Paper Notes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Paper Notes\n",
    "\n",
    "## Out-of-sample extension of graph adjacency spectral embedding, Levin\n",
    "\n",
    "### Out-of-sample problem description. \n",
    "\n",
    "Working with embeddings where you have some training set $D = \\{z_1, z_2, ..., z_n\\}$ and you want to embed each each training sample in a lower dimensional ($d$) space. Let $X \\epsilon R^{n\\times d}$ be that embeding where the nth row corresponds to the embedding of $z_n$. The out of sample problem is to embed a z you havent seen using only $X$\n",
    "\n",
    "### Laplacian Embedding\n",
    "\n",
    "Laplacian embedding is a graph embedding. Given Adjacency matrix $A \\epsilon R^{n \\times n}$. Laplacian $L = D^{-1/2}AD^{-1/2}$. Note, $D \\epsilon R^{n \\times n}$ where $d_{ii} = \\sum_j A_{ij}$. The embedding is given by the rows of $U_L \\epsilon R^{n \\times d}$ whose columns are the d orthonormal eigenvectors corresponding to the top d eigenvalues of L (not including 1). \n",
    "\n",
    "### Out of sample extension\n",
    "\n",
    "In order to get the out of sample extension we do the following:\n",
    "\n",
    "$min_{f(x)\\epsilon R^d} \\sum_{i=1}^n{(K(x, x_i) - \\frac{1}{n}\\sum_{t=1}{d}{\\lambda_t f_t(x_i) f_t(x)})}$\n",
    "\n",
    "Note: \n",
    "$f_t(x_i) = (v_t)_i$ which is the ith component of $v_t$\n",
    "\n",
    "### Question, is Laplacian Spectral Embedding the same as Laplacian eigenmaps embedding?\n",
    "\n",
    "## Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering, Belkin\n",
    "\n",
    "#### The laplacian eigenmap embedding has a property where it conserves locality. This means that it emphasizes natural spatial clusters in the data. \n",
    "\n",
    "### LSE algorithm: \n",
    "![](spectral_clustering_alg.png)\n",
    "![](spectral_clustering_alg_2.png)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Laplacian Eigenmaps and Sp ectral Techniques for Emb edding and Clustering.pdf\r\n",
      "Laplacian Eigenmaps for Dimensionality Reduction and Data Representation.pdf\r\n",
      "Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering.pdf\r\n",
      "Out-of-sample extension of graph adjacency spectral embedding.pdf\r\n",
      "Paper Notes.ipynb\r\n",
      "figure_to_reproduce.png\r\n",
      "spectral_clustering_alg.png\r\n",
      "spectral_clustering_alg_2.png\r\n"
     ]
    }
   ],
   "source": [
    "!ls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Proposed experiment to make sure it works\n",
    "Replicate figure 1 in [paper](https://arxiv.org/pdf/1802.06307.pdf) from Levin\n",
    "\n",
    "![](figure_to_reproduce.png)\n",
    "\n",
    "How the figure was created:\n",
    "\n",
    "1) RDPG with parameters with number of nodes 50, 100, and 500 (100 trials each)\n",
    "\n",
    "2) Embed with the OOS LSE Algorithm \n",
    "\n",
    "3) Produce the plots\n",
    "\n",
    "\n",
    "I could create these plots on the [OOS LSE code](https://github.com/neurodata/primitives-interfaces/tree/master/jhu_primitives/ooslse) already written, then test my implementation to ensure results are the same.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Initial testing \n",
    "\n",
    "Goal: Make sure the LSE looks similar to the figure pictured above\n",
    "\n",
    "Note: Some of the following code (namley the code for plotting) was adapted from [Alex's code](https://github.com/loftusa/graspy-personal/blob/master/oos/notebooks/paper_fig_recreation.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "from scipy.stats import rankdata\n",
    "\n",
    "from sklearn.decomposition import TruncatedSVD\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "from graspy.simulations import rdpg\n",
    "from graspy.embed.base import BaseEmbed\n",
    "from graspy.plot import heatmap, pairplot\n",
    "from graspy.utils import (\n",
    "    import_graph,\n",
    "    is_fully_connected,\n",
    "    augment_diagonal,\n",
    "    pass_to_ranks,\n",
    "    is_unweighted,\n",
    ")\n",
    "\n",
    "from scipy.linalg import orthogonal_procrustes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _profile_likelihood_maximization(U, n_elbows):\n",
    "    \"\"\"\n",
    "    Inputs\n",
    "        U - An ordered or unordered list of eigenvalues\n",
    "        n - The number of elbows to return\n",
    "    Return\n",
