The first minimum of the mutual information function using a number of different *kth* nearest neighbors.

Mutual information first minimum.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using ChaosTools, DataFrames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>k</th><th>N10e2</th></tr></thead><tbody><tr><th>1</th><td>1</td><td>15</td></tr><tr><th>2</th><td>2</td><td>16</td></tr><tr><th>3</th><td>3</td><td>11</td></tr><tr><th>4</th><td>4</td><td>12</td></tr><tr><th>5</th><td>5</td><td>13</td></tr><tr><th>6</th><td>100</td><td>7</td></tr><tr><th>7</th><td>250</td><td>5</td></tr><tr><th>8</th><td>500</td><td>2</td></tr></tbody></table>"
      ],
      "text/plain": [
       "8×2 DataFrames.DataFrame\n",
       "│ Row │ k   │ N10e2 │\n",
       "├─────┼─────┼───────┤\n",
       "│ 1   │ 1   │ 15    │\n",
       "│ 2   │ 2   │ 16    │\n",
       "│ 3   │ 3   │ 11    │\n",
       "│ 4   │ 4   │ 12    │\n",
       "│ 5   │ 5   │ 13    │\n",
       "│ 6   │ 100 │ 7     │\n",
       "│ 7   │ 250 │ 5     │\n",
       "│ 8   │ 500 │ 2     │"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 10e2\n",
    "\n",
    "ks = [ collect(1:5); [ Int(N*0.1), Int(N*0.25), Int(N*0.5) