{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Diffusion maps for single-cell data analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By means of this notebook, you can solve all the programming tasks of chapter 4. You can download all the needed files (data1.mat and guo.xlsx) from the homepage. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import scipy as sp\n", "import sklearn as skl\n", "import sklearn.manifold\n", "import sklearn.cluster\n", "import time\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "import matplotlib.patches as mpatches\n", "\n", "from scipy.io import loadmat \n", "from pandas import read_excel\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from sklearn.decomposition import PCA\n", "\n", "#add here your required imports" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "#### Task 1: Implement the diffusion maps algorithm.\n", "It is recommended to solve this task by defining a class for diffusion maps and implement a fit_transform function, which returns the embedding of a given data set. This standardizes the code when comparing diffusion maps with other dimensionality reduction methods." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# your code goes here" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "class DiffMap():\n", " \"\"\"\n", " Class Diffusion Maps\n", " \n", " Parameters\n", " ----------\n", " n_comp: int, optional, default = 2\n", " number of dimensions in which the data will be embedded\n", " sigma: optional, default = 10\n", " bandwidth of the Gaussian kernel\n", " alpha: optional, default = 1\n", " the density rescaling parameter\n", " \"\"\"\n", " \n", " def __init__(self, n_components = 2, sigma = 10, alpha = 1):\n", " self.ndim = n_components\n", " self.sigma = sigma\n", " self.alpha = alpha\n", " self.P = None\n", " \n", " \n", " def gaussian_kernal(self, x1, x2):\n", " n1 = np.size(x1,0)\n", " n2 = np.size(x2,0)\n", " norms = np.empty((n1,n2))\n", " for j in range(n2):\n", " norms[:,j] = np.linalg.norm(np.subtract(x1[:,:],x2[j,:]),axis=1)**2\n", " return np.exp(-norms / (2*self.sigma**2))\n", " \n", " def compute_eigs(self, A, k = None):\n", " if(k==None):\n", " k = self.ndim\n", " n = np.shape(A)[1]\n", " eigvals, eigvecs = sp.linalg.eigh(A, eigvals=(n-k-1,n-1))\n", " return np.flip(eigvals,0), np.flip(eigvecs,1)\n", " \n", " def fit_transform(self, X):\n", " \"\"\"\n", " Computes the embedding\n", " \n", " Parameters\n", " ----------\n", " X: array\n", " input data\n", " \n", " Returns\n", " -------\n", " evecs: array [n_cells, n_comp]\n", " array of n_comp eigenvectors or diffusion coordinates\n", " \"\"\"\n", " K = self.gaussian_kernal(X,X)\n", " Q_diag = np.sum(K, axis=1)\n", " Q_alpha = np.diag(np.power(Q_diag, -self.alpha))\n", " K_alpha = np.dot(np.dot(Q_alpha, K), Q_alpha)\n", " np.fill_diagonal(K_alpha, 0)\n", " D_alpha_diag = np.sum(K_alpha, axis=1)\n", " D_alpha_inv = np.diag(np.power(D_alpha_diag, -1))\n", " P = np.dot(D_alpha_inv, K_alpha)\n", " eigvals, eigvecs = self.compute_eigs(P)\n", " self.P = P\n", " return np.multiply(eigvecs[:,1:],eigvals[1:])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 2: Perform a diffusion map analysis on the Buettner data set. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def load_buettner_data(): \n", " #load buettner data\n", " file = loadmat('data//data1.mat')\n", " data = file.get('in_X')\n", " data = np.array(data)\n", "\n", " #group assignments\n", " labels = file.get('true_labs')\n", " labels = labels[:,0] -1\n", "\n", " #group names\n", " stage_names = ['1', '2', '3']\n", "\n", " return data, stage_names, labels" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def plot_3d_data(data, stage_names, labels):\n", " fig = plt.figure()\n", " ax = fig.add_subplot(111, projection='3d')\n", " \n", " colors = matplotlib.cm.ScalarMappable().to_rgba(range(max(labels)+1))\n", "\n", " ax.scatter(data[:,0],data[:,1],data[:,2], c = colors[labels])\n", "\n", " legend_stages = []\n", " for i in range(np.size(stage_names)):\n", " legend_stages = legend_stages + [mpatches.Patch(color=colors[i], label=stage_names[i])]\n", "\n", " plt.legend(handles=legend_stages)\n", " \n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "buettner_data, buettner_stage_names, buettner_labels = load_buettner_data()\n", "buettner_diff_map = DiffMap(n_components=3, sigma=20, alpha=1)\n", "buettner_data_diff_transformed = buettner_diff_map.fit_transform(buettner_data)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_3d_data(buettner_data_diff_transformed, buettner_stage_names, buettner_labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 3: Perform a PCA analysis of the Buettner data set." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(182, 3)\n", "(182, 8989)\n" ] } ], "source": [ "buettner_pca = PCA(n_components=3)\n", "buettner_pca.fit(buettner_data)\n", "buettner_data_pca_transformed = buettner_pca.transform(buettner_data)\n", "print(np.shape(buettner_data_pca_transformed))\n", "print(np.shape(buettner_data))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_3d_data(buettner_data_pca_transformed, buettner_stage_names, buettner_labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While after the PCA dimensioality reduction all the points are ordered in some kind of cloud without any further structure, the Diffusion map reduction orders the point along a path in R3." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Single-cell data analysis\n", "\n", "In the following, we will apply diffusion maps to the Guo data. In the file, you will find some necessary information:\n", "\n", "1. the input data, which is a matrix with a certain number of cells as row number and a certain number of genes as column number,\n", "2. the names of the measured genes and\n", "3. an assignment of each cell to an embryonic stage. These assignments have to be converted into numerical labels to use them for the scatter plots.\n", "\n", "### Pre-processing\n", "#### Task 4: Pre-process the Guo data.\n", "\n", "Take a look at the file guo.xlsx. The naming annotation in the first column refers to the embryonic stage, embryo number, and individual cell number, thus 64C 2.7 refers to the 7th cell harvested from the 2nd embryo collected from the 64-cell stage. In the first row, you will find the names of the measured genes." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def load_guo_data(normalize = True):\n", " #load guo data\n", " data_frame = read_excel('data//guo.xlsx', sheet_name = 'Sheet1')\n", "\n", " #data\n", " adata = data_frame.as_matrix()\n", " data = adata[:,1:]\n", " embryonic_stages = adata[:,0]\n", "\n", " #genes\n", " genes_tmp = data_frame.axes[1][1:]\n", " genes_names = [genes_tmp[k] for k in range(genes_tmp.size)]\n", " \n", " # your code goes here\n", " # sort out one cell stages\n", " non_stage_one_indices = np.where([(not ename.startswith('1C')) for ename in embryonic_stages])[0]\n", " data = data[non_stage_one_indices,:]\n", " labels = embryonic_stages[non_stage_one_indices]\n", " # sort out invalid data\n", " non_currupted_indices = np.where([(not np.any(values > 28)) for values in data])[0]\n", " data = data[non_currupted_indices,:]\n", " labels = labels[non_currupted_indices]\n", " # normalize data\n", " if(normalize):\n", " control_genes = ['Actb', 'Gapdh'] \n", " control_gene_indices = np.where(np.isin(genes_names, control_genes))[0]\n", " data = np.subtract(data.T, np.mean(data[:,control_gene_indices],axis=1), where=(data!=28.0).T).T\n", " threshold = max(data[data!=None])\n", " data[np.where(data==None)]=np.ceil(threshold)\n", " # round to three decimals\n", " data = np.around(data.astype(float), decimals=3)\n", " \n", " #stage_names and creating labels\n", " stage_names = ['2C', '4C', '8C', '16C', '32C', '64C'] \n", " \n", " labels = np.array([np.where([label.startswith(sname) for sname in stage_names])[0][0] for label in labels])\n", " \n", " #labels = np.array([next(np.where([name.startswith(sname) for name in stage_names])[0][0]\n", " # for sname in stage_names if ename.startswith(sname)) for ename in embryonic_stages]) \n", " \n", " return data, stage_names,labels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 5: Perform a diffusion map analysis of the pre-processed Guo data." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def plot_2d_data(data, stage_names, labels):\n", " fig = plt.figure()\n", " \n", " colors = matplotlib.cm.ScalarMappable().to_rgba(range(max(labels)+1))\n", "\n", " plt.scatter(data[:,0],data[:,1], c = colors[labels])\n", "\n", " legend_stages = []\n", " for i in range(np.size(stage_names)):\n", " legend_stages = legend_stages + [mpatches.Patch(color=colors[i], label=stage_names[i])]\n", "\n", " plt.legend(handles=legend_stages)\n", " \n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "diff_map_pre_processed_guo = DiffMap(sigma=10, alpha=1, n_components=2)\n", "data_pre_processed_guo, stage_names_pre_processed_guo, labels_pre_processed_guo = load_guo_data()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Time taken: 0.07343006134033203s \n", "\n" ] } ], "source": [ "diff_map_time = time.time()\n", "transformed_data_pre_processed_guo = diff_map_pre_processed_guo.fit_transform(data_pre_processed_guo)\n", "diff_map_time = time.time() - diff_map_time\n", "print(\"Time taken: \" + str(diff_map_time) + \"s \\n\")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAD8CAYAAABzTgP2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzt3Xl4VOX58PHvfWbLZA9kYQkYkEUQFAFBXFCxKCoVRVQsLVi07lZfl6pttYqtrbbWrf5aFbEuVdyVuiOIUjc2AQFl3wIkBBLIntme948ZYiaZ7JOV+3Ndc2XmnOecuWcY5p5nPWKMQSmllDrEausAlFJKtS+aGJRSSoXRxKCUUiqMJgallFJhNDEopZQKo4lBKaVUGE0MSimlwmhiUEopFUYTg1JKqTD2tg6gKVJTU01WVlZbh6GUUh3K8uXL9xlj0uor1yETQ1ZWFsuWLWvrMJRSqkMRke0NKadNSUoppcJoYlBKKRVGE4NSSqkwHbKPQSmlmsvr9ZKdnU15eXlbhxJ1MTExZGZm4nA4mnS8Jgal1GEpOzubhIQEsrKyEJG2DidqjDHs37+f7Oxs+vTp06RzaFOSUuqwVF5eTteuXTtVUgAQEbp27dqsmpAmBqXUYauzJYVDmvu6NDEopZQKo30MSikFXNz9CgpyD0btfCkZSby6Z3adZXbu3Mn06dPJzc1FRLjyyiu58cYbAfjb3/7G7NmziYmJweFwcMMNNzB9+vSoxVcXTQxKKQVRTQoNPZ/dbuehhx5i+PDhFBUVMWLECMaPH8/nn3/O/PnzWbJkCYmJiRQWFvLWW29FNb4642q1Z1JKKRWme/fudO/eHYCEhAQGDRrErl27uP/++1m0aBGJiYkAJCYmMmPGjFaLS/sYlFKqHdi2bRvffvsto0ePpqioiL59+7ZZLJoYlFKqjRUXF3PhhRfyyCOPtHUogCYGpZRqU16vlwsvvJBp06YxefJkEhMTiY+PZ8uWLW0WkyYGpZRqI8YYLr/8cgYNGsTNN99cuf3OO+/kuuuuo7CwEAjWKJ5//vlWi0s7nxth3679lBwsJXNAD2x2W1uHo5SKopSMpKgPV63PF198wQsvvMDQoUMZNmwYAPfffz/XXHMNxcXFHH/88TgcDhwOB7fcckvUYquPGGNa7cmiZeTIkaY1L9RTkHuA357zJzav2o4xBpvNYuodF3DZrKmtFoNSKrq+//57Bg0a1NZhtJhIr09ElhtjRtZ3rNYY6mGM4eZT7yZ7w57KbX5fgP/88Q1csU4uvWNyG0anlFLRp30M9diyeju7N+VE3PfirNcJBAKtHJFSSrUsrTHUI39PAYFA5OY2b4WPbWt2sOZ/6xGBMeeNJLVn11aOUCmloksTQz36De8LAkTIDQbDNSNuJ+AP1hr+8es5XPW36Uy+8dzWDVIppaJIm5LqkZKexAkTa+mrMVQmBQje/+fN/yZna24rRaeUUtGniaEBZr39G37yi7FYliAiWDaLHv26RS5s4IX73mDZx6t46Ff/5PEbZrN+2ebWDVgppZpBh6s2gtfjZf/uApLSErl38t9YPn9VxHJduiVTWlRGeUkFliU4YhxM+/0ULr3jglaOWClVm+rDOS+8+HEKCkqidv6UlDjeePWGesv5/X5GjhxJz549effdd/F6vdx111288cYbJCQk4HK5uPvuuzn77LMb9fzNGa6qNYZGcDgddMtKxx0Xw8izjq21XGF+EeUlFQAEAoaKUg8vznqNvOz9rRWqUqqRopkUGnO+Rx99NOwL/K677mLPnj2sWbOGFStW8Pbbb1NUVBTV2OoTlcQgIhNEZL2IbBKROyLsHysiK0TEJyJTqu2bISIbQ7fWW1e2mc67bgLuhJga2212Gz6Pv8Z2vz/A0g9XtkZoSqkOIjs7m/fee48rrrgCgNLSUp5++mkef/xxXC4XABkZGVx88cWtGlezE4OI2IAngLOBwcClIjK4WrEdwGXAS9WO7QL8ARgNjAL+ICIpzY2pNThdDmaveZjBYwYEr68qcNTo/px9xbjgKKZq/F4/H85ZyOevf4XX4239gJVS7c5NN93Egw8+iGUFv4o3bdpE7969K6/D0FaiMVx1FLDJGLMFQETmApOAdYcKGGO2hfZVnw12FjDfGJMf2j8fmAC8HIW4Wlx6r1Qe/eJPeCqCX/ROl4Pvv9nAu/+aH7H8919v4L5L/g4GErrEc9ZlpzNj1iXExLpaM2ylVDvw7rvvkp6ezogRI1i0aFFbhxMmGk1JPYGdVR5nh7ZF9VgRuVJElonIsry8vCYF2lKcLgdOlwOApNRE7I46FtgL9fUX5Rfz+t//yyU9fkX2ht2tEKVSqj354osvmDdvHllZWUydOpWFCxdyzz33sGPHjspVVdtKh+l8NsY8ZYwZaYwZmZaW1tbh1CqtV1ccMY4Gly8tLOPPP3+sBSNSSrVHf/7zn8nOzmbbtm3MnTuXcePG8eabb3L55Zdz44034vF4AMjLy+O1115r1diikRh2Ab2qPM4MbWvpY9slh9PBtN81bmG9Dcs2c9WwW1n9+br6CyulWkRKSly7ON8f//hH0tLSGDx4MEOGDGHixImt3ufQ7HkMImIHNgBnEPxSXwr8zBizNkLZfwPvGmNeDz3uAiwHhoeKrABGHOpzqE1bzWNojCuG/D+2r8tu1DGuWCcPfXovA4/v10JRKaUO0WW3a9fsGoMxxgdcD3wEfA+8aoxZKyKzROS8UDDHi0g2cBHwpIisDR2bD9xHMJksBWbVlxQ6igfm303vQT2JiXMFRy01QEWph6dvf7GFI1NKqbpFZRE9Y8z7wPvVtt1d5f5Sgs1EkY6dA8yJRhztSdfuKcxe8zDff72B3O15FBUU88VbS/h24RpMLau1Aqz+bB3bv8/miEER3y6llGpxurpqCxIRBo8ZyOAxAwE475oJBAIBvnxnCX+85BH8vpoT4Ywx3H7mLEb85FjG/exkhv/kmAbXOJRSKho6zKikzsKyLE6+4ATOv2FCrWX27yrg4+cWcc/kv/LwVU+2YnRKKaWJoc1c8cDPsdnrfvvLSypY+NL/dHVWpVSr0sTQRux2OxMuPwNnPXMePOUevnlvORBsZiovrdDLiSqlWpT2MbSha/4+g/278lnxyWoQwVPmqVHG7rDhjovhi7eX8H//71n2ZefjinVywa/PYfo9F2Oz1THLWinVYGP/9CT7i0ujdr6u8bF8/rur6i338MMPM3v2bESEoUOH8uyzz2Kz2aKy9HZTaWJoQy63i/vm3cGeLblsWL6ZB2f8A095+AJ7YlkkZiRx72/n4svsDj274du9j9cefo+KUg9XP9RhFqRVql2LZlJo6Pl27drFY489xrp163C73Vx88cXMnTuXH374oXLpbZfLRW5uLp999llU46uLJoZ2oHvfDLr3zcDldvGnqQ9j2S0w4PP5uXn21Tw0ezG+bqlgC7b8maxulHdJ5I1H3uWkC0Yx9OTOO0lHqc7O5/NRVlaGw+GgtLSULl268PTTT7N169Y2W3pbE0M7csLEEbya8zTLPl6NCQQYceaxLF+1g3JDZVIAwGaDhFhMYhy/PftP/HvD43Tt3iFWK1dKVdGzZ09uvfVWevfujdvt5swzzyQrK6vNl97Wzud2xh3v5pTJoxk7ZQxxibGsW7c7PCkcIoJJjMPvD/DBMwtaP1ClVLMVFBTwzjvvsHXrVnbv3k1JSQlvv/12W4eliaG96949GWekZbyNQco9eMu9umy3Uh3UJ598Qp8+fUhLS8PhcDB58mS2bdvW5ktva2Jo584YNxiHs1qLXyAAfj/sO0hMnIujTzyqbYJTSjVL7969+frrryktLcUYw4IFCzjuuOPafOltTQztXHx8DI/8fRpZWanBK4YGAlBUirVsPXa7RUKXeH7y81Mqy1eUVfDhnIU8MP1xnr/3Vfbt2t9msSvVkXSNj231840ePZopU6YwfPhwhg4dSiAQ4Morr2zzpbebvex2W+gIy263hNycA7z35HwWPLsQT5mHky4YzYxZl5CSngRAUUEx14+6k/ycAspLKnC4HNgcNv7y4e85+sSBbRy9Uu2LLrtdOx2V1IFkdEtm5h8uYuYfLoq4/z9/eoO9O/fh8/gA8FZ48VZ4ue2Meznx/OOZ/OtzKhf0U0qp2mhTUifyvze+qUwKVXkrvHz+6lf8ZvwsPpijI5iUUnXTGkMnUte6S8YYKko9/OOGOSx4cTE52/Zy1Kh+/OLuizhicK9aj1NKHX60xtCJnHvVeFyxzjrLeMo8rFq0ltxteXz++tdcP/q3bF61rXUCVEp1CJoYOpHzrz+bUecMx+V2Ilb4xX1MlwT8Q/viH9aPQPeuGBFMwFBeUs4zd/ynjSJWSrVH2pTUidjsNu5+9Ra2r9vJB88s5L///AhPuZdA3x6YXulgD06UM0nxmO5dsb7dgBhY982GNo5cKdWeaGLohI4Y3IurH5pBcnoiz//5bcqPyACrSuXQHlxribRk2HuALhnJAJSVecgvKCEtNQFn9Ul1SnVyo995hH3lJVE7X2pMHN9MuqnOMjNnzuTdd98lPT2dNWvWVG5//PHHeeKJJ7DZbJx77rk8+OCDACxZsoRbb72V3NxcYmNjGTFiBI899hixsdGdg6H/+zuxqbdfQPzgI/jHPxfg8Va7vrTdRiA1mbiSMi7+zfk8+tjHfPDRaixLEBF+Me1Epl5yQtsErlQbiGZSaOj5LrvsMq6//nqmT59eue3TTz/lnXfeYdWqVbhcLvbu3QtAbm4uF110EXPnzmXMmDEAvP766xQVFWliUI2Tmp6I3WGrmRgCBrsxXHrnBWypCPDhx6vxVBnq+vyLX9ClSxxnjh/ayhErdfgYO3Ys27ZtC9v2z3/+kzvuuKNyye309HQAnnjiCWbMmFGZFACmTJnSInFp53MnN2J4Hxz2movwOV12/vHmzVz8m/N5992VVFSEz38oL/fy4ktftVaYSqmQDRs2sHjxYkaPHs2pp57K0qVLAVizZg0jRoxolRg0MXRyDoeNvz4wlS5d4oh1O4mLdRHjcnDLzWczYGAPysq8+Pz+iMfm5xe3crRKKZ/PR35+Pl9//TV//etfufjii2ntpYu0Kekw0K9fBq++fD3rvt9FebmXowf3xO0OzneIj3eRlBTL/v01k8DAAd1bO1SlDnuZmZlMnjwZEWHUqFFYlsW+ffs4+uijWb58OZMmTWrxGLTGcJiwLGHI0ZmMHNGnMikAiAjXXXMGLpe9yjaIcTm46lent0WoSh3Wzj//fD799FMg2Kzk8XhITU3l+uuv57nnnuObb76pLPvmm2+Sm5sb9Ri0xqA47dRBJCa6ef6FL9i95wAD+mfwyxmncOSRGZVlCgpK+PSz7ykprmDE8CwGDeqBiNRxVqU6ltSYuKgPV63PpZdeyqJFi9i3bx+ZmZnce++9zJw5k5kzZzJkyBCcTifPPfccIkJGRgZz587l1ltvZe/evViWxdixY5kwYULUYj5El91W9Vq6dAt33/smGPD6/Diddk4c05/f3vFTLEuTg+qYdNnt2mlTkqqTx+Nj1h/foaLCR4XHRyBgKC/38uVXG/niy+CM6f17Clj12Vr27c5v42iVUtGgTUmqTt+tyQZq1iqDw1m/5O/3v0NhYRn2whKsbTmcPHE4tz93PXaHfrSU6qi0xqDqJERKC0GbNuZy0BvAuF1405KpOK4///twJc/+/uXWDFEpFWVRSQwiMkFE1ovIJhG5I8J+l4i8Etr/jYhkhbZniUiZiKwM3f4VjXhU9Awd2qvWTuawhGFZ4LBTMXwgLy/P5oILH+WzxT+0SoxKqehqdmIQERvwBHA2MBi4VEQGVyt2OVBgjOkHPAw8UGXfZmPMsNDt6ubGo6LL4bBxz90XEBPjwOWyY7MJNptEThYilbeDhWXcO+tt5jz7WatPzlFKNU80agyjgE3GmC3GGA8wF6g+A2MS8Fzo/uvAGaJjHTuMEcOzePk/1zLx3GGVCaGhX/YvvvQVZ0/8G7u0Y1qpDiMaPYQ9gZ1VHmcDo2srY4zxichBoGtoXx8R+RYoBH5vjFkchZhUlMXHuViwcB0+X6DRx3o8fn4x4yke/PMljBiRpfMfVLv053UzKfYdiNr54u3J3Dl4Tp1lysvLGTt2LBUVFfh8PqZMmcK9997LtGnTWLZsGQ6Hg1GjRvHkk0/icAQv3fvBBx9w1113UVpaisvlYty4cTz00ENRixvavvN5D9DbGHMccDPwkogkRiooIleKyDIRWZaXl9eqQSrYvGVvjYX2Gus3d77Cdb9+PmwVV6Xai2gmhYaez+VysXDhQlatWsXKlSv58MMP+frrr5k2bRo//PAD3333HWVlZcyePRsILqR3/fXX8+KLL7Ju3TqWLVtGv379oho3RCcx7AKqXk0+M7QtYhkRsQNJwH5jTIUxZj+AMWY5sBkYEOlJjDFPGWNGGmNGpqWlRSFs1Rh2u1Vr81FjLurzww97+NtD71NcXE7u3oMEAtr/oA5fIkJ8fDwAXq8Xr9eLiHDOOecgIpXrJWVnZwPw4IMP8rvf/Y6jjjoKAJvNxjXXXBP1uKKRGJYC/UWkj4g4ganAvGpl5gEzQvenAAuNMUZE0kKd14hIX6A/sCUKMako65OVRlKiu8b2mBgH111zBhdNGVXvLGhjQXmKxbzVPzDx0ke5bObTXPKzJ/j6m80tFbZS7Z7f72fYsGGkp6czfvx4Ro/+sSXe6/XywgsvVC570VpLbzc7MRhjfMD1wEfA98Crxpi1IjJLRM4LFXsG6Coimwg2GR0a0joWWC0iKwl2Sl9tjNFeynZIRLjv3gtJiI/B7XbidNpwueyMOaEf554zjGuuGscnH93Olb86LeLx3jgh7xgnhVl2inrZyRvsIC/NkFtYzO8ffIsNm3Ja9wUp1U7YbDZWrlxJdnY2S5YsCbvE57XXXsvYsWM55ZRTWjWmqExPNca8D7xfbdvdVe6XAxdFOO4N4I1oxKBaXr9+Gbw69zq++HIjBw6UcszQXvTrlxFWZurFJ/Dhh6vZsfPH/G6Agn4OjD28RlGWYaMs3QYGJj/5Ev3K3Fw76STG/2SodlCrw05ycjKnn346H374IUOGDOHee+8lLy+PJ598srLMoaW3jz322BaNpa07n1UH43I5GHf6YCZfMLJGUjjk2GN6hzUreeMl8idNBCwBm2Dswsb4Mu6c+xFnTvobK1ftaKFXoFT7kZeXx4EDwU7qsrIy5s+fz1FHHcXs2bP56KOPePnll7GsH//z3Hbbbdx///1s2BBcpywQCPCvf0V/XrAmBhV15503HIfjx8uJGova19WoSoTyNBt7Btq46fcv6xXkVKuKtye3+vn27NnD6aefzjHHHMPxxx/P+PHjmThxIldffTW5ubmMGTOGYcOGMWvWLACOOeYYHnnkES699FIGDRrEkCFD2LIl+t2yuuy2ahGLPvuehx7+EGMM5V4fOUPsGFsDm4eMAQPHJnRlzu3TiNEF+VQL0GW3a6f/41SLOO3UQZx04gA2b9lLbKyT91d8zxNfLSVgCNZTDcEV+iIRAYFVxfmMuPtx4lwOZk0ez4RjBrbeC1DqMKY1BtVqduYf4J3l69hzsIgFazdRVO5p9Dm6xLm5c+JpnDPsqBaIUB1OtMZQO+1jUK2mV5dkrh9/IjkHiiit8DbpHPklZdz2ygec/dc57Mo/GOUIlVKgiUG1svziUlZs342/mTXVHfkHOfOvc/hy47boBKaUqqSJQbWqUo8XK4pzFK559m28fn/UzqeU0s5n1cp6JCeS6HZR7q22kN6hGkQjk4aXAE99uoSTB2RR5qrgoLecEam9SI2Ji1LESh1+NDGoVmVZwh8vPItfvziPCq8vOL3BHxyeiq2eg6sIxPrxZnowbsPf8xby973BZTvcDju+gJ/pA47n5qGn4bLpR1w1TGDviRDYF70TWqlY6V/WW+zAgQNcccUVrFmzBhFhzpw5jBkzBoCHHnqIW2+9lby8PFJTU4HDY9ltdRg6acARvHb9NC46fiiJ5TaS9hridzV8Ke6AM4DnyApMrAkOebWCN2MZSv1ePCbA7PXfMPj1BzjhnUdYsGt9i70W1YlEMyk04nw33ngjEyZM4IcffmDVqlWVI4l27tzJxx9/TO/evSvLttay2zpcVbWpsjIP7763kn9/s4Jt9rIGHePt6cHf1dfgnzU2hMl9hvLZni3kV5SS4U7gpiFj2Vy4jz2lRZzWox8TMo/CaWtElUV1eNWHcwZyIq743yxWtw117j948CDDhg1jy5YtNdYHmzJlCnfddReTJk1i2bJlpKamMn36dE477TRmzpxZ73PrBDfVYbndTi6aMorFZTlsW9ew5bcD7kCj6rp+DK9tXV35eFfpQW5b8t/Kx/N2rOH3dicuy4bdsnFur0HcOPRUEhyuhj+JUk2wdetW0tLS+OUvf8mqVasYMWIEjz76KJ988gk9e/assVjemjVruOWWW1o8Lm1KUu3CkMwMXPaG/WK3Si1o/BVGa2WAEp+HfE8Ze8uLeXbjUk6e9xg5pUXRexKlIvD5fKxYsYJrrrmGb7/9lri4OO655x7uv//+yvWR2oLWGFS7cNGoY/j34hV4/H4itW4aRwBfig9sYJUKfkPdy2o0U7HPw0n/fYyJvY6m2FtOdskBhqdmct3gk9lbXkxBRSnHdunBpqL9bCncz4CkNEakZupy4apRMjMzyczMrLw4z5QpU7jnnnvYunVrZW0hOzub4cOHs2TJklZbdlsTg2oXUuLcvHztVO7/7yK+2bwDp91OSqybvKJiSmIr8GWFls8Q8AdASkOXGk0wLZYcAN7dubby/qai/by6dRUSDIMAwSq3w7Jhsyz6J6Zx57Fn8OXebTgtG+f2Hkzv+JSWC051eN26daNXr16sX7+egQMHsmDBAoYPH86CBQsqy2RlZVX2Mdx2221MnjyZk08+mQEDBhAIBHjqqae4+uqroxqXJgbVbhyRmsKTv7yg8rHPH+Clr7/lvh0fhTd62sDEBnDsdBIoC+BPa3hHdDQcqqxAMDlUBPwQ8LMqfzeXfvoiYLCJxeNr/8ftx57OjAGjWi841XRWatSHqzbE448/zrRp0/B4PPTt25dnn3221rJVl90uLS1FRJg4cWK0Iq6ko5JUu7Y4ZwvXf/kmxd6KGvuk2MKIgdhDk+NCO1qwiakpBial88iY8xmQlFa5rczn5bM9myn1eTipWx8y3AltGOHhSRfRq53WGFS7ZhOLiJ0OgIkLhCcAQ/AnfDsbdbr+4F6mLniezyZeR4IzhiV7d/Crxa9gAL8J4PH7Gda1JzcNHcuJ6VnaT6HanCYG1a4dn9YrmBwiqf79Wb3xvx3xBPw8tnYx+8pLeH/n9/hM+LCqFfuz+dXiVxnXvR+PnTg5qutJKdVY7ey/j1LhHJaNJ0+5iFi7E4fVgKpAO20ZLfN7eX7jMubtWFsjKRxS4ffxWc5mPt29sZWjO3x1xKb0hmju69LEoNq949N689V5v6ZnbFL9hQVScuJJdcXhtjlaPrhGqC0hVFXq8/LfHetaIRoVExPD/v37O11yMMawf/9+YmJimnwObUpSHUK8w8XRKd3YXpxfZ6XAYdn45KqrSHS72Fy4jzuWvMuagpwGfSk3h92ysIuF1+8ngGlWxeVARWmz41mxL5sHVy9k/YG99IhN4sYhYzkzUy+NWlVmZibZ2dnk5eW1dShRFxMTQ2ZmZpOP11FJqsNYsS+b6Yv+Q5m/9gX3UmPi+GbSTZWP8ytKuXLxq3x/IBebWJT7vKE+6qZ97o9OziDW7mTtgRxKfV5cNjs2EZ45ZSpJzhgW7dlMjM3Got2bWZy7pUnP4rRsXDv4JG44+pQmxbg89D6VV3mfYmwO7h1+FlP6tuzEKNW+6agk1ekMT83kD8PPYtaKjynze2t86drFYnzP8IXQurhieen0X/D8xqV8unsTlsDXeTua1BdhF4vpA45nctYxLM7Zwtd7t5MWE8d5RwypvP7DwOR0AHzG8FXedryBxl9EyBPw8891X/CzI4fTtQnXlXhw1cKwpABQ7vfywOqFTO5zjHZsq3ppYlAdykV9h3HeEUN4a9tq7vt2Pn5j8Ab8xNjsJDnd3DRkbFj5Cr+Pn336Aj8c2Fvjy7I6h1jYLIuTMvqwcPfGGrnDZbOTGhOHJcKp3Y/k1O5H1nquEamZwaYlmnZ1OYdlY8X+bMb3bHzzzw8H90bcXuStoMhbTpLT3aSY1OFDE4PqcFw2O1OPHM4p3Y7kP5uWs7Uon1FpvZnS99gaK6K+uXU16w/k1ZoU7GJhtyyOTOjKzIGjGdejP/srSvkid2vYMQK47Q5OzujboBiP7dKDEzOy+DJ3G2V+b/C5EPwN7H8wQIoztkHPVV13dyIbvTXbzR2WRZxdV4xV9dPEoDqsnnFJ/ObYcXWWeW/nusov5kiSnTE8e+qlDE7pVrkt0RnDI2PO57Zv/osxhgCGrq44Zo+9BLvVsIF8IsL/nTSFV7d8yytbVuI3hvN6D2bB7k2sK8ihtI6YBEhyxjA8tWmdhzcNGcut38wLe91um4PLBoxqcPzq8KaJQXVq8fVcU8Fps4clhUPG9xzIkkn9WFuQg9tuZ2BSeqNnJNsti5/1G8HP+o2o3DZz4Al8mP0DH2b/QIxlC3ZkF+xh7YG9uCwbAQxpMfE8M3Zqk/sCJvQ6ioOecv66eiElPg92y+Ky/qP4f0NObdL51OFHE4Pq1Kb1G8H/crZGrDU4xOLsXrWvleO02TgutWdU47FbFhN7D2Zi78Fh28t8Xlbn7ybe4WJwckazl8W45MhhXNT3WA56yoh3uBo2OVCpEK1Xqk7tlG59uXzgaBzVmlBiLDs94pK4bvBJbRRZOLfdwej0Izg6pVvU1kqyREhxxWpSUI0WlRqDiEwAHiW4fNlsY8xfqu13Ac8DI4D9wCXGmG2hfXcClwN+4NfGmI+iEZNSh/y/oacyrd9w5u/awMp9uzDACRlHMLHXYGLs7Wt2tGocYwwrCj5l0d7XKPIW0M2dxdndZ3BEXOddNbU1NHuCm4jYgA3AeCAbWApcaoxZV6XMtcAxxpirRWQqcIEx5hIRGQy8DIwCegBKsIn2AAAaWElEQVSfAAOMMXWO8dMJbkp1LpsK9/Fd/h4y45IYmdqrwbWm/+XN45Ocl/GaH5dld4iLy4+8l16xA+o48vDUmhPcRgGbjDFbQk88F5gEVF3wZRJwT+j+68A/JPgvPwmYa4ypALaKyKbQ+b6KQlxKqXbOFwjw6y/f5LOczZWd7d1jE/nPaT8nzR1f57F+42Nh7ithSQHAayqYn/MSM/veE7Y9p2wbi/PeYXfZZrwBD37jo7u7L4OTRpNgT6abO4sibz7rC7/loDePOHsiPuMj092PocknYdW2ym8nFI3E0BPYWeVxNjC6tjLGGJ+IHAS6hrZ/Xe3Y6Pb2KdXJ5Ffk8FHOC2wqXk2MFcuY1HM5MfVcLOl4fQlz1n/DZzmbw+aMbC8q4JZv5vH8aT+r89hi7wECtTQu5JRtw3g3YopmgWc5fpxsLEngu5JU/FXWay8symd90TIEC0Pt62m9uvNhetrjSHMlExcznMHJJ9A7dmCnTRYdZlSSiFwJXAnQu3fvNo5GqbZR6M3n/zbdRrm/DEOAcn8Jn+S8TF5FNhdkXtvW4TXaS5tX1Jh86DMBluTtoMhTToKz9hVCY+2J1Hapvl4xiZj8S8CUAAYbPkbFlpFiK+XlwiNqlK8rKSRbHn6WtINUewVgsPgICiFQGLrMa6g13m9BEVm4Yy7DHTsIcQzrsBddikZi2AX0qvI4M7QtUplsEbEDSQQ7oRtyLADGmKeApyDYxxCFuJXqcL7a9z6egCfsi8xrKlhZ8BlnZEwl0dGlDaNrvNomHwpQEfBR1wVPHZaTMann8NW+92v0MZyb5ARf8Iv8x+2G/q5iUmwVFPhrn99iJ8CpsXkc5y7AAhzixyEGWz3f8XYDXWQbpuweTBkYCaUtqy+4ToSKj4MF3ZOQuGsRq/HrYLWWaNSDlgL9RaSPiDiBqcC8amXmATNC96cAC02w13seMFVEXCLSB+gPLIlCTEp1SttLvsdvan6Z2sRBbvmONoioec7sORBHhOaYnnFJpMbU3ccAML7bNE5Om4TLciNYJDm6MqXXDSRbeUDN98lnhDRbzeuH/8hwWfI2TorbR5LNR4LNh6uepCDy4y3s8aECgS1Q9iIE9gZvJc9h8qdhWngp+OZodo0h1GdwPfARweGqc4wxa0VkFrDMGDMPeAZ4IdS5nE8weRAq9yrBjmofcF19I5KUOpylx/RiR+n6Gk0ffuMjxZneRlE13U1DxvLp7k0c8JRR5vfitGzYLYu/jjqvQcdbYvGTblMZl3ExPuPBIS5EhEDh5+BZRvXkYBfDvjpqC1mOUrrZy3DIjzWN6LcGecC/HTyLwdU+Z6NHpY/BGPM+8H61bXdXuV8OXFTLsX8C/hSNOJTq7E5KncjKgs/Cmk5s4uCIuIGkunq0YWRN0zUmjo/Ovoq3tq1mad5O+iR04ZIjj6N7bGKjzmOJhVN+7I+QuOmYslegSu3KZyy2euI54I8DfBE7nHvYy7BJK7RUm1LwrunciUEp1TrSYjKZ3ud3vJ39Twq8exGEoxNP4PzMq9s6tAZZc+BLPs97i2LfQY6MH8q4jEtIcabz8/4j+Xn/eofXN5jYekCXlzCF94B3JRCDPfZCMrr8kpldC0l2puELeDjozefbgoXsLc+myHeAA4EifMbCLuEJw5go1xzEDbamX2GtpekV3JTqgIwxlPtLsFtOHJazrcNpkEV732BR7uuVtR3BwmVzc0P/h0l2prbY8wbb8qVBI4SM8eDbeyoS2I8VKh4wwb6J/X4n6baKyu1NTxQCkoKkL0Kk6ddlbtIzN3CCW+cchKtUJyciuO3xHSYpeALlLMp9LawJzBDA4y9ncd5bLfrcIlaDh42KOLF3fY0yqz9+I/iMsMcXw5MFR/J/Bf25Z98QXj3QE58J1iJqvVF1PFQc2AYAjuDNMRTpOrfVk0JjaFOSUqrF5ZXvCk7Aq9ZAEcDPluI1bRNULcSeSXz6u8zf8yQr8ufjIQZDgHRXOr/s+4fKIcHGBMAcxOAMjk31rgL8IEOA3cH79r5YtuCwVBM4EDy/ldw2L6wRNDEopVpcgiMFv4l8Fb32OJpKRDizx9WMSbuE7LJNJNq70MPdN6zmIWIFm4QObbCNqXKGml/+HSEhHKJNSUqpFpfo6ELf+KHYJHw1W4e4GJt+QRtFVb8ERwqDEo+nZ+yRHXYWc1NoYlBKtYqpvW9hYMJwbGLHYblw2+I5P/MasuIG13+walXalKSUahUum5tpWbdT5ium1F9MsjMNWwdc+O9woIlBKdWq3PZ43Pb6l7tQbUebkpRSSoXRxKCUUiqMJgallFJhNDEopZQKo4lBKaVUGE0MSimlwmhiUEopFUYTg1JKqTCaGJRSSoXRxKCUUiqMLomhDiuF3nw2FK3ALg6OShxJTGitfKXUjzQxqMPGF3n/5eOcF7GwQIS3s//FpUfcysDEEW0dmlLtijYlqXYpYALklu9gX8VujDH4jZ/vC5eyaO/rrDn4Fb6At1Hnyynbzsc5/8FnvHhMBZ5AOV5Twcvb/0a5v6SFXoVSHZPWGFS7s7V4La/s+DsVgTKMCZDg6ELABCj1F+INeHBYTmJtCVzV78+Vl1msz7cFiyJeQUxE+KFwGcNSTo32y1Cqw9Iag2pXCr35PL/tjxT5CkK/6j3ke3I44N2LJ1AevIB8oJyD3v28k/2vBp/XZ7yY6hccBowx+Gq55KRShytNDKpdWVmwiIAJ1FvOEGBD0QoCxt+g8w5JGoPDckY8z4CE4xodp1KdmSYG1a4c9ObjMw3rP6j5+792WXGDOSbpZBziAgTBwiFOzuz28wY3Ryl1uNA+BtWu9I0fwrL8+Q1KDpZYeAMeXDZ3vWVFhAsyr+W4lNNYe/Br7JaDYcmn0s19RDTCVqpT0cSg2pTxZQMesPVBRDgq8XiSHKns9+yp91gxFqsOLGZU1zMb9FwiQp/4o+kTf3Qzo1aqc9PEoNqE8W3DFFwH/h2ABVYiJP8dm/N4run3IPev+yUB6u4U9uEhp3x75eOdpRt5f/ccdpdtwW2L55S0SZyY+lNEpIVfjVKdiyYG1eqM8WLyp0FgH5U9BYEyTMGvIPVjdpXtwVB/p7JDXGS4euMJlLO/PIdnNt+N11QAUOQrYH7OyxT5DjKh+y9a8NUo1floYlCtr2IxmFJqdB8bH+XFL/Ls9v816DSC8EnuS7y7+2lErBrzFLymgq/2vcfp6VMa1A+hlApq1qgkEekiIvNFZGPob0ot5WaEymwUkRlVti8SkfUisjJ0S29OPKr9M4EiTPlHYDwR9nr4Lv/1Bp3HbSUQIECpv4gAgYiT1wBsYqPAs7cZESt1+GnucNU7gAXGmP7AgtDjMCLSBfgDMBoYBfyhWgKZZowZFrrp/+BOzFQsxuw9Gco/AGqOOvLhZLMn+Ms+2fJwcmwep8Xm0t1eVqNsWaAIX8TkEs5vfCQ5U5sdu1KHk+Y2JU0CTgvdfw5YBNxercxZwHxjTD6AiMwHJgAvN/O5VQdiAiWYAzcANb/kg1zs8wrrKhI5LqaAnybsRjAIcErcPpaWdeHD4u6Nek6HuDgu5VTcuoKqUo3S3BpDhjHm0LjCHCAjQpmewM4qj7ND2w55NtSMdJfo8JHOy/M/oJZ/XklkB6fx9IE+xIifnybsxiEGu4BNwCmG49359LKX1vs0FjZAcFoxnJh6LhN7/iqqL0Opw0G9NQYR+QToFmHX76o+MMYYEWnMZFQINiPtEpEE4A3gF8DztcRxJXAlQO/evRv5NKrN1TFh7YB1HE/v2QXYGBxTQMBQI4fYMQyNOcDO4lgAusVksb9iN94qzUkOcTKl140MSjoeC5sOU1WqiepNDMaYn9S2T0RyRaS7MWaPiHQHIvUR7OLH5iaATIJNThhjdoX+FonISwT7ICImBmPMU8BTACNHjmxsAlJtzXUSROgg9uNkQ9F33NSlGKcEyPPXXM/oEGOCX/ROy82VR/6JrSVr+TjnRfIrckhxduPM7tMYlHh8i70EpQ4Xze1jmAfMAP4S+vtOhDIfAfdX6XA+E7hTROxAsjFmn4g4gInAJ82MR7VTYqVgEu+CwvsAP+DD4MAf8DLCnY8t9OM+1vJFbN/0IayqSAbgij734bK5OSpxJEcljmytl6DUYaO5ieEvwKsicjmwHbgYQERGAlcbY64wxuSLyH3A0tAxs0Lb4oCPQknBRjApPN3MeFQ7ZLyrMcXPgG872PqB/4fQHi/OalnAJgSbkgwEgn8wCF+UpLLb58bChpH6V19VSjVdsxKDMWY/cEaE7cuAK6o8ngPMqVamBNBrKnZygbL5cPAWoILqE9pq6wGwDu0IgAeLfx/owx5fcBirw3JR4itsqXCVUuiy26oFGROAoj8A5TRukewgmwUODAOdPyYCv/HSK7Z/9IJUStWgiUG1CBPIx1R8DoHiZp3HYRkGuoLncIiLU9MvJNaeEI0QlVK10LWSVFQZ48Ec/C2Ufwg4CNYWGnJc8G/1EaYBA8UBO12c3ZnYYyYDE7X1UamWpjUGFVWm8H4o/xjwACUNO8ZAScDGfr8Tf7UWJx/C0vLunJFxsSYFpVqJJgYVNcZ4oOxNGlpLCB4DayrSyEl4gaT098jzu/EEoCIgeAx8UpxBtq8rg5NOaLnAlVJhNDGo6DHlUM/FdcKKG/iuIpFXCzN4aftDFHvWkuaIQ8TCEijyOymSo7jyyPtxWq6Wi1spFUb7GFT0SAJIGpj6L8sZMFBuLD4ILYznpIz4otuwibdyslsXu4dLElYirq4tGbVSqhqtMaioMP59mOLHoQG/7AMG1lUk8q/8fhQHHAAcE5MP1a7aFswPXihfEPV4lVK10xqDajbj24HZfyGYMoKdznUrDDh4pTB8IcQkmx9HpBnNxguBvChFqpRqCK0xqGYzRQ+AKaQhScFnYF1FzXkIO7yJGCJcflNs4NTRSEq1Jk0MqvkqFlHXzOZDezxGKA44+KwkeAVXt/jIsJXjIMBGTyJl0gOIqXKkG5wnIY6hLRS4UioSbUpSzRIofZVIl+n8kUWh38len431ngS+LU8hYIRLEncwyFUYukYbfFqSxpwDQ7m+5xQofxuwg/siJPbi1ngZSqkqNDGoJjEmgCm8E8rerr2Q60wk+XGeWDeDMv+PS2NMS9rGQGdxaJZzsD5xRtxeSoo3Y8X/E+Ivb9nglVJ10qYk1SgmUEKg5BVM/mVQ9i61NyFZEDcTESErbjAAgsGFr0pSqFJaYHxc/cNclVItT2sMqsGMf09w9FGgBCiru7C4EccQjHcdUxIOUmz/gSSbr9altgFirbqapJRSrUUTg2owU3gfBPIJXkKnLi5IuANT8m8ofhQnXlJsNRfIq04kPkqRKqWaQxODariKz6k/KTgg+V+Ioy+BvHFIaNJafUkBgNhfNjdCpVQUaB+DagRbHfscQAyS8hRWzEnkHHgOjL+O8sG1ksyh8zpOROKvjl6oSqkm0xqDqpPxbcaUzAHfJrBlgn8b4cNTbWB1B/d5SOxFiK0nxhjWFHzAuLh6Ti4gVk8k+RHEeWzLvQilVKNoYlC1Mp6lmPwrCM5o9hP8uAQAN2CCs5JtPZEuLyJWcuVxW4q/wy31L70tAIH9ILEtEb5Sqok0MahamYN3ET76KLSktmMQ4v4p2I4E52ikWgeCreQpxsQWNKxfQewQ2AXodZyVai80MaiITKAY/Nsj7/StR2LnRj7Ou4ZMPmlYUgAwHrAf1bQglVItQjufVWTiotbOZqm5CN4hpvRVpJaRSz92Nh/iDvZN2Lo1NUqlVAvQxKAiEnGAeyJQ/foKMRA7vfYDvdtqncQmAoIAiWDrDQm3IIl/jE7ASqmo0aYkVStJuBvj3weeb0CcYCrAPRGJqznfIODZBAWXN+DqbRa4z8ZKuq9lglZKNZsmBlUrsWKRLrMxvh3g3wX2IxFbeo1ygdK3oPD2Bp7VD/7d0Q1UKRVVmhhUvcTeG+y9I+4z/txGJAWAGHCdEp3AlFItQvsYVLOYsncaUVrAloq4p7RYPEqp5tPEoJrHt6WBBQVcZyFd30IsXSxPqfZMm5JUkwU8a6H8zYYVtjKR5L8joh85pdo7rTGoJgn490H+BQ0sbYf46zQpKNVBNCsxiEgXEZkvIhtDf1NqKfehiBwQkXerbe8jIt+IyCYReUVEnM2JR7WiwnsaUdiGuE5sqUiUUlHW3BrDHcACY0x/YEHocSR/BX4RYfsDwMPGmH5AAaAX++0AAmUfQcXHDSzththf6OxmpTqQ5iaGScBzofvPAedHKmSMWQAUVd0mwZXXxgGv13e8aj8Cvlw4eGPDCkvfYL9Cwm0tG5RSKqqa2+ibYUzlVNccIKMRx3YFDhhjQkt2kg30bGY8qgUZ44d9E6j/Km4AgqS/j4h2YynV0dSbGETkEyBSO8Dvqj4wxhgRMRHKRYWIXAlcCdC7d+TJVqplmZKngZKGFe7ypiYFpTqoehODMeYnte0TkVwR6W6M2SMi3YG9jXju/UCyiNhDtYZMYFcdcTwFPAUwcuTIFktAqg5l8xpUTFLmIM6jWzgYpVRLae5PunnAjND9GUCDp8EaYwzwKXBoGmyjjldtIFBfbcEC1zhw6ggkpTqy5iaGvwDjRWQj8JPQY0RkpIjMPlRIRBYDrwFniEi2iJwV2nU7cLOIbCLY5/BMM+NRLSRQMreelVMtiL8JSX5Cm5CU6uAk+MO9Yxk5cqRZtmxZW4dx2DCBYszeEwhe+7kW9gFI1//WuMynUqr9EJHlxpiR9ZXTn3aqft7l1Ho1t0OSZ2tSUKqT0MSg6idxUOt12QD7MCy7TmBTqrPQxKDq5zgOal0R1Y2kPNaq4SilWpYmBlUvERuS8gxYqUAMlc1KjuFI2se63IVSnYwud6kaRBwDIe1z8CwBUwTO4xGrS1uHpZRqAZoYVIOJ2EFXSVWq09OmJKWUUmE0MSillAqjiUEppVQYTQxKKaXCaGJQSikVRhODUkqpMJoYlFJKhdHEoJRSKowmBqWUUmE0MSillAqjiUEppVQYTQxKKaXCaGJQSikVRhODUkqpMJoYlFJKhdHEoJRSKowYY9o6hkYTkTxge1vHEZIK7GvrIJqgI8bdEWOGjhl3R4wZOmbcrRnzEcaYtPoKdcjE0J6IyDJjzMi2jqOxOmLcHTFm6Jhxd8SYoWPG3R5j1qYkpZRSYTQxKKWUCqOJofmeausAmqgjxt0RY4aOGXdHjBk6ZtztLmbtY1BKKRVGawxKKaXCaGKohYh0EZH5IrIx9DellnIzQmU2isiM0LYEEVlZ5bZPRB4J7btMRPKq7LuivcQd2r5IRNZXiS89tN0lIq+IyCYR+UZEstpDzCISKyLvicgPIrJWRP5SpXzU32sRmRB6fzaJyB0R9tf6PonInaHt60XkrIaeMxqaGreIjBeR5SLyXejvuCrHRPystIOYs0SkrEpc/6pyzIjQa9kkIo+JiLSTmKdV+84IiMiw0L4WfZ8jMsboLcINeBC4I3T/DuCBCGW6AFtCf1NC91MilFsOjA3dvwz4R3uNG1gEjIxwzLXAv0L3pwKvtIeYgVjg9FAZJ7AYOLsl3mvABmwG+oaeaxUwuCHvEzA4VN4F9Amdx9aQc7Zx3McBPUL3hwC7qhwT8bPSDmLOAtbUct4lwAmAAB8c+qy0dczVygwFNrfG+1zbTWsMtZsEPBe6/xxwfoQyZwHzjTH5xpgCYD4woWoBERkApBP8wmoNUYm7nvO+DpwRxV9bTY7ZGFNqjPkUwBjjAVYAmVGKq7pRwCZjzJbQc80NxV5Vbe/TJGCuMabCGLMV2BQ6X0PO2WZxG2O+NcbsDm1fC7hFxBXl+KIac20nFJHuQKIx5msT/MZ9nsiftbaO+dLQsW1GE0PtMowxe0L3c4CMCGV6AjurPM4Obavq0K+Cqr38F4rIahF5XUR6RS3ioGjE/WyoynpXlQ9t5THGGB9wEOjajmJGRJKBnwILqmyO5nvdkH/v2t6n2o5tyDmbqzlxV3UhsMIYU1FlW6TPSnuIuY+IfCsin4nIKVXKZ9dzzraM+ZBLgJerbWup9zkie0s/QXsmIp8A3SLs+l3VB8YYIyJNHb41FfhFlcf/BV42xlSIyFUEfz2Mi3hkLVo47mnGmF0ikgC8QTD25xt5jhpa+r0WETvB/0yPGWO2hDY3+71WQSJyNPAAcGaVzS3yWYmCPUBvY8x+ERkBvB2Kv90TkdFAqTFmTZXNrf4+H9aJwRjzk9r2iUiuiHQ3xuwJVUH3Rii2CzityuNMgu2Bh85xLGA3xiyv8pz7q5SfTbB9vd3EbYzZFfpbJCIvEawePx86pheQHfoSTgKqvpY2iznkKWCjMeaRKs/Z7Pc6QgxVax2ZoW2RylR/n+o6tr5zNldz4kZEMoG3gOnGmM2HDqjjs9KmMYdq5xWh2JaLyGZgQKh81WbGaL/XzXqfQ6ZSrbbQwu9zRNqUVLt5wKHROjOAdyKU+Qg4U0RSJDiS5szQtkMupdo/cuiL75DzgO+jFnFQk+MWEbuIpIbidAATgUO/XKqedwqwsFrzWJvEHIr1jwT/g91U9YAWeK+XAv1FpI+IOAn+J55Xx2up+j7NA6aGRqX0AfoT7AhtyDmbq8lxh5rn3iM4OOCLQ4Xr+ay0dcxpImILxdaX4Hu9JdRcWSgiJ4SaY6YT+bPW6jGHYrWAi6nSv9AK73NkrdnT3ZFuBNv9FgAbgU+ALqHtI4HZVcrNJNiRuAn4ZbVzbAGOqrbtzwQ78VYBn1bf35ZxA3EER1CtDsX4KGAL7YsBXguVXwL0bScxZwKG4Jf+ytDtipZ6r4FzgA0ER5/8LrRtFnBefe8TwWazzcB6qoyGiXTOFvg8Nylu4PdASZX3diXBwRS1flbaQcwXhmJaSXAwwk+rnHMkwS/WzcA/CE3ybeuYQ/tOA76udr4Wf58j3XTms1JKqTDalKSUUiqMJgallFJhNDEopZQKo4lBKaVUGE0MSimlwmhiUEopFUYTg1JKqTCaGJRSSoX5/8xodtaYKWN9AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_2d_data(transformed_data_pre_processed_guo, stage_names_pre_processed_guo, labels_pre_processed_guo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 6: Comparison with the un-pre-processed data." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "diff_map_guo = DiffMap(sigma=10, alpha=1, n_components=2)\n", "data_guo, stage_names_guo, labels_guo = load_guo_data(normalize=False)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "transformed_data_guo = diff_map_guo.fit_transform(data_guo)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_2d_data(transformed_data_guo, stage_names_guo, labels_guo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comparing the preprocessed against the non preprocessed data, we can see, that the preprocessed data produces much clearer lines. But the general structure looks quite the same." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparison with other dimensionality reduction methods\n", "\n", "#### Task 7: Compare diffusion maps with two other methods." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Time taken: 0.026772022247314453s \n", "\n" ] } ], "source": [ "guo_pca = skl.decomposition.PCA(n_components=2)\n", "pca_time = time.time()\n", "pca_transformed_guo_data = guo_pca.fit_transform(data_pre_processed_guo)\n", "pca_time = time.time() - pca_time\n", "print(\"Time taken: \" + str(pca_time) + \"s \\n\")" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_2d_data(pca_transformed_guo_data, stage_names_pre_processed_guo, labels_pre_processed_guo)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Time taken: 6.442171096801758s \n", "\n" ] } ], "source": [ "guo_tsne = skl.manifold.TSNE(n_components=2)\n", "tsne_time = time.time()\n", "tsne_transformed_guo_data = guo_tsne.fit_transform(data_pre_processed_guo)\n", "tsne_time = time.time() - tsne_time\n", "print(\"Time taken: \" + str(tsne_time) + \"s \\n\")" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_2d_data(tsne_transformed_guo_data, stage_names_pre_processed_guo, labels_pre_processed_guo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The reductions of pca and tsne seem not to show our features as well, as the deiffsion map reduction. Also, while the runtime of pca is compareable with the diffusion map runtime, the runtime of tsne is much larger." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameter selection\n", "\n", "#### Task 8: Bandwidth comparison." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "def run_diff_map_with_bandwidth(sigma = 10,\n", " alpha = 1,\n", " data = data_pre_processed_guo,\n", " stage_names = stage_names_pre_processed_guo,\n", " labels = labels_pre_processed_guo):\n", " diff_map = DiffMap(sigma=sigma, alpha=alpha, n_components=2)\n", " start = time.time()\n", " reduced_data = diff_map.fit_transform(data)\n", " stop = time.time() - start\n", " print(\"Diffusion Map run for sigma = \" + str(sigma) + \"\\n\" + \"time: \" + str(stop) + \"s\")\n", " plot_2d_data(reduced_data, stage_names, labels)\n", " print(\"\\n\")" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Diffusion Map run for sigma = 100\n", "time: 0.1050102710723877s\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Diffusion Map run for sigma = 50\n", "time: 0.10408639907836914s\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Diffusion Map run for sigma = 10\n", "time: 0.07808732986450195s\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Diffusion Map run for sigma = 5\n", "time: 0.07761526107788086s\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "Diffusion Map run for sigma = 1\n", "time: 0.08069324493408203s\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] } ], "source": [ "for sigma in [100, 50, 10, 5, 1]:\n", " run_diff_map_with_bandwidth(sigma=sigma)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While for big sigma all the points are pushed towards one point in the middle, for small sigma, all points align along the axis. For sigma around 10 the results seem to be best." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 9: Implement the rule for $\\sigma$ and plot the embedding with the $\\sigma$ chosen by this rule." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "def lafon_sigma(X):\n", " n = np.shape(X)[0]\n", " dists = np.empty((n,n))\n", " for i in range(n):\n", " dists[i] = np.linalg.norm(np.subtract(X, X[i]),axis=1)\n", " dists[i,i] = float('inf')\n", " min_dists = np.min(dists, axis=1)**2\n", " return np.sqrt(sum(min_dists)/(2*n)) " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Diffusion Map run for sigma = 11.434130928749875\n", "time: 0.06356549263000488s\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n" ] } ], "source": [ "run_diff_map_with_bandwidth(sigma=lafon_sigma(data_pre_processed_guo))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Well with this rule sigma indeet seems to be arount ten and looks pretty good." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cell group detection\n", "\n", "Now, we want to apply spectral clustering to detect cell groups in the single-cell data.\n", "\n", "#### Task 10: Implement the spectral clustering algorithm using k-means with $\\Lambda$ as input." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "def spectral_clustering(lam, X):\n", " diff_map = DiffMap(n_components=lam-1, sigma=lafon_sigma(X), alpha=1)\n", " diff_map.fit_transform(X)\n", " eigvals, eigvecs = diff_map.compute_eigs(diff_map.P, k=lam-1)\n", " k_means = skl.cluster.KMeans(n_clusters = lam)\n", " k_means.fit_transform(eigvecs[:,1:])\n", " return k_means.cluster_centers_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 11: Plot the first 20 eigenvalues of transition matrix $P$ for the Guo data and identify $\\Lambda$." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "diff_map_lafon_sigma = DiffMap(n_components=2, sigma=lafon_sigma(data_pre_processed_guo), alpha = 1)\n", "lafon_transformed_data = diff_map_lafon_sigma.fit_transform(data_pre_processed_guo)\n", "guo_p_eigvals, guo_p_eigvecs = diff_map_lafon_sigma.compute_eigs(diff_map_lafon_sigma.P, 20 - 1)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "5\n" ] } ], "source": [ "temps = np.append(np.arange(20), guo_p_eigvals).reshape(2,20).T\n", "plot_2d_data(temps, ['eigenvalues'], np.int_(np.zeros(20)))\n", "spectral_gap = np.argmax([guo_p_eigvals[i] - guo_p_eigvals[i+1] for i in range(19)]) +1\n", "print(spectral_gap)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 12: Perform the spectral clustering algorithm for the Guo data." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "guo_cluster_centers = spectral_clustering(spectral_gap, data_pre_processed_guo)\n", "plot_2d_data(np.append(lafon_transformed_data[:,:2], guo_cluster_centers[:,:2], axis=0), np.append(stage_names_pre_processed_guo,['cluster centers']), np.append(labels_pre_processed_guo, np.int_(np.zeros(spectral_gap)+7)))" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "spectral_gap_2 = 7\n", "guo_cluster_centers_2 = spectral_clustering(spectral_gap_2, data_pre_processed_guo)\n", "plot_2d_data(np.append(lafon_transformed_data[:,:2], guo_cluster_centers_2[:,:2], axis=0), np.append(stage_names_pre_processed_guo,['cluster centers']), np.append(labels_pre_processed_guo, np.int_(np.zeros(spectral_gap_2)+7)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Even if the original spectral gap we find is 5, the gap is also quite big for Lambda = 7, so we also tried this out for a spectral gap. And the result looks even more convincing, that the one for five cluster centers. We see, that the cluster centers pretty well define ths cell stages. Where some close stages share a center and later stages have more than one center." ] } ], "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 2 }