    "        elbows - A numpy array containing elbows\n",
    "    \"\"\"\n",
    "    if type(U) == list:  # cast to array for functionality later\n",
    "        U = np.array(U)\n",
    "\n",
    "    if n_elbows == 0:  # nothing to do..\n",
    "        return np.array([])\n",
    "\n",
    "    if U.ndim == 2:\n",
    "        U = np.std(U, axis=0)\n",
    "\n",
    "    if len(U) == 0:\n",
    "        return np.array([])\n",
    "\n",
    "    elbows = []\n",
    "\n",
    "    if len(U) == 1:\n",
    "        return np.array(elbows.append(U[0]))\n",
    "\n",
    "    # select values greater than the threshold\n",
    "    U.sort()  # sort\n",
    "    U = U[::-1]  # reverse array so that it is sorted in descending order\n",
    "    n = len(U)\n",
    "\n",
    "    while len(elbows) < n_elbows and len(U) > 1:\n",
    "        d = 1\n",
    "        sample_var = np.var(U, ddof=1)\n",
    "        sample_scale = sample_var ** (1 / 2)\n",
    "        elbow = 0\n",
    "        likelihood_elbow = -1000000\n",
    "        while d < len(U):\n",
    "            mean_sig = np.mean(U[:d])\n",
    "            mean_noise = np.mean(U[d:])\n",
    "            sig_likelihood = 0\n",
    "            noise_likelihood = 0\n",
    "            for i in range(d):\n",
    "                sig_likelihood += np.log(norm.pdf(U[i], mean_sig, sample_scale))\n",
    "            for i in range(d, len(U)):\n",
    "                noise_likelihood += np.log(norm.pdf(U[i], mean_noise, sample_scale))\n",
    "\n",
    "            likelihood = noise_likelihood + sig_likelihood\n",
    "\n",
    "            if likelihood > likelihood_elbow:\n",
    "                likelihood_elbow = likelihood\n",
    "                elbow = d\n",
    "            d += 1\n",
    "        if len(elbows) == 0:\n",
    "            elbows.append(elbow)\n",
    "        else:\n",
    "            elbows.append(elbow + elbows[-1])\n",
    "        U = U[elbow:]\n",
    "\n",
    "    if len(elbows) == n_elbows:\n",
    "        return np.array(elbows)\n",
    "\n",
    "    if len(U) == 0:\n",
    "        return np.array(elbows)\n",
    "    else:\n",
    "        elbows.append(n)\n",
    "        return np.array(elbows)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1234)\n",
    "\n",
    "def produce(inpt, out_samp, max_dimension = 1, which_elbow = 1, n_in_sample = 1000):\n",
    "    \"\"\"\n",
    "    Perform Out of Sample Laplacian Spectral Embedding on a graph.\n",
    "    max_dimension >= 1\n",
    "    which_elbow is 1 or 2\n",
    "    n_in_sample >= 1\n",
    "    \n",
    "    \"\"\"\n",
    "    g = inpt.copy()\n",
    "\n",
    "    n = g.shape[0]\n",
    "    D = np.linalg.pinv(np.diag(g.sum(axis=1))**(1/2))\n",
    "    L = D @ g @ D\n",
    "\n",
    "    if max_dimension >= n:\n",
    "        max_dimension = n - 1\n",
    "    d_max = max_dimension\n",
    "\n",
    "    in_sample_n = n_in_sample\n",
    "\n",
    "    if in_sample_n > n:\n",
    "        in_sample_n = n\n",
    "    #print(\"n = \", n)\n",
    "#     in_sample_idx = np.random.choice(n, in_sample_n)\n",
    "    in_sample_idx = np.setdiff1d(np.arange(n), out_samp)\n",
    "    #print(\"in_sample_idx = \", in_sample_idx)\n",
    "#     out_sample_idx = np.setdiff1d(list(range(n)),in_sample_idx)\n",
    "    out_sample_idx = out_samp\n",
    "    #print(\"out_sample_idx = \", out_sample_idx)\n",
    "\n",
    "    in_sample_A = L[np.ix_(in_sample_idx, in_sample_idx)]\n",
    "    #print(\"in_sample_A shape = \", in_sample_A.shape)\n",
    "    out_sample_A = L[np.ix_(out_sample_idx, in_sample_idx)]\n",
    "    #print(\"out_sample_A shape = \", out_sample_A.shape)\n",
    "\n",
    "    tsvd = TruncatedSVD(n_components = d_max)\n",
    "    tsvd.fit(in_sample_A)\n",
    "\n",
    "    eig_vectors = tsvd.components_.T\n",
    "    eig_values = tsvd.singular_values_\n",
    "    elbow = _profile_likelihood_maximization(eig_values, which_elbow)[-1]\n",
    "\n",
    "    eig_vectors = eig_vectors[:, :elbow + 1].copy()\n",
    "    eig_values = eig_values[:elbow + 1].copy()\n",
    "    d = len(eig_values)\n",
    "\n",
    "    in_sample_embedding = eig_vectors.dot(np.diag(eig_values**0.5))\n",
    "\n",
    "    out_sample_embedding = out_sample_A @ eig_vectors @ np.diag(1/np.sqrt(eig_values))\n",
    "    embedding = np.zeros((n,d))\n",
    "    embedding[in_sample_idx] = in_sample_embedding\n",
    "    embedding[out_sample_idx] = out_sample_embedding\n",
    "\n",
    "    return embedding, in_sample_idx, out_sample_idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Needs updating... not working\n",
    "\n",
    "def trial(n, directed=False):\n",
    "    # known parameters\n",
    "    labels = [\"blue\"]*n + [\"red\"]*n\n",
    "    lamb = np.array([0.4, 1-.4])\n",
    "    x1 = np.array([.2, .7])\n",
    "    x2 = np.array([.65, .3])\n",
    "    latents = np.vstack((x1, x2))\n",
    "    \n",
    "    # generate latent positions\n",
    "    latents = np.repeat(latents, n, axis=0)\n",
    "\n",
    "    # generate M from rdpg\n",
    "    M = rdpg(latents, directed=directed)\n",
    "\n",
    "    # index out oos\n",
    "    p = np.repeat(lamb, n) / n\n",
    "    i = np.random.choice(n*2, p=p)\n",
    "    label = labels[i]\n",
    "    a = np.delete(M[i, :], i)\n",
    "    if directed:\n",
    "        a2 = np.delete(M[:, i], i)\n",
    "        a = (a, a2)\n",
    "    A = np.delete(np.delete(M, i, 0), i, 1)\n",
    "    latents_ = np.delete(latents, i, 0)\n",
    "\n",
    "    # embed without oos stuff\n",
    "    embding, insmpl, outsmpl = produce(A, max_dimension=2, n_in_sample=A.shape[0]-1)\n",
    "    \n",
    "    # Procrustes alignment\n",
    "#     R, _ = orthogonal_procrustes(ase.latent_left_, latents_)\n",
    "#     if directed:\n",
    "#         R_right_, _ = orthogonal_procrustes(ase.latent_right_, latents_)\n",
    "\n",
    "    # predict oos\n",
    "    w = embding[outsmpl]\n",
    "#     if not directed:\n",
    "#         w = w @ R\n",
    "#     else:\n",
    "#         w_left_ = w[0] @ R\n",
    "#         w_right_ = w[1] @ R_right_\n",
    "#         w = (w_left_, w_right_)\n",
    "\n",
    "    return w, label"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Try one trial first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=50\n",
    "labels = [\"blue\"]*n + [\"red\"]*n\n",
    "lamb = np.array([0.4, 1-.4])\n",
    "x1 = np.array([.2, .7])\n",
    "x2 = np.array([.65, .3])\n",
    "latents = np.vstack((x1, x2))\n",
    "\n",
    "latents = np.repeat(latents, n, axis=0)\n",
    "\n",
    "# generate M from rdpg\n",
    "M = rdpg(latents, directed=False)\n",
    "\n",
    "# # index out oos\n",
    "# p = np.repeat(lamb, n) / n\n",
    "# i = np.random.choice(n*2, p=p)\n",
    "# label = labels[i]\n",
    "# a = np.delete(M[i, :], i)\n",
    "\n",
    "# #A = np.delete(np.delete(M, i, 0), i, 1)\n",
    "# print(A.shape)\n",
    "# latents_ = np.delete(latents, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fa1efe5f090>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "heatmap(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from graspy.simulations import sbm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from graspy.embed import LaplacianSpectralEmbed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_verts = 250\n",
    "labels_sbm = n_verts * [0] + n_verts * [1]\n",
    "P = np.array([[0.8, 0.2],\n",
    "              [0.2, 0.8]])\n",
    "\n",
    "latents = np.repeat(P, n_verts, axis=0)\n",
    "\n",
    "undirected_sbm = sbm(2 * [n_verts], P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "309\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f8e30b3d410>"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "oos_idx = np.random.choice(n_verts*2)\n",
    "print(oos_idx)\n",
    "colors = np.array([\"red\"]*n_verts+[\"blue\"]*n_verts)\n",
    "\n",
    "embding, insmpl, outsmpl = produce(undirected_sbm, np.array([oos_idx]), max_dimension=2, n_in_sample=1000)\n",
    "\n",
    "R, sca = orthogonal_procrustes(embding[insmpl], latents[insmpl])\n",
    "\n",
    "newembed = embding[insmpl] @ R\n",
    "outembed = embding[outsmpl] @ R\n",
    "\n",
    "plt.scatter(newembed[:, 0], newembed[:, 1], color=colors[insmpl])\n",
    "plt.scatter(outembed[:, 0], outembed[:, 1], color=colors[outsmpl])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "lse = LaplacianSpectralEmbed(n_components=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xhat = lse.fit_transform(undirected_sbm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = pairplot(Xhat, title='LSE adjacency spectral embedding')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "R, sca = orthogonal_procrustes(Xhat, latents)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f8e5e48b810>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "newembed = Xhat@R\n",
