozpw3nT3VvzPnU\n0uDGxMSgtLRUHB8+fBjR0dE6bl2r8PBwVFZWAgCKi4uVrg9v2rx5M1auXInMzExERET4rB4NxXye\nYUo+Aea0hik5ZT7P8Ld8amlw+/bti9zcXADAzp07ERMTg+bNm+u4da3i4+NFfTZu3Ih+/fp5/Z7l\n5eVIT0/HqlWr0LJlS5/VwxOYT7PyCTCngFk5ZT79M5/a1lLOyMjAtm3bEBQUhNmzZ6NLly46bouC\nggIsXLgQBw4cQEhICNq0aYOMjAykpqbi1KlTiI2Nxfz589GkSROv1iM7OxvLly/HRRddJL62YMEC\npKWlaa2HpzCfZuUTYE5Nyynz6X/55OYFREREGnClKSIiIg3cXmnKl6uYkHcwp2ZhPs3DnAY2txrc\nrVu3Yv/+/cjOzsa+ffswY8YMZGdn11qWGyH7Tn02t2ZO/R/zaR7m1CzO8ulWg+toFZPa3oIrKChA\ncnKyO7chD8nKykKvXr3qLMOcBg7m0zzMqVkc5dOtBre0tBRdu3YVxzWrmNSW+Jq5X1lZWWjbtq07\ntyM3FRUVITk52aX5d8yp/2M+zcOcmsVZPj2yW1BdLzrXdGe0bdsW7du398TtqJ7c6VJiTv0X82ke\n5tQsjvLp1lvK/raKCTUcc2oW5tM8zGngc6vB9bdVTKjhmFOzMJ/mYU4Dn1tdyj169EDXrl0xatQo\nsYoJBTbm1CzMp3mY08Dn9hjutGnTPFkP8gPMqVmYT/Mwp4GNK00RERFpwAaXiIhIAza4REREGrDB\nJSIi0oANLhERkQZscImIiDTwyNKOjcmJEydE3KxZM5c+88svvyjHH3/8sYgHDRqknLvkkktEnJeX\nJ+LWrVvXq55EdLYtW7aIeOrUqSI+ePCgUm7//v3a6kSNB59wiYiINGCDS0REpAG7lJ148sknleNF\nixaJeMeOHcq5Tp06iVheZHz8+PFKubffflvEQUFByrl9+/aJeO7cuSJevHhxfardKG3dulU5Xrt2\nrYg/+ugjERcUFCjl7Dlw5KqrrhLxPffco5y76667RNyiRQuXrkf6vfjiiyLOz88XcYcOHXxRHWpk\n+IRLRESkARtcIiIiDdilXIvy8nIRP/vss8q5c875398ocpcUAMycOVPE7733noiPHTumlDv33HNF\nfP311yvn5M9R7U6fPi1iOT9TpkxxWE7mahcyADRp0kTER44cEfHkyZOVcs8884yIP/nkE+Uc9yz1\nnaKiIuX4ueeeq7Xc8uXLdVSH/IT9LfSOHTvWWm7Pnj3K8cmTJ0V85ZVX1vu+fMIlIiLSgA0uERGR\nBmxwiYiINOAYbi3kcZ7//Oc/yrmePXuKWJ4KUpdevXopx3/7299EXFhYqJyTx3C7d+/u0vUbmw8/\n/FDEkyZNclguLCxMxAsXLhRxYmKiy/eSryGP8+zevVspt2LFChFv2LBBOXf33Xe7fD9qOHk1uLFj\nxyrnqqurRXzxxReLePDgwV6vF7lP/j383XffKeeeeOIJEcur+NVFHosFgPDw8FrLyd9LgPpeyJ//\n/Gfl3P333+/0vnzCJSIi0oANLhERkQbsUv4vecrH0qVLHZa74447RLx9+3bl3KWXXipiudvTvvHA\nr7/+KuIhQ4Yo5+SuzzFjxjirdqPkaGH5yMhI5fif//yniN15hb8ul19+uXLMaSX+Q17lbePGjQ7L\nBQcHizgkhL8Kfa2srEzE9uE6+fepvZvXE+SpoK566623lGN2KRMREfkJNrhEREQasMElIiLSgAMX\n/1VVVSViecN4++vizZs3F/Htt9+unHv11VdrvfZXX32lHN98880i3rt3r3KuTZs2Lta48crKyqr1\n671791aOPTFuK08jycjIEPErr7yilHvhhRdELO8qRPr9+9//dqlcv379vFyTxsM+BhoREVFrOfty\nq/IUOnlpXPvvzLpERUWJOCYmRsT2aZXXXnuty9esYX/HRv53yVMGXcUnXCIiIg1canALCwuRmJiI\nl19+GQBw6NAhjBkzBklJSZg8ebLyREj+j/k0D3NqFubTTE67lE+ePIk5c+agT58+4mvLli1DUlIS\nBg8ejCVLliAnJwdJSUlerai3ybuKHD58WMQLFixQyj3wwAO1xnZ1bUAvTyfS3YVsQj7btm2r7V6v\nvfaaiB977DGH5eQN6b/88kuv1snOhJw2hH3VoLlz5zos26JFCxE/+uijXqtTQwRKPuVpPPZpcgkJ\nCSKeOnWqiHNycpRyixYtculeF1xwgYhTU1OVc6NHjxaxfWqgv3H6hBsaGorMzEylbzw/Px8DBw4E\ncOY/Ni8vz3s1JI9iPs3DnJqF+TSX0yfckJCQsyaFV1RUIDQ0FMCZAeuSkhLv1I48jvk0D3NqFubT\nXA1+S9myLE/UIyCdOnVKOf7ggw9EvGPHDhHn5uYq5eS36vxNIOSz5i99QH1bWF6NBlA3j5ZXAauP\nH374waVy7du3d+v6OgRCThti+vTpyvFnn33msOzzzz8vYne/J3zNX/JZUVEhYvvvtPXr19ca16Xm\nDwpAXXEPUGeEdOjQoV719CduvaUcHh6OyspKAEBxcbHS9UGBh/k0D3NqFubTDG41uPHx8eKpbePG\njZzPFuCYT/Mwp2ZhPs3gtEu5oKAACxcuxIEDBxASEoLc3FxkZGQgNTUV2dnZiI2NxdChQ3XUlTyA\n+TQPc2oW5tNcThvcuLg4rF279qyvr1mzxisV8jdff/21ciyPC44YMUI5J4/jvfHGGyJu0qSJl2pX\nfybn076KjTx2JK9iUxf7uLyrK94kJye7VM4bTM6pI/KOUTVzVWsjTwMCgG7dunmtTp4SKPmMjY0V\ncdOmTd26xhVXXCHiLVu2iNjRSlWBjitNERERacAGl4iISANuXuCEfaH8v/71ryKWu0MAdVUif+pG\nNo08fiV3vckbzgPAs88+K+K6upTlKVy33nqrcu7HH3+s9TP21cPuuOOOOmpMniavUHTs2DGH5ewb\njATqVCB/JG8E/8033zgs16xZMxE/+eSTyjl5FapzzjH/+c/8fyEREZEfYINLRESkAbuU/0teAL2u\nlVyGDRsm4vT0dOWcO/sjUv21bt1axE888YSI5QXTAXUTivnz54vYPqVi8ODBIpY3sbCTu5H//Oc/\nK+eCg4Od1Joa6vvvvxfxunXrHJaTF7Cva8MJaphff/1VxPK+0XbyilT235HyrkeN4fcnn3CJiIg0\nYINLRESkARtcIiIiDRrVGK48zmBfyUUeCwwKCnJ4DXncVvfm8XS2Tp06idi+pVlVVZWIH3/88Vpj\nO/t0LnnXkgcffFDEHLPVLyMjQ8RHjhxxWK5nz54ivuSSS7xap8asZcuWIra/+yCv/rVq1SoRP/TQ\nQ0q5uXPnilieWvfUU085vFcg4xMuERGRBmxwiYiINGhUXcryZgN/+9vf3LoGu5H9i7xhRGpqqnLu\nj3/8o0vXkLuRP/jgA+Vc3759G1A7aoht27Ypx6+88oqI5al79iGg+++/37sVo7PYN4mQh19SUlJE\nfPDgQaWcPLyzfPlyEctT+uznoqOjG1ZZH+ITLhERkQZscImIiDRgg0tERKSBcWO4ZWVlyvGKFStE\n/Oabb4q4rqk/sl69enmmYuR1HTp0cOtzBQUFIuZuMr516tQpEd97773KOflnW/75vemmm5Ry8lKd\n5HvydD37z+jKlStFLC/zmJ2drZS7/vrrRTxhwgRPV1EbPuESERFpwAaXiIhIAyO6lPPy8kRs727Y\ntWtXg67NjcX9jzwl5NVXXxWxu9NB3n//fRGzS1k/uStx4sSJIpa7+u2aNm0q4qVLlyrnmjdv7sHa\nkTfJm9MPGTJExPLPNaBO1xs7dqxyLjQ01DuV8wI+4RIREWnABpeIiEiDgOlSPn36tIjlhbEB4J57\n7qn3Nc45x7W/NRITE10qR/p8+umnIr7zzjtF3KpVK6XcX/7yFxFPmjRJxIcOHVLKTZ06VcT2N147\nduzYsMqSU++++66I16xZ47CcvEG5/BbrxRdf7J2KkVbff/+9w3PffPONiF2dYeKP+IRLRESkARtc\nIiIiDVzqUk5PT8f27dtRVVWFlJQUdOvWDdOnT0d1dTWio6OxaNGigHpTrLFjPs3DnJqF+TST0wZ3\ny5Yt2LNnD7Kzs1FWVoZhw4ahT58+SEpKwuDBg7FkyRLk5OQgKSnJqxU9efKkiO0r0Ljapy+P29b1\nmfPOO0/El112matVDAj+ks/6yM/PV47HjBlTazl5hxIAGD58uIivueYaEXfu3FkpV1FRIeK9e/cq\n5wJhDDfQcrpz507l+O6773bpc6NHjxbxzTff7NE6+ZNAy6ennHvuuQ7PyVPH5GmBgcZpl3Lv3r3F\nPLfIyEhUVFQgPz8fAwcOBAAkJCQo82DJvzGf5mFOzcJ8mstpgxscHIzw8HAAQE5ODvr374+KigrR\nnREVFYWSkhLv1pI8hvk0D3NqFubTXC5PC9q0aRNycnKwevVq3HDDDeLrgfx4L7vvvvtEPHv2bBHL\nK9qYJJDy+dZbbynH+/fvF/Hll18u4j/84Q8Or9GuXTsR23Mqdynbu+nke8nTUvxRoOTUvrnAsWPH\nai133XXXKcdPP/20t6rkl/w9n5WVlSLevXu3cu7KK6906Rryv8W+6bxs5MiRIg7ksWuX3lLevHkz\nVq5ciczMTERERCA8PFz8ZxcXFyMmJsarlSTPYj7Nw5yahfk0k9MGt7y8HOnp6Vi1ahVatmwJAIiP\nj0dubi4AYOPGjejXr593a0kew3yahzk1C/NpLqddyhs2bEBZWRmmTJkivrZgwQKkpaUhOzsbsbGx\nGDp0qFcrSZ7DfJqHOTUL82kupw3uyJEjlf7zGnUtweav5LG7mr8Wa8gbzdf1enqgC8R82seHZAkJ\nCSKOiIhw6XryLzIAmDVrlojtL6McOXJExG3btnXp+roFQk7lZfscjdkC6tS9devWKefknWVMFgj5\nBNRdez7//HPl3JdffiniyMhIEZeXlyvlHnvsMRGvWLHC4b0GDBjgbjX9CleaIiIi0oANLhERkQYB\ns1tQzbw04OyuFXm3ILlrGFA3kJc3t5avR/6trtW+jh8/LmL7dAlHq4nV1aVpJ298bdrKPjpdeOGF\nIpa7GAE1H/IUMH/twqczPvvsMxH/+OOPyrlu3bqJ+IILLhDxTz/9pJSTp93JVq1apRz379/f7Xr6\nEz7hEhERacAGl4iISIOA6VKW3160L17vaDF7Mt9LL70k4pAQ9dtZ3qRAXnv2nXfecXg9+2bmN954\nY0OrSDY//PCDr6tAHpCZmSniW265RTkn57iufMtDe88++6yI5aFAQP39H8jM+FcQERH5OTa4RERE\nGrDBJSIi0iBgxnCp8Zo7d26dx0Sk36BBg0S8bds25Vx1dbVL15Cn/DWGqZp8wiUiItKADS4REZEG\n7FImIqIG6d69u6+rEBD4hEtERKQBG1wiIiIN2OASERFpwAaXiIhIAza4REREGnj9LeWaCdBFRUXe\nvhXZ1PyfuzoJ3VXMqW8wn+ZhTs3iLJ9eb3BLSkoAAMnJyd6+FTlQUlKCjh07evR6AHPqK8yneZhT\nszjKZ5BlWZY3b1xZWYmCggJER0cjODjYm7cim+rqapSUlCAuLg5hYWEeuy5z6hvMp3mYU7M4y6fX\nG1wiIiLiS1NERERasMElIiLSgA0uERGRBmxwiYiINGCDS0REpIG27fnmzZuHHTt2ICgoCDNmzNC6\nnVNhYSEmTpyIsWPHYvTo0Th06BCmT5+O6upqREdHY9GiRQgNDfV6PdLT07F9+3ZUVVUhJSUF3bp1\n80k9PIH5NCufAHMKmJVT5tMP82lpkJ+fb02YMMGyLMvau3evNWLECB23tSzLsk6cOGGNHj3aSktL\ns9auXWtZlmWlpqZaGzZssCzLshYvXmxlZWV5vR55eXnW+PHjLcuyrJ9//tkaMGCAT+rhCcynWfm0\nLObUsszKKfPpn/nU0qWcl5eHxMREAECnTp1w9OhRHD9+XMetERoaiszMTMTExIiv5efnY+DAgQCA\nhIQE5OXleb0evXv3xtKlSwEAkZGRqKio8Ek9PIH5NCufAHMKmJVT5tM/86mlwS0tLUWrVq3EcevW\nrcXSY94WEhJy1oofFRUVohshKipKS12Cg4MRHh4OAMjJyUH//v19Ug9PYD7NyifAnAJm5ZT59M98\n+uSlKcuPFrfSXZdNmzYhJycHs2bN8mk9PMmf6s58eoY/1Z85bTh/qntjzqeWBjcmJgalpaXi+PDh\nw4iOjtZx61qFh4ejsrISAFBcXKx0fXjT5s2bsXLlSmRmZiIiIsJn9Wgo5vMMU/IJMKc1TMkp83mG\nv+VTS4Pbt29f5ObmAgB27tyJmJgYNG/eXMetaxUfHy/qs3HjRvTr18/r9ywvL0d6ejpWrVqFli1b\n+qwensB8mpVPgDkFzMop8+mf+dS2eUFGRga2bduGoKAgzJ49G126dNFxWxQUFGDhwoU4cOAAQkJC\n0KZNG2RkZCA1NRWnTp1CbGws5s+fjyZNmni1HtnZ2Vi+fDkuuugi8bUFCxYgLS1Naz08hfk0K58A\nc2paTplP/8sndwsiIiLSgCtNERERaeD2SlOurmLCjZB9p76bWzOn/o35NA9zahZn+XSrwd26dSv2\n79+P7Oxs7Nu3DzNmzEB2dnatZQsKCpCcnOzObchDsrKy0KtXrzrLMKeBg/k0D3NqFkf5dKvBdbSK\nSW1vwdW8ip6VlYW2bdu6cztyU1FREZKTk12aDsCc+j/m0zzMqVmc5dOtBre0tBRdu3YVxzWrmNSW\n+JrujLZt26J9+/bu3I4ayJUuJeY0cDCf5mFOzeIonx55aYovOpuHOTUL82ke5jTwuNXg+tsqJtRw\nzKlZmE/zMKeBz60G199WMaGGY07NwnyahzkNfG6N4fbo0QNdu3bFqFGjxComFNiYU7Mwn+ZhTgOf\n2/Nwp02b5sl6kB9gTs3CfJqHOQ1sXGmKiIhIAza4REREGrjdpUzkb4YPH64cHzx4UMRDhgwR8cyZ\nM7XViYioBp9wiYiINGCDS0REpAEbXCIiIg04hkvGqFnYvcaLL74o4n/9618itk+t+O6770Q8ffp0\n5dzVV1/tySoSNQqLFy8W8erVq0W8a9cupZy8POXvfvc7EU+YMEEpl5CQIOJA3m6QT7hEREQasMEl\nIiLSgF3KZIwHHnhAOR43bpyI9+zZI+KbbrpJKVdRUSHi9957TzmXkpIi4nnz5ok4LCysYZUlMoj8\n8wWoU+8WLFgg4sjISKXc7t27RfzBBx+I+IYbblDKxcXFifjdd99VzrVr186NGvsGn3CJiIg0YINL\nRESkAbuUyVihoaEi7tq1q4i///57pdyRI0dEvGjRIuXcZ599JuJLLrlExG+88YZS7je/+U2D6kr+\n6+jRo8pxixYtGlTORJWVlcqxPGwzadIkl65RXV0t4k2bNinnkpOTRXzjjTcq5+Sf0YiICJfu5St8\nwiUiItKADS4REZEGbHCJiIg04Biul8hTTYqKipRzd999t4g7duyonHv++edFLI9Bkve0bNlSxHPn\nzlXO/fOf/xTxww8/LOL4+Hil3JIlS0Ts6pgV6VdQUCDin376ScTylC8A+OWXX0R86NAh5dz5559f\n67Xt5W6//XYRP/300/WvbADp1q2bcvzaa6/V+xryClKDBg1Szj333HMillekAoBHH31UxM8++2y9\n76sTn3CJiIg0YINLRESkgV91KZ8+fVo5/vXXX0X81ltvuXQN+0om8qLXnnDgwAERb9u2TTmXmZkp\n4n379on422+/dXg9uRygdkWzS9n3BgwYIOJPP/1UxPbF1SdPnixi+7SFzp07e6l2ZpN/FgDg5Zdf\nFvGJEydEbP8ZkjetkBfHB4BTp06JWJ6GUpfzzjtPOZa7outy+PBhl8qRc0OHDhWx/Xf8l19+qbs6\nbuMTLhERkQZscImIiDRgg0tERKSBX43h2sdEG8Pm30uXLlWOG9NycIFm586dIrbvWNK6dWsRM4ee\nMWzYMOX4/fffr/c1OnXqVOdxjdTUVOVYnqLSs2dP5VzTpk3rXQ/ynMTEROVYHsOV3/tp0qSJtjq5\nyqUn3MLCQiQmJoqXFg4dOoQxY8YgKSkJkydPVuaskf9jPs3DnJqF+TST0wb35MmTmDNnDvr06SO+\ntmzZMiQlJWHdunXo2LEjcnJyvFpJ8hzm0zzMqVmYT3M57VIODQ1FZmamMuUlPz8fTz75JIAz025W\nr16NpKSkBldmw4YNauVC/le9hQsXNvj6ZWVlIpb/PXZyV7Y8LQQAevXqJWJ5U2RA3THj2muvFfF3\n332nlJM3Lx88eLCzanuUznz6K7nbCVBXFfr444+Vc/LqUj///LOImzdvrpRbsWKFiNu0aeORerqq\nMea0S5cuIl65cqVyTl7lyL6ClD1v/qgx5tMZ+XdrXl6eck5eacofu5FlThvckJAQpeEDzsyPq5kj\nGhUVhZKSEu/UjjyO+TQPc2oW5tNcDX5L2T6xnAIb82ke5tQszGfgcust5fDwcFRWViIsLAzFxcWI\niYnxSGXkrgEAuPXWW0Xco0cPj9yjxpw5czx6PQAoLy8Xsb0bWfb3v/9dxM2aNfN4PerLW/n0Vykp\nKcrx5ZdfLmI5NwDwf//3fyKW31a1v9XqbwIpp3KX/oIFC0T84YcfKuWGDBkiYnmziEsvvVQp169f\nP09X0ecCKZ+eYN/QXq1FoPoAAAv8SURBVB7asb8wds8992ipkye49YQbHx+P3NxcAMDGjRuN/AZv\nTJhP8zCnZmE+zeD0CbegoAALFy7EgQMHEBISgtzcXGRkZCA1NRXZ2dmIjY1V1rkk/8Z8moc5NQvz\naS6nDW5cXBzWrl171tfXrFnjlQqRdzGf5mFOzcJ8msuvVpqyr+Di6XFbb3N1XK9du3ZergnZff31\n1yL+4IMPlHPLli0TsbzrD8Adm3SQdwKrmfpSm8cff1zE9nFbCkxVVVUi/uyzz0Qsj+UDUN7K3r59\nu3IuPDzcS7XzPK6lTEREpAEbXCIiIg38qks50Pzwww/K8erVq2std9NNNynHHTt29FqdGhu5S2rG\njBnKuWeffVbE48aNE/GuXbuUclyMXq+vvvpKOb7zzjtd+tzdd98t4iuvvFLE9g0JnnrqKRH7+8pD\njV1hYaGIr7vuOoflat7QBgJ7SI5PuERERBqwwSUiItKAXcr1dPr0aRHPnDlTOWdfHaXG+vXrlWN2\nYXqOvPmDfWWiqKgoEc+fP1/E/P/3LXllLwAYNGiQiO37DMv27t1ba2xXVFQkYk6l8W9XXHGFiOXf\nrVlZWUq5sWPHiti+yY08vODv+IRLRESkARtcIiIiDdjgEhERacAx3HqSNyh/6aWXHJaTdzrimKFn\n7d+/X8TyqlH2/2d5+k8grUZjunPPPVc5tu/Q5Ap55aELL7xQOffCCy+I+LHHHlPOde7cud73Iv2S\nk5OV4z179oj4xhtvVM7JP+ctW7b0bsUaiE+4REREGrDBJSIi0oBdyk7YNzu2b14uk7szXnzxRREH\nBwd7vmKNiDzNA1CnCMj++te/KsetW7f2VpXIx6Kjo0VsX8nt9ddfF/GOHTuUc+xSDky///3vRSxv\nNgKom9PLw3xBQUHer1g98QmXiIhIAza4REREGrDBJSIi0oBjuLWwLEvE6enpyjl5dwv7GIG8jJy/\nv54eSI4ePaocb968WcTnnXeeiHv06KGtTkSkT0REhIjtU70effRREU+ZMkXEPXv29H7F6olPuERE\nRBqwwSUiItKAXcq1kDeWt+8IJBs5cqRyPHToUK/VqTH705/+pBzLXf7yZuby7kBktuPHj4vYPvVH\n1qxZMx3VIY2mTZumHBcUFIh4wIABIv7888+VcvZdqnyBT7hEREQasMElIiLSgF3K/3XixAkR9+/f\n32E5+W25p556yqt1ojPsb4PLx+eff36Dr19ZWSniL7/80uG5FStWiPjee+9Vyg0ZMqTB9TDJkSNH\nlOOwsLBaY3evKa8uZN+Mvn379iJmXvTIyMhQjuVN4X/729969F723wd/+ctfRCx/j9x8881KuX37\n9nm0Hu7gEy4REZEGLj3hpqenY/v27aiqqkJKSgq6deuG6dOno7q6GtHR0Vi0aBFCQ0O9XVfyEObT\nPMypWZhPMzltcLds2YI9e/YgOzsbZWVlGDZsGPr06YOkpCQMHjwYS5YsQU5ODpKSknTUlxqI+TQP\nc2oW5tNcThvc3r17o3v37gCAyMhIVFRUID8/H08++SQAICEhAatXrw745I8fP17E8rQgu8zMTBFf\neumlXq2TNwRiPvv06aMcr127VsSxsbEito/tyFNCLrnkEhHbp5HIO0KVlZUp5+RN7SsqKkT85ptv\nKuVycnJErHt6mD/m9KGHHlKOH3nkERHbVwSrqqoScV5enoi//vprpdzixYtF/P333zu890cffVSf\nqvodf8ynM/afB/ldCHmqjjeeys8991wRDxw4UMQ7d+70+L0ayukYbnBwMMLDwwGc+aXSv39/VFRU\niP+4qKgolJSUeLeW5DHMp3mYU7Mwn+Zy+aWpTZs2IScnB7NmzVK+Li9CQIGD+TQPc2oW5tM8Lr00\ntXnzZqxcuRLPPfccIiIiEB4ejsrKSoSFhaG4uBgxMTHerqdHnD59WsSLFi1Szq1fv77Wz7zyyivK\n8R133OH5imkWaPkcPny4clxdXS3icePGidjepXz11VeLeOPGjQ6vL3cBjxo1Sjl3zTXXiPinn34S\n8erVq5VyJ0+edHh9Hfwtp3IXPqBODbFPC5J/Lg8fPuzwmnJ3ZKdOnUT8j3/8QynXrl27+lXWD/lb\nPp155plnlOPf/OY3IpbrOm/ePKWcPGTjKnkDGUD9HS0PO9x11131vra3OX3CLS8vR3p6OlatWiV2\nwImPj0dubi6AM7/I+vXr591akscwn+ZhTs3CfJrL6RPuhg0bUFZWpmx7tGDBAqSlpSE7OxuxsbFc\nQziAMJ/mYU7Nwnyay2mDO3LkyLMW6QfUvV8pcDCf5mFOzcJ8mqtRLe0o7yqRmprqsJy8q4R9abjg\n4GDPV4zqVPPGZg35l9HgwYNF/M477yjlPvjgAxHL07nkaQSAOh5YF3nJQHlsl85m3yR8165dIpan\nUAHqz5Q89iePzwPADTfcIOIOHTp4pJ7kGVdddZVyLC+jmJycLOIWLVoo5SZNmiTiuLi4Wj8PAP/6\n179E/O677yrnmjRpIuLly5eL2L78qj/g0o5EREQasMElIiLSwPguZXnVmbp2DpFfUHjiiSdEHBkZ\n6Y1qUQPIUwnk2N6F5I9dSo2Fvdv+hRdeEHHNikk1QkL+92vIPp2IAtMFF1wgYkdDO8CZZSxryFOG\nDhw4oJSTp2MuWbJEOfe73/1OxG3atHGzxnrwCZeIiEgDNrhEREQaGNelLC9EDwCPPvqoiOXF5zt3\n7qyUk1coOecc/h1C5Ely13+XLl18WBPSTR4yeOCBB5Rz9mPTsWUhIiLSgA0uERGRBmxwiYiINDBu\nDPett95Sjrdu3VprOXkTc4DjtkRE5F1sZYiIiDRgg0tERKSBcV3K9m2rEhMTRbxp0yYRyxsZAOqi\n6URERJ7GJ1wiIiIN2OASERFpwAaXiIhIA+PGcOVlxADg/fff91FNiIiI/odPuERERBp4/Qm3uroa\nAFBUVOTtW5FNzf95TQ48hTn1DebTPMypWZzl0+sNbklJCQAgOTnZ27ciB0pKStCxY0ePXg9gTn2F\n+TQPc2oWR/kMsizL8uaNKysrUVBQgOjoaAQHB3vzVmRTXV2NkpISxMXFISwszGPXZU59g/k0D3Nq\nFmf59HqDS0RERHxpioiISAs2uERERBqwwSUiItKADS4REZEG2laamjdvHnbs2IGgoCDMmDED3bt3\n13VrFBYWYuLEiRg7dixGjx6NQ4cOYfr06aiurkZ0dDQWLVqE0NBQr9cjPT0d27dvR1VVFVJSUtCt\nWzef1MMTmE+z8gkwp4BZOWU+/TCflgb5+fnWhAkTLMuyrL1791ojRozQcVvLsizrxIkT1ujRo620\ntDRr7dq1lmVZVmpqqrVhwwbLsixr8eLFVlZWltfrkZeXZ40fP96yLMv6+eefrQEDBvikHp7AfJqV\nT8tiTi3LrJwyn/6ZTy1dynl5eWJf2k6dOuHo0aM4fvy4jlsjNDQUmZmZiImJEV/Lz8/HwIEDAQAJ\nCQnIy8vzej169+6NpUuXAgAiIyNRUVHhk3p4AvNpVj4B5hQwK6fMp3/mU0uDW1pailatWonj1q1b\ni5VQvC0kJOSsCcgVFRWiGyEqKkpLXYKDgxEeHg4AyMnJQf/+/X1SD09gPs3KJ8CcAmbllPn0z3z6\n5KUpy4/W2tBdl02bNiEnJwezZs3yaT08yZ/qznx6hj/VnzltOH+qe2POp5YGNyYmBqWlpeL48OHD\niI6O1nHrWoWHh6OyshIAUFxcrHR9eNPmzZuxcuVKZGZmIiIiwmf1aCjm8wxT8gkwpzVMySnzeYa/\n5VNLg9u3b1/k5uYCAHbu3ImYmBg0b95cx61rFR8fL+qzceNG9OvXz+v3LC8vR3p6OlatWoWWLVv6\nrB6ewHyalU+AOQXMyinz6Z/51LaWckZGBrZt24agoCDMnj0bXbp00XFbFBQUYOHChThw4ABCQkLQ\npk0bZGRkIDU1FadOnUJsbCzmz5+PJk2aeLUe2dnZWL58OS666CLxtQULFiAtLU1rPTyF+TQrnwBz\nalpOmU//yyc3LyAiItKAK00RERFpwAaXiIhIAza4REREGrDBJSIi0oANLhERkQZscImIiDRgg0tE\nRKQBG1wiIiIN/h9rkrv0z1RFBQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fdcb68bc5f8>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "1xqAiQTbQhkY",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### t-SNE pytorch implementation"
      ]
    },
    {
      "metadata": {
        "id": "6mcjcYIkQp_L",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Compute the joint distribution $$P(i,j)$$"
      ]
    },
    {
      "metadata": {
        "id": "LDTQQ8XIG1pt",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "6d1fe02a-34e7-41df-cc74-d424d23d787d"
      },
      "cell_type": "code",
      "source": [
        "#@title\n",
        "X = X.cuda()\n",
        "\n",
        "import math\n",
        "Perp = 40\n",
        "N = X.shape[0]\n",
        "d = X.shape[1]\n",
        "\n",
        "dist2 = torch.empty(N, N).cuda()\n",
        "for i in range(N):\n",
        "    dist2[i] = torch.sum(torch.pow(X[i].view(1, d).expand_as(X) - X, 2), dim = 1)\n",
        "        \n",
        "\n",
        "maxSigma2 = torch.max(dist2, dim=0)[0]\n",
        "dist2 = dist2 + torch.diag(maxSigma2)\n",
        "Pconditional = torch.empty_like(dist2).cuda()\n",
        "\n",
        "bits = math.log2(Perp)\n",
        "print(bits)\n",
        "with torch.no_grad():\n",
        "    for i in range(N):\n",
        "        l, r = 0, 1*maxSigma2[i]\n",
        "        entropy = 0\n",
        "        while math.fabs(entropy - bits) > 1e-2:\n",
        "            m = (r+l)/2\n",
        "            Pconditional[i] = torch.nn.functional.softmax(-dist2[i] / m, 0)\n",
        "            Pconditional[i] = Pconditional[i] / (1.0 - Pconditional[i][i])\n",
        "            Pconditional[i][i] = 1.0\n",
        "            entropy = -torch.sum( Pconditional[i] * \n",
        "                  torch.clamp( torch.log2(Pconditional[i]), min=-200) ).item()\n",
        "            if entropy > bits:\n",
        "                r = m\n",
        "            else:\n",
        "                l = m\n",
        "        Pconditional[i,i] = 0\n",
        "    P = (Pconditional + Pconditional.t() ) / 2 / N             \n",
        "    P[i,i] = 0"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "5.321928094887363\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "Mg26PCacQxcR",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Setup optimizer"
      ]
    },
    {
      "metadata": {
        "id": "uRmblpjajRP3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "798afdc9-6256-479e-eaf5-bdce1e5e70f5"
      },
      "cell_type": "code",
      "source": [
        "#@title\n",
        "rcParams['font.size'] = 14\n",
        "rcParams['figure.figsize'] = 5,5\n",
        "from IPython import display\n",
        "\n",
        "N = X.shape[0]\n",
        "d = 2\n",
        "Y = torch.empty(N, d, requires_grad=True, device=torch.device(0))\n",
        "Y.required_grad = True\n",
        "delta = torch.empty(N, N, d).cuda()\n",
        "\n",
        "Y.required_grad= True\n",
        "\n",
        "learning_rate = 1e3\n",
        "optimizer = torch.optim.SGD([Y], lr=learning_rate, momentum=0.0)\n",
        "init = torch.randn(N, d).cuda()\n",
        "_ = Y.data.copy_(1e-2 * init)\n",
        "\n",
        "ttt = 10\n",
        "totalIt = 1500\n",
        "de = (ttt-1) / 1000\n",
        "it = 0\n",
        "\n",
        "def optimize():\n",
        "    global it, delta, ttt, optimizer, P, Y    \n",
        "    for iii in range(10):\n",
        "        it = it + 1\n",
        "        with torch.no_grad():\n",
        "            delta = Y.view(N, 1, d).expand_as(delta) - Y.view(1, N, d).expand_as(delta)\n",
        "            dist = torch.reciprocal(torch.sum(delta * delta, dim=2) + 1.0)\n",
        "            dist = dist - torch.eye(N).cuda()\n",
        "            total = torch.sum(dist)\n",
        "            Q = dist / total\n",
        "\n",
        "            if it == 1000:\n",
        "                learning_rate = 1e2\n",
        "                optimizer = torch.optim.Adam([Y], lr=1e-1)#, momentum=0.8)\n",
        "\n",
        "            if it < 1000:\n",
        "                ttt = ttt - de\n",
        "\n",
        "                if ttt < 1.0:\n",
        "                    ttt = 1.0\n",
        "\n",
        "                coeff = (ttt*P -Q) * dist\n",
        "                gradient = 4 * torch.sum( coeff.view(N,N, 1).expand_as(delta) * delta,dim=0) - 1e-7 * Y.data\n",
        "            else:    \n",
        "                coeff = (P -Q) * dist\n",
        "                gradient = 4 * torch.sum( coeff.view(N,N, 1).expand_as(delta) * delta,dim=0)\n",
        "\n",
        "            Y.grad = -gradient\n",
        "            optimizer.step()\n",
        "\n",
        "\n",
        "\n",
        "    loss = torch.sum(P * torch.log(Q + 1e-20))\n",
        "    return loss.item()    "
      ],
      "execution_count": 27,
      "outputs": []
    },
    {
      "metadata": {
        "id": "zoIWon5BSljp",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 741
        },
        "outputId": "197a50a8-da14-4625-8134-73c0d2ea978c"
      },
      "cell_type": "code",
      "source": [
        "#@title\n",
        "from IPython.display import HTML\n",
        "import numpy as np\n",
        "import matplotlib.animation\n",
        "\n",
        "rcParams['figure.figsize'] = 10,10\n",
        "plt.style.use('seaborn-white')\n",
        "fig, ax = plt.subplots()\n",
        "\n",
        "plt.axis('off')\n",
        "plt.close()\n",
        "\n",
        "sc = ax.scatter(Y.detach()[:, 0], Y.detach()[:, 1], \n",
        "                c=target.numpy(), s= 5, cmap=\"tab10\", alpha=0.7)\n",
        "ax.set_xlim(-60,60)\n",
        "ax.set_ylim(-60, 60)\n",
        "ax.grid(False)\n",
        "\n",
        "\n",
        "def animate(f):\n",
        "    global Y\n",
        "    optimize()    \n",
        "    x, y = Y.detach()[:, 0], Y.detach()[:, 1]\n",
        "    sc.set_offsets(np.c_[x,y])\n",
        "    sc.autoscale\n",
        "\n",
        "ani = matplotlib.animation.FuncAnimation(fig, animate, frames=250)\n",
        "HTML(ani.to_html5_video())"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<video width=\"720\" height=\"720\" controls autoplay loop>\n",
              "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlACHnqm1kYXQAAAKtBgX//6ncRem9\n",
              "5tlIt5Ys2CDZI+7veDI2NCAtIGNvcmUgMTQ4IHIyNzk1IGFhYTlhYTggLSBILjI2NC9NUEVHLTQg\n",
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