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@BadreeshShetty
Created March 26, 2019 18:53
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Importing Libraries\n",
"import numpy as np \n",
"import pandas as pd \n",
"import random,math \n",
"import matplotlib.pyplot as plt "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# Generating random numbers between zero and one from uniform \n",
"# distribution with the given dimension\n",
"def random_point_gen(dimension): \n",
" return [random.random() for _ in range(dimension)] \n",
"\n",
"# Root mean sum of squares of Euclidean distances (2-norm) between points \n",
"def distance(a,b): \n",
" diff = [a_i-b_i for a_i,b_i in zip(a,b)] \n",
" sum_of_sqrs = sum(a_i**2 for a_i in diff) \n",
" return math.sqrt(sum_of_sqrs) \n",
"\n",
"# Calculating the distances \n",
"def random_distances_comparison(dimension,number_pairs): \n",
" return [distance(random_point_gen(dimension),random_point_gen(dimension)) \n",
" for _ in range(number_pairs)] \n",
" \n",
"def mean(x): \n",
" return sum(x) / len(x) "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Dimensions in range of 1 to 200 with interval of 5\n",
"dimensions = range(1, 201, 5)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 0.3304377974569266\n",
"6 0.9718366726979907\n",
"11 1.3428297800724869\n",
"16 1.5916756747360146\n",
"21 1.8606501665486392\n",
"26 2.05939278034058\n",
"31 2.2575232751731726\n",
"36 2.4368760200852035\n",
"41 2.620080307069328\n",
"46 2.7625945084356123\n",
"51 2.89338869628594\n",
"56 3.04103478287079\n",
"61 3.1837540168385114\n",
"66 3.2946307081057804\n",
"71 3.4335738927751285\n",
"76 3.5609023888328744\n",
"81 3.6705963579722676\n",
"86 3.7747621910195295\n",
"91 3.885202293008529\n",
"96 3.9871994289025343\n",
"101 4.091623861134935\n",
"106 4.194797436760151\n",
"111 4.299946953926221\n",
"116 4.392107797538249\n",
"121 4.500000117577843\n",
"126 4.569193064205523\n",
"131 4.670386854961063\n",
"136 4.743869381556361\n",
"141 4.8403658613650995\n",
"146 4.916156206138143\n",
"151 5.011904217530445\n",
"156 5.097331764593295\n",
"161 5.15738876580636\n",
"166 5.251041104914\n",
"171 5.325070508861497\n",
"176 5.422322753425231\n",
"181 5.48791272897287\n",
"186 5.565523375530461\n",
"191 5.6312761071627975\n",
"196 5.715461971073279\n"
]
}
],
"source": [
"avg_distances = [] \n",
"\n",
"dummy = np.empty((20,2)) \n",
"dist = pd.DataFrame(dummy) \n",
"dist.columns = [\"Dimension\",\"Avg_Distance\"] \n",
" \n",
"random.seed(34) \n",
"i = 0 \n",
"for dims in dimensions: \n",
" distances = random_distances_comparison(dims, 1000) \n",
" avg_distances.append(mean(distances)) \n",
" \n",
" dist.loc[i,\"Dimension\"] = dims \n",
" dist.loc[i,\"Avg_Distance\"] = mean(distances) \n",
" \n",
" print(dims,mean(distances))\n",
" i = i+1 "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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2eZzrNMYYY8qQMl3tZowxpmwqU9VuxhhjQkPQV7vVq1dPo6KivA7DGGPKlNWrVx9V1fqFD+mNoE8+UVFRrFq1yuswjDGmTBGR3E+mCCpW7WaMMSbgLPkYY4wJOEs+xhhjAi7or/nkJSMjgwMHDpCamlr4wCagIiIiaNasGeHhRXl4sTGmvCqTyefAgQNERkYSFRWF2Buvg4aqcuzYMQ4cOECrVq28DscYE8TKZLVbamoqdevWtcQTZESEunXr2hmpMaZQZTL5AJZ4gpQtF2NMUZTZ5GOMMaHqYEIKL363g01xCV6HUmrK5DUfY4wJNZlZ2SzYFs8HK/exYNsRshWqVgqjc5OaXodWKuzMpwTmzp2LiLB161a/jjcqKoquXbvStWtXOnXqxCOPPEJaWhoAcXFxXHFF/i/+PHnyJP/973/9Go8xpvTsP36a5+dtY8Az87nt3VWsj03g9kGtWXz/YG49zy8vFQ5KlnxKYMaMGZx77rl88MEHfh/3ggUL2LBhAytXrmT37t2MHz8egCZNmvDRRx/l+ztLPsYEv6TUDD5bF8cNb61k4HMLeGnBTjo2rsGr1/dm+eQLuH9oB1rUrep1mKWqzFe7/eWzTWyOS/TrODs1qcFjIzsXOExycjLLli1jwYIFjBo1iscff5yrrrqKcePGMWLECABuvPFGRo4cyfDhw7nxxhvZunUrHTt2JCYmhpdffpk+ffoUGkv16tWZMmUKzZs35/jx4yQmJnLJJZewceNGNm3axE033UR6ejrZ2dnMnj2bP//5z+zatYsePXpw0UUX8dhjjzF69GhOnDhBRkYGTz31FKNHjyYmJobhw4dz7rnnsnz5cpo2bconn3xClSpV2LlzJxMnTiQ+Pp6wsDBmzZpF69atee6555g5cyZpaWmMGTOGv/zlL34pb2PKg8OJqXy7+TDzNh/mh13HSM/KpnHNCP5wQVuu7NOMZrVDO9nkVuaTj1c+/vhjhg0bRrt27ahTpw5r1qxh7NixfPjhh4wYMYL09HS+++47XnnlFV5++WVq167N+vXr2bhxIz169DijadWoUYNWrVqxY8cOGjZs+HP3KVOmcNddd3HttdeSnp5OVlYWf//739m4cSNr164FIDMzk7lz51KjRg2OHj1Kv379GDVqFAA7duxgxowZvP7661x55ZXMnj2b6667jmuvvZbJkyczZswYUlNTyc7OZt68eezYsYOVK1eiqowaNYrFixczcOBA/xWqMSFEVdl+OJlvNx/i282HWXfAaTzQsm5Vbujfkos6NaRPVB3CKpTPFqJlPvkUdoZSWmbMmMHdd98NwNixY5kxYwZPPvkkd955J2lpaXz99dcMHDiQKlWqsHTpUu666y4AunTpQrdu3c54enm99K9///48/fTTHDhwgMsuu4y2bdvm+bs//elPLF68mAoVKhAbG8vhw4cBaNWq1c+JsHfv3sTExJCUlERsbCxjxowBnCcWAMybN4958+bRs2dPwDnz27FjhyUfY3KJPZnCxz/FMmfNAXbFnwKge/Na3D+0PRd1akjbBtXtlgRCIPl44dixY8yfP5+NGzciImRlZSEiPPvsswwaNIhvvvmGDz/8kKuvvhrIO3GciaSkJGJiYmjXrh0JCb80vbzmmms4++yz+eKLLxg6dChvvPEG0dG/vkA5bdo04uPjWb16NeHh4URFRf18E2jlypV/Hi4sLIyUlJR8Y1VVHnroISZMmFCieTEmFCWlZvDVxkPMWXOAH3YfB6BvVB1uGtCKizo1pGGNCI8jDD7W4KAYPvroI2644Qb27t1LTEwM+/fvp1WrVixdupSxY8fy9ttvs2TJEoYOHQrAueeey8yZMwHYvHkzGzZsKPK0kpOTmTRpEpdeeim1a9f+Vb/du3cTHR3NnXfeyahRo1i/fj2RkZEkJSX9PExCQgINGjQgPDycBQsWsHdvwa/4qFGjBs2aNePjjz8GIC0tjdOnTzN06FDeeustkpOTAYiNjeXIkSNFng9jQk1GVjYLth3hzhk/cdbT/+OBj9ZzODGNey9qx5IHBjNzYn+u69fSEk8+7MynGGbMmMHkyZN/1e3yyy9n+vTpvPjii9xwww2MGjWKSpUqATBp0iTGjRtHt27d6NmzJ926daNmzYLb7g8ePBhVJTs7mzFjxvDnP//5N8N8+OGHvP/++4SHh9OoUSMeffRR6tSpw4ABA+jSpQvDhw/nwQcfZOTIkfTp04cePXrQoUOHQufvvffeY8KECTz66KOEh4cza9YshgwZwpYtW+jfvz/gNIR4//33adCgQVGLzZgyLzktk0Xb4vl28yHmbz1CYmomtaqG83+9mzOmV1N6Nq9lVWpFJCWtEiptffr00dxvMt2yZQsdO3b0KKIzl5WVRUZGBhEREezatYsLL7yQ7du3/5ycQk1ZWz7GFCSnldq3mw/zvdtKrXbVcC7s2JAhnRpyfvv6VK4Y5nWYvyEiq1W18Ca1HrEznwA4ffo0gwcPJiMjA1XllVdeCdnEY0woSMvM4pO1cUxbsY91+08CEFW3KuPOaclFnRrRu2XtcttKzV8s+QRAZGQkuc/eAM4+++yfn1yQ47333qNr166BCs0Y4yMhJYPpK/bx9rI9HElKo33DSO4f2p4hnRrSxlqp+VWZTT6qWuZXhBUrVngdgt8FezWuMXk5mJDCW0v3MGPlfpLTMhnQpi7P/V93BratV+b3M8GqTCafiIgIjh07Zu/0CTI5L5PLuTfImGC3OS6RN5bs5tN1cShwcdfGjB8YTZemofkwz2BSJpNPs2bNOHDgAPHx8V6HYnLJeY22McHqwInTfLbuIJ+sjWXroSSqVgrj+v4tuXlAK5rXKV+PuPFSmUw+4eHh9ppmY0yRxSel8eWGg3y6Lo7Ve08A0LNFLR4b2YkxPZtSq6o1AAq0Mpl8jDGmMGmZWXy54SBz1sSybOdRshU6NHIaEIzq3sTOcjxmyccYE1KOJacxbcU+3vthL/FJabSoU5VJg9owqkcT2jWM9Do847LkY4wJCdsPJ/HW0j3M/SmWtMxsBrWvz80DWnGetVgLSpZ8jDFlVna2smhHPG8t3cOSHUeJCK/A5b2bcfOAKNo0sLOcYGbJxxhTpiSkZLBs51EWbYtn0fZ4DiWm0rBGZe4f2p5r+ragdjVrPFAWWPIxxgS17GxlU1wii7YfYdH2eNbsO0lWthIZUZGBbeszpHNDhndpTKWK9pD+ssSSjzEmKG07lMSMlfv4fH0cR5PTAejatCaTBrXm/Hb16dG8FhXDLOGUVZ4kHxGJAZKALCAzmJ+8aowJnNSMLL5Yf5DpK/exeu8JKoVV4KLODbmwQwMGtqtPveqVCx+JKRO8PPMZrKpHPZy+MSZI7DicxPSV+5izJpaElAyi61Xj4REdubx3M+rYNZyQZNVuxhhPZGUr32w6xNRlMayMOU54mDC0cyOuObsF/aPtuY2hzqvko8A8EVHgVVV9zaM4jDEBdiotk1mr9vPWshj2HT9N8zpVmDy8A1f0bmbVauWIV8lngKrGiUgD4FsR2aqqi3N6ish4YDxAixYtPArRGONPhxNTmbo8hukr9pGQkkGvFrV4aHgHhnRuZC9mK4c8ST6qGuf+PyIic4G+wGKf/q8Br4HzGm0vYjTG+MeWg4m8sWQPn66LJTNbGda5EbeeF03vlrW9Ds14KODJR0SqARVUNcn9PAR4ItBxGGNKz+HEVD5dG8fHa2PZFJdIlfAwrunbgpvPbUXLutW8Ds8EAS/OfBoCc92LiRWB6ar6tQdxGGP8KDE1g683HuKTtbEs33UMVejWrCZ/vqQTl/ey1xaYXwt48lHV3UD3QE/XGON/2dnKwu1HmL06lm+3HCY9M5uWdavyhwvacmmPJkTXr+51iCZIWVNrY8wZS83IYu5Psby+ZDe7409Rt1olrj6rOZf2bEqP5rWsmbQplCUfY0yRnTiVzns/7OXd72M4mpxOl6Y1eGFsD0Z0bUy4PerGnAFLPsaYQu09doo3l+5h5qr9pGZkM7h9fW4bGG03g5pis+RjjMnTqbRMvt18mE/XxbFg2xHCK1Tg0p5NuPW8aHsjqCkxSz7GmJ+lZmSxcFs8n62L47uth0nNyKZxzQgmDWrNuP5RNKgR4XWIJkRY8jGmnMvMymbpzqN8tu4g8zYdIiktk7rVKnFln+aM7N6E3i1qU8GeQGD8zJKPMeVUWmYWs1fHMmXRLvYdP01kREWGdWnEqB5N6B9d196VY0qVJR9jyplTaZlMX7GP15fs5khSGt2b12Ly8A5c2LEBlSuGeR2eKScs+RhTTpw8nc7U5TFMXR7DydMZnNO6Lv+6qgfntLYWaybwLPkYE8JUlR1Hkpm1aj/TVuzjdHoWF3VqyKRBrenZwh7sabxjyceYEKOqbIpL5OuNh/hy40F2x5+igsCo7k24fVAb2jeyZtLGe5Z8jAkBqsra/Sf5euMhvtp4iH3HT1NBoF90XW46J4qhnRtZM2kTVCz5GFOGpWVmMXPVAaYs3EXsyRTCw4RzWtdj0qDWXNSpIXXtzaAmSFnyMaYMysjK5qPVB3hp/k5iT6bQu2Vt/jikHRd2bEjNKuFeh2dMoSz5GFOGZGZlM+enWP4zfwf7j6fQo3kt/nZZV85rW89arJkyxZKPMWVAZlY2n6yN48X5O9h77DTdmtXkidFdGNSuviUdUyZZ8jEmiCWnZfLRqv1MXR5DzLHTdGpcgzdu6MOFHRtY0jFlmiUfY4LQvmOnmbo8hlmr9pOUlkmP5rWYMrwDQzo1suesmZBgyceYIKGqfL/rGG8ti+G7rYcJE2FE18bcNCDKbgg1IceSjzEey8jK5uOfYnlz6R62HkqiTrVK/H5QG67r15JGNe3eHBOaLPkY45H0zGzmrDnAywt3sv94Ch0aRfLs5d0Y1aMJEeH2gE8T2iz5GBNg6ZnOPTovL3Du0enWrCaPXdLZGhGYcsWSjzEBkvM0glcW7CQuIZXuzWvx1KVdGNTemkub8seSjzGlLDUjiw9/3M+URbs4mJBKrxa1+Nvl3RhoN4aacsySjzGl5FRaJtNW7OW1xXs4mpzGWVG1ee6K7gxoY+/PMcaSjzF+lpCSwbvLY3hz2R5Ons7g3Db1+MMFPTk7uq7XoRkTNCz5GOMnx0+l8/ayPUxdFkNSWiYXdmjA7y9oQy+7R8eY37DkY0wJxSel8caS3bz3w15SMrIY3qURkwa1oUvTml6HZkzQ8iT5iEgYsAqIVdVLvIjBmJI6nJjKq4t2M33lXtIzsxnZvQl3DG5D24b2plBjCuPVmc9dwBaghkfTN6bY4k6mMGXRLj74cT9Z2cqYnk35/eA2tKpXzevQjCkzAp58RKQZcDHwNHBvoKdvTHHtP36aVxbtYtaq/ajCFb2bMWlQG1rUrep1aMaUOV6c+fwbeADIt25CRMYD4wFatGgRoLCMyduu+GReWbiLj3+KRQSu7NOc2we1plltSzrGFFdAk4+IXAIcUdXVIjIov+FU9TXgNYA+ffpogMIz5lc2xyXy8sKdfLnhIJUrVuC6fi0ZPzCaJrWqeB2aMWVeoM98BgCjRGQEEAHUEJH3VfW6AMdhTL7W7DvBy/N38t3WI1SvXJGJ57fmlnNbUa96Za9DMyZkBDT5qOpDwEMA7pnPfZZ4TLBYvusoL83fyfJdx6hVNZx7L2rHuP5R1Kwa7nVoxoScYicfEWkI/BVooqrDRaQT0F9V3/RbdMYEwOq9J/jHN9v4fvcxGkRW5pGLO3J13xZUq2y3wRlTWkqydU0F3gYedr9vBz4EipR8VHUhsLAE0zemRDbFJfD8vO3M33qEetUr8djITlzdt4W9S8eYAChJ8qmnqjNF5CEAVc0UkSw/xWVMqdl5JJl/fbudLzYcpGaVcB4Y1p4bz4miaiU70zEmUEqytZ0SkbqAAohIPyDBL1EZUwr2Hz/Nv/+3g7k/HaBKeBh3XtCGW86LpmYVu6ZjTKCVJPncC3wKtBaRZUB94Aq/RGWMH+05eoqXF+xk7k+xhFUQbjm3FRPPb01da71mjGeKnXxUdY2InA+0BwTYpqoZfovMmBLaeSSJl+bv5NN1cYSHVeCG/i2ZMLA1jWpGeB2aMeVeSVq7/R6YpqpGqrmEAAAZT0lEQVSb3O+1ReRqVf2v36Izphi2HkrkP/Odm0MjKoZx63nR3HpeKxpEWtIxJliUpNrtNlV9OeeLqp4QkdsASz7GE5viEnjxux18s+kw1StX5Hb35lCrXjMm+JQk+VQQEVHVnAYHYUAl/4RlTNHtPJLEv77dwRcbDhIZUZE7L2zLzQOiqFXVVkdjglVJks83wEwRmYLT4m0i8LVfojKmCPYeO8UL/9vBx2tjrfWaMWVMSZLPg8AE4HacBgfzgDf8EZQxBYk9mcJL83cwc9UBwsOE286LZsL5ralTzc50jCkrStLaLRt4xf0zptQdS07jP/N3Mn3FPgCu79eSSYNa06CGNSQwpqwpSWu3AcDjQEt3PAKoqkb7JzRjHFnZyvQVe3num22cSs/iyj7NuOOCtjS1VxsYU2aVpNrtTeAeYDVgj9UxpWLNvhM8+slGNsYmck7ruvxlVGfaNsz3PYTGmDKiJMknQVW/8lskxvg4mpzGM19tZdbqAzSsUZn/XN2TS7o1RkS8Ds0Y4wclST4LROQ5YA6QltNRVdeUOCpTbmVlK9NW7OUf32zjdHoWEwZG84cL21LdXm9gTEgpyRZ9tvu/j083BS4owThNObbhQAKT56xnU5xTxfbE6M60aWBVbMaEopK0dhvsz0BM+ZWakcUL3+3gtcW7qVOtEi9d05OLu1oVmzGhrER1GSJyMdAZ+Lmtq6o+UdKgTPmxKuY4D8xez+74U1zZpxkPj+hkr602phwoSVPrKUBVYDDOzaVXACv9FJcJcafTM3n26228830MTWpW4d2b+zKwXX2vwzLGBEhJznzOUdVuIrJeVf8iIs/jND4wpkDLdh5l8pz17D+ewrj+LXlgWAeqWYMCY8qVkmzxKe7/0yLSBDgGtCp5SCZUHUpI5Z/fbmPmqgNE16vGrIn9OSuqjtdhGWM8UJLk87mI1AKeA9bgtHSzZ7uZ3ziWnMYrC3fx3g97yVZlwvnR3PO7dkSEh3kdmjHGIyVJPs+qahowW0Q+x2l0kOqfsEwoSEzN4I3Fu3lz6R5SMrK4rFcz7rqwLc3rVPU6NGOMx0qSfL4HegG4SShNRNbkdDPl1+n0TN5Zvpcpi3aRkJLBxV0bc89Fbe2eHWPMz844+YhII6ApUEVEeuI8UBSgBk7rN1NOqSof/Lif5+dt52hyGoPb1+ePQ9rTpWlNr0MzxgSZ4pz5DAVuBJoBz/NL8kkC/uSfsExZc+DEaSbP3sDSnUfpG1WHKdf1oo81JjDG5OOMk4+qvgO8IyKXq+rsUojJlCE5ZztPf7EFVeWvY7pydd/m9nQCY0yBSnLNp5mI1MA543kd51rPZFWd55fITNCLO5nC5DkbWLw9nv7RdXn2im7WmMAYUyQlST43q+oLIjIUaADcBLyN8zptE8JUlVmrD/DkZ5vJzFaeHN2Za89uSYUKdrZjjCmakiSfnD3NCOBtVV0nRahrEZEIYDFQ2Z3+R6r6WAniMAF0ODGVybPXs2BbPH1b1eG5K7rRsm41r8MyxpQxJUk+q0VkHs5TDR4SkUgguwi/SwMuUNVkEQkHlorIV6r6QwliMQHw+fo4Hp67kbTMLB4b2Ylx/aPsbMcYUywlST63AD2A3ap6WkTq4lS9FUhVFUh2v4a7f1qCOEwpS0jJ4LFPNvLx2ji6N6/Fv67sTnT96l6HZYwpw4pzn08HVd2Kk3gAos+0ZZOIhAGrgTbAy6q6Ilf/8cB4gBYtWpxpiMaPlu08yn2z1nEkKY17fteO3w9uTcWwCl6HZYwp44pz5nMvTmJ4Po9+RXqTqapmAT3cZ8PNFZEuqrrRp/9rwGsAffr0sbMiD6RmZPHs19t4a9keoutVY87t59C9eS2vwzLGhIji3Ocz3v1f4jeZqupJEVkIDAM2FjK4CZCNsQnc8+FadhxJZlz/lkwe3pEqlewhoMYY/ynWNR/3+s41QAe30xZguqoeL8Jv6wMZbuKpAvwOeKY4cRj/Ss3I4uUFO3ll4S7qVKvEOzf35Xx7wZsxphQU55pPR2A+8A3wE06T67OAP4nIBe71oII0xnlCQhhQAZipqp+faRzGvxZuO8Kjn2xi3/HTXNqjCY+N7EztapW8DssYE6KKc+bzJHCXqs707SgilwNPA5cX9GNVXQ/0LMZ0TSk4lJDKE59v4ssNh4iuX43pt57NOW3qeR2WMSbEFSf5dFXVK3J3VNXZIvJXP8RkAiAzK5t3v9/L8/O2kZmt3DekHbcNjKZyRbu2Y4wpfcVJPqeK2c8EibX7T/Lw3A1sikvk/Hb1eWJ0Z3tKgTEmoIqTfBqIyL15dBfArk4HsdSMLP7xzTbeXLaHBpGV+e+1vRjepZE9gdoYE3DFST6vA/m9kvKNEsRiStHqvSe4f9Y6dh89xXX9WvDgsA5ERoR7HZYxppwqzn0+fymNQEzpSM3I4p/fbueNJbtpXLOKNSgwxgSFkjzbzQS5n/ad4L5Z69gVf4przm7Bn0Z0pHplW+TGGO/ZnigEpWVm8e//7eDVRbtoVCOC927py3lt7XKcMSZ4WPIJMfuPn+a2d1ex9VASY89qzsMXd7RrO8aYoOPX5CMivVR1jT/HaYrup30nuO3dVaRnZvP2TWcxuH0Dr0Myxpg8+fvZ+Lf7eXymiL7eeJCxr/1A1UoVmTNpgCUeY0xQ8+uZj6re5s/xmcKpKm8s2cNfv9pCz+a1eP2GPtStXtnrsIwxpkDFTj4i0iuPzgnAXlXNLH5Ipqgys7J57NNNTFuxj4u7Nub5K7sTEW6PxzHGBL+SnPn8F+gFrMd5ukEX93NdEZmoqvP8EJ/JR3JaJndMX8PCbfHcPqg19w9pT4UK9qQCY0zZUJJrPjFAT1Xto6q9cZ5UvRHn/TzP+iE2k4+DCSlc8cpyluw4yt8u68qDwzpY4jHGlCklOfPpoKqbcr6o6mYR6amqu+1ZYaVn/YGT3PrOKlLSs5h601l2/44xpkwqSfLZJiKvAB+4368CtotIZSCjxJGZ3/hqw0HumbmWutUq8+7tfenQqIbXIRljTLGUJPncCEwC7sa55rMUuA8n8QwucWTmZ6rKfxfu4rlvttGrRS1eu6EP9axFmzGmDCtJ8hkGvKSqz+fRL7kE4zU+0jKzeGjOBuasiWV0jyY8c3k3a9FmjCnzStLgYBRONdt7InKxiNijevzs+Kl0rntjBXPWxHLvRe3491U9LPEYY0JCsROGqt4kIuHAcOAa4L8i8q2q3uq36MqxnUeSuHnqKg4npvKfq3sysnsTr0Myxhi/KdHZiqpmiMhXgAJVgNGAJZ8SWrbzKBPfX03limF8ML4fPVvU9jokY4zxq2JXu4nIMBGZCuwErsB5i2ljP8VVbn214SA3vr2SJjWr8MkdAyzxGGNCUklbu30ATFDVNP+EU77N/HE/k+esp2eL2rw17ixqVrVXIRhjQlNJrvmM9f0uIgOAa1T19yWOqhx6Y8lunvpiCwPb1WfKdb2oWsnabxhjQleJ9nAi0gOnscGVwB5gjj+CKk9UlefnbeelBTu5uGtj/nVVDypV9PebLowxJriccfIRkXbAWOBq4BjwISCqajeWnqHsbOXxzzbx7vd7GXtWc54e05Uwe0abMaYcKM6Zz1ZgCTBSVXcCiMg9fo2qHMjIyua+Wev4ZG0cEwZGM3l4B+yZeMaY8qI49TuXA4eABSLyuohciPN4nUKJSHMRWSAiW0Rkk4jcVYzpl3mpGVlMfG81n6yN4/6h7S3xGGPKnTM+81HVucBcEakGXArcAzR0HzI6t5D3+GQCf1TVNSISCax2b0zdXJzgy6Kk1AxufWcVK2OO8+SlXbi+X0uvQzLGmIAr9pVtVT2lqtNU9RKgGbAWmFzIbw6q6hr3cxKwBWha3BjKmuOn0rnm9RWs3nuCf1/VwxKPMabc8kt7XlU9Drzq/hWJiEThvIBuhT9iCHYHE1K4/s2V7D9+mtdu6M0FHRp6HZIxxnjGk5tJRKQ6MBu4W1UT8+g/HhgP0KJFiwBH538xR09x7RsrSEjJ4J2b+9Ivuq7XIRljjKcCfkOJ+zDS2cA0Vc3zviBVfc19PXef+vXL9ps6txxM5Iop33M6PZMZt/WzxGOMMQT4zEecJl1vAltU9Z+BnLYXVu89wU1vr6RqpYp8ML4/bRpEeh2SMcYEhUCf+QwArgcuEJG17t+IAMcQEEt2xHPdGyuoU60SsyZa4jHGGF8BPfNR1aUU8Z6gsuzHmOPcMnUV0fWr8e4tfWkQGeF1SMYYE1Ts6ZV+djgxldvfX0PT2lX4cHx/ezK1McbkwZKPH6VnZnP7+6s5nZ7J9NvOtsRjjDH5sOTjR098vok1+07y32t70a6hXeMxxpj82LP7/WTmqv28/8M+JpwfzYiu9kJXY4wpiCUfP1h/4CSPfLyRAW3qcv+Q9l6HY4wxQc+STwkdS05j4nurqV+9Mv+5uhcVw6xIjTGmMHbNpwQys7L5w4yfOHoqndkTz6FOtUpeh2SMMWWCHaaXwHPfbGP5rmP8dUxXujar6XU4xhhTZljyKaYv1h/k1cW7ub5fS67o3czrcIwxpkyx5FMMG2MTuP+jdfRuWZs/X9LJ63CMMabMseRzhg4mpHDLOz9Sq0o4r1zbi0oVrQiNMeZMWYODM3AqLZNbpq7iVFoWH93enwY17JltxhhTHHbYXkRZ2cpdH/zE1kOJ/OeannRoVMPrkIwxpsyyM58ieuqLzfxvyxGeHN2Zwe0beB2OMcaUaXbmUwTvfh/D28tiuHlAK67vH+V1OMYYU+ZZ8inEgq1HePzTTfyuYwMevrij1+EYY0xIsORTgM1xidwxfQ0dG9fghbE9CasQ8u/BM8aYgLDkk48jianc8s6PREaE8+a4s6hW2S6PGWOMv9geNQ/Z2cqkaWtISMlg5oT+NKppTaqNMcafLPnk4dN1cazae4JnL+9Gl6b2zDZjjPE3q3bL5XR6Jn//aitdm9a0Z7YZY0wpseSTy5RFuzmUmMqjIztRwRoYGGNMqbDk4yP2ZAqvLtrFJd0ac1ZUHa/DMcaYkGXJx8czX20FYPLwDh5HYowxoc2Sj2v13uN8ui6O8QOjaVa7qtfhGGNMSLPkg9O0+onPNtOwRmUmnt/a63CMMSbkWfIB5v4Uy7oDCTw4rIPdTGqMMQFQ7pPPqbRMnvl6K92b1+LSHk29DscYY8qFgCcfEXlLRI6IyMZATzsvUxbt4khSGo9eYk2rjTEmULw485kKDPNgur9x4MRpXlu8m9E9mtC7ZW2vwzHGmHIj4MlHVRcDxwM93bz87autiMCDw6xptTHGBFJQXvMRkfEiskpEVsXHx5fKNH6MOc4X6w8yYWBrmtSqUirTMMYYk7egTD6q+pqq9lHVPvXr1y+VaUxZuIv6kda02hhjvBCUyae0JaRksHhHPKO7N6FKpTCvwzHGmHKnXCaf77YcJiNLGdGtsdehGGNMueRFU+sZwPdAexE5ICK3BDqGLzccpHHNCHo0qxXoSRtjjMGDl8mp6tWBnqavxNQMFm8/ynX9Wtp9PcYY45FyV+323ZbDpGdlc3G3Rl6HYowx5Va5Sz5frD9EoxoR9GxuN5UaY4xXylXySUp1WrkN79rIqtyMMcZD5Sr5fLflCOmZ2Vzc1Vq5GWOMl8pV8vlyw0Ea1YigVwurcjPGGC+Vm+STnJbJwu3xDOtiVW7GGOO1cpN8vtty2KlysxtLjTHGc+Um+Xy54SANIivT26rcjDHGc+Ui+ZxKy2ThtniGW5WbMcYEhXKRfL7beoS0zGxGWCs3Y4wJCuUi+Xy5/iD1IyvTJ6qO16EYY4yhHCSfU2mZLNh2hOFdGhFmVW7GGBMUQj75LNhmVW7GGBNsQj75fLnhIPWqV+Ysq3IzxpigEdLJ53R6JvO3WpWbMcYEm5BOPgu2xpOaYVVuxhgTbEI6+ThVbpXo28qq3IwxJpiEbPJJSc9i/tYjDO1sVW7GGBNsQjb5LNx2hJSMLHt9gjHGBKGQTT5VKoVxYYcGVuVmjDFBqKLXAZSWQe0bMKh9A6/DMMYYk4eQPfMxxhgTvCz5GGOMCThLPsYYYwLOko8xxpiAs+RjjDEm4Cz5GGOMCThLPsYYYwLOko8xxpiAE1X1OoYCiUg8sLcYP60HHPVzOP5isRWPxVY8FlvxlPXYWqpq/UAEUxxBn3yKS0RWqWofr+PIi8VWPBZb8VhsxWOxlS6rdjPGGBNwlnyMMcYEXCgnn9e8DqAAFlvxWGzFY7EVj8VWikL2mo8xxpjgFcpnPsYYY4KUJR9jjDEBF3LJR0SGicg2EdkpIpM9jqW5iCwQkS0isklE7nK7Py4isSKy1v0b4VF8MSKywY1hldutjoh8KyI73P+1PYirvU/ZrBWRRBG528tyE5G3ROSIiGz06ZZnWYnjRXcdXC8ivQIc13MistWd9lwRqeV2jxKRFJ/ym1JacRUSX77LUUQecsttm4gMDXBcH/rEFCMia93uAS23AvYbnq9vfqWqIfMHhAG7gGigErAO6ORhPI2BXu7nSGA70Al4HLgvCMorBqiXq9uzwGT382TgmSBYpoeAll6WGzAQ6AVsLKysgBHAV4AA/YAVAY5rCFDR/fyMT1xRvsN5WG55Lkd321gHVAZaudtyWKDiytX/eeBRL8qtgP2G5+ubP/9C7cynL7BTVXerajrwATDaq2BU9aCqrnE/JwFbgKZexVNEo4F33M/vAJd6GAvAhcAuVS3OUy78RlUXA8dzdc6vrEYD76rjB6CWiDQOVFyqOk9VM92vPwDNSmPaRZFPueVnNPCBqqap6h5gJ842HdC4RESAK4EZpTHtwhSw3/B8ffOnUEs+TYH9Pt8PECQ7exGJAnoCK9xOd7inyG95UbXlUmCeiKwWkfFut4aqehCcjQBo4FFsOcby651AMJRbjvzKKpjWw5txjopztBKRn0RkkYic51FMkPdyDJZyOw84rKo7fLp5Um659htlYX0rslBLPpJHN8/bkotIdWA2cLeqJgKvAK2BHsBBnFN8LwxQ1V7AcOD3IjLQozjyJCKVgFHALLdTsJRbYYJiPRSRh4FMYJrb6SDQQlV7AvcC00WkRqDjIv/lGBTlBlzNrw94PCm3PPYb+Q6aRzfP93uFCbXkcwBo7vO9GRDnUSwAiEg4zgo0TVXnAKjqYVXNUtVs4HVKqWqhMKoa5/4/Asx14zicc8ru/j/iRWyu4cAaVT0MwVNuPvIrK8/XQxEZB1wCXKvuhQG3OuuY+3k1zjWVdoGMy512fssxGMqtInAZ8GFONy/KLa/9BkG8vhVHqCWfH4G2ItLKPWoeC3zqVTBu3fGbwBZV/adPd9/62DHAxty/DUBs1UQkMuczzkXqjTjlNc4dbBzwSaBj8/GrI9BgKLdc8iurT4Eb3FZI/YCEnOqSQBCRYcCDwChVPe3Tvb6IhLmfo4G2wO5AxeUTR37L8VNgrIhUFpFWbnwrAxze74Ctqnogp0Ogyy2//QZBur4Vm9ctHvz9h9PyYzvO0cnDHsdyLs7p73pgrfs3AngP2OB2/xRo7EFs0Tgti9YBm3LKCqgLfAfscP/X8ajsqgLHgJo+3TwrN5wkeBDIwDnSvCW/ssKpBnnZXQc3AH0CHNdOnGsAOevcFHfYy91lvQ5YA4z0qNzyXY7Aw265bQOGBzIut/tUYGKuYQNabgXsNzxf3/z5Z4/XMcYYE3ChVu1mjDGmDLDkY4wxJuAs+RhjjAk4Sz7GGGMCzpKPMcaYgLPkY0KGiGS5Tx3eJCLrROReEang9usjIi96FNdyL6ZrTDCzptYmZIhIsqpWdz83AKYDy1T1MW8jM8bkZmc+JiSp88ig8TgPsBQRGSQin8PP75N5R0Tmue9tuUxEnhXn3UZfu482QUR6uw+SXC0i3/g82mShiDwjIitFZHvOgyZFpLPbba370My2bvdk97+I866dje60rnK7D3LH+ZE47+GZ5t7ljoj8XUQ2u+P7R6DL0ZjSUtHrAIwpLaq62612y+vJ3K2BwTjvSfkeuFxVHxCRucDFIvIF8B9gtKrGu4niaZynRIPzvpy+4rwI7TGcx7JMBF5Q1Wnu453Cck3zMpyHaXYH6gE/ishit19PoDPOM7mWAQNEZDPO42c6qKqK+1I4Y0KBJR8T6vJ64i/AV6qaISIbcJLE1273DTgvD2sPdAG+dU9CwnAex5Ij52GPq93hwUliD4tIM2CO/vqR/OA8NmWGqmbhPCRyEXAWkAisVPd5YuK8QTMK5108qcAbbjL8/Izm3JggZtVuJmS5D4HMIu8nc6cBqPNk5Qz95eJnNs5BmQCbVLWH+9dVVYfk/r07/oruuKbjvAIiBfhGRC7IHVIB4ab5fM7CObPKxHni82ycF4d9ndcPjSmLLPmYkCQi9YEpwEtavFY124D6ItLfHV+4iHQuZJrRwG5VfRHngZndcg2yGLhKRMLc+AZSwFObxXmfS01V/RK4G6fKzpiQYNVuJpRUcauswnFeovYe8M+Cf5I3VU0XkSuAF0WkJs628m+cpxvn5yrgOhHJAA4BT+TqPxfoj/N0ZAUeUNVDItIhn/FFAp+ISATOWdM9xZkXY4KRNbU2xhgTcFbtZowxJuAs+RhjjAk4Sz7GGGMCzpKPMcaYgLPkY4wxJuAs+RhjjAk4Sz7GGGMC7v8BhzGl0mJ3osAAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(dist[\"Dimension\"],dist[\"Avg_Distance\"])\n",
"plt.title(\"Average Distance with Number of Dimensions for 1k Observations\")\n",
"plt.xlabel('Dimensions') \n",
"plt.ylabel('Avg. Distance') \n",
"plt.legend(loc='best') \n",
"plt.show();"
]
}
],
"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": "3.6.6"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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