    "plt.figure()\n",
    "plt.scatter(newembed[:, 0], newembed[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f8e7d42bbd0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "heatmap(undirected_sbm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.70069433  0.7134616 ]\n",
      " [ 0.7134616  -0.70069433]]\n"
     ]
    }
   ],
   "source": [
    "print(R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f8e5e8ddb50>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Paper Figure Recreation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nn= 26\n",
      "nn= 50\n",
      "nn= 250\n"
     ]
    }
   ],
   "source": [
    "num_trials = 100\n",
    "\n",
    "ptp_lst = []\n",
    "col_lst = []\n",
    "\n",
    "for nn in [26, 50, 250]:  \n",
    "    points_to_plot = []\n",
    "    colors = []\n",
    "    print(\"nn=\", nn)\n",
    "    for ii in range(num_trials):\n",
    "        n=int(nn/2)\n",
    "        labels = [\"blue\"]*n + [\"red\"]*n\n",
    "        \n",
    "        n_verts = n\n",
    "        labels_sbm = n_verts * [0] + n_verts * [1]\n",
    "        P = np.array([[0.7, 0.3],\n",
    "                      [0.3, 0.7]])\n",
    "\n",
    "        latents = np.repeat(P, n, axis=0)\n",
    "\n",
    "        undirected_sbm = sbm(2 * [n_verts], P)\n",
    "\n",
    "        oos_idx = np.random.choice(nn)\n",
    "\n",
    "        embding, insmpl, outsmpl = produce(undirected_sbm, np.array([oos_idx]), max_dimension=2, n_in_sample=1000)\n",
    "\n",
    "        R, sca = orthogonal_procrustes(embding[insmpl], latents[insmpl])\n",
    "\n",
    "        os_adj_embd = embding[outsmpl] @ R\n",
    "\n",
    "        points_to_plot.append(os_adj_embd)\n",
    "        colors.append(labels[oos_idx])\n",
    "\n",
    "    ptp_lst.append(points_to_plot)\n",
    "    col_lst.append(colors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "titles = [\"n=50\", \"n=100\", \"n=500\"]\n",
    "\n",
    "plt.figure(figsize=(15, 5))\n",
    "for ii, ptp in enumerate(ptp_lst):\n",
    "    plt.subplot(1, 3, ii+1)\n",
    "    plt.title(titles[ii])\n",
    "    plt.xticks([], \" \")\n",
    "    plt.yticks([], \" \")\n",
    "    points_to_plot = np.array(ptp_lst[ii])\n",
    "    plt.scatter(points_to_plot[:, 0, 0], points_to_plot[:, 0, 1], c=col_lst[ii])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.choice(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recreation of Paper Figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_trials = 100\n",
    "\n",
    "ptp_lst = []\n",
    "col_lst = []\n",
    "\n",
    "for nn in [50, 100, 500]:  \n",
    "    points_to_plot = []\n",
    "    colors = []\n",
    "    for ii in range(num_trials):\n",
    "\n",
    "\n",
    "        n=int(nn/2)\n",
    "        labels = [\"blue\"]*n + [\"red\"]*n\n",
    "        lamb = np.array([0.4, 1-.4])\n",
    "        x1 = np.array([.2, .7])\n",
    "        x2 = np.array([.65, .3])\n",
    "        latents = np.vstack((x1, x2))\n",
    "\n",
    "        latents = np.repeat(latents, n, axis=0)\n",
    "\n",
    "        M = rdpg(latents, directed=False)\n",
    "\n",
    "        oos_idx = np.random.choice(nn)\n",
    "\n",
    "        embding, insmpl, outsmpl = produce(M, np.array([oos_idx]), max_dimension=2, n_in_sample=1000)\n",
    "\n",
    "        R, sca = orthogonal_procrustes(embding[insmpl], latents[insmpl])\n",
    "\n",
    "        os_adj_embd = embding[outsmpl] @ R\n",
    "\n",
    "        points_to_plot.append(os_adj_embd)\n",
    "        colors.append(labels[oos_idx])\n",
    "\n",
    "    ptp_lst.append(points_to_plot)\n",
    "    col_lst.append(colors)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f9bcc934310>"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "points_to_plot = np.array(points_to_plot)\n",
    "plt.scatter(points_to_plot[:, 0, 0], points_to_plot[:, 0, 1], c=colors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [],
   "source": [
    "for ii in range(len(ptp_lst)):\n",
    "    ptp_lst[ii] = np.array(ptp_lst[ii])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(100, 1, 2), (100, 1, 2), (100, 1, 2)]"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[ptp.shape for ptp in points_to_plot]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f9bcc880310>"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 5))\n",
    "\n",
    "plt.subplot(1, 3, 1)\n",
    "plt.title(\"n=50\")\n",
    "plt.scatter(ptp_lst[0][:, 0, 0], ptp_lst[0][:, 0, 1], c=col_lst[0], s=10)\n",
    "\n",
    "plt.subplot(1, 3, 2)\n",
    "plt.title(\"n=100\")\n",
    "plt.scatter(ptp_lst[1][:, 0, 0], ptp_lst[1][:, 0, 1], c=col_lst[1], s=10)\n",
    "\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.title(\"n=500\")\n",
    "plt.scatter(ptp_lst[2][:, 0, 0], ptp_lst[2][:, 0, 1], c=col_lst[2], s=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in_sample_idx =  [  0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17\n",
      "  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35\n",
      "  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53\n",
      "  54  55  56  57  58  59  60  61  62  63  64  65  66  67  68  69  70  71\n",
      "  72  74  75  76  77  79  80  82  83  84  85  86  87  88  89  90  91  92\n",
      "  93  94  95  96  97  98  99 100 101 102 103 104 105 106 107 108 109 110\n",
      " 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129\n",
      " 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147\n",
      " 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165\n",
      " 166 167 168 169 170 171 172 173 174 175 177 178 179 180 181 182 183 184\n",
      " 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202\n",
      " 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220\n",
      " 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238\n",
      " 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256\n",
      " 257 258 259 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275\n",
      " 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293\n",
      " 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311\n",
      " 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329\n",
      " 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347\n",
      " 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365\n",
      " 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384\n",
      " 385 386 387 388 389 390 391 392 393 394 395 397 398 399 400 401 402 403\n",
      " 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421\n",
      " 422 423 424 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440\n",
      " 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458\n",
      " 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476\n",
      " 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495\n",
      " 496 497 498 499]\n",
      "out_sample_idx =  [176  73 396 111 260 366 425  78  81 477]\n"
     ]
    }
   ],
   "source": [
    "n=500\n",
    "n=int(nn/2)\n",
    "labels = [\"blue\"]*n + [\"red\"]*n\n",
    "lamb = np.array([0.4, 1-.4])\n",
    "x1 = np.array([.2, .7])\n",
    "x2 = np.array([.65, .3])\n",
    "latents = np.vstack((x1, x2))\n",
    "\n",
    "latents = np.repeat(latents, n, axis=0)\n",
    "\n",
    "M = rdpg(latents, directed=False)\n",
    "\n",
    "oos_idx = np.random.choice(nn, 10)\n",
    "\n",
    "embding, insmpl, outsmpl = produce(M, oos_idx, max_dimension=2, n_in_sample=1000)\n",
    "\n",
    "R, sca = orthogonal_procrustes(embding[insmpl], latents[insmpl])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f9bd1c07f50>"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "labels = np.array(labels)\n",
    "\n",
    "plt.figure()\n",
    "inn = embding[insmpl]\n",
    "inn_colors = labels[insmpl]\n",
    "out_colors = labels[outsmpl]\n",
    "\n",
    "embding[insmpl] = (embding[insmpl] @ R)*sca\n",
    "# embding[outsmpl] = embding[outsmpl] @ R\n",
    "\n",
    "\n",
    "plt.scatter(embding[insmpl, 0], embding[insmpl, 1], c=labels[insmpl], marker='o', s=5)\n",
    "plt.scatter(embding[outsmpl, 0], embding[outsmpl, 1], c=labels[outsmpl], marker='x', s=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "250"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(np.where(inn_colors=='red')[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([303, 211, 294,  53, 204, 372, 152, 143, 177, 279])"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.choice(nn, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.153889925906824"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sca"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modifying Graspy Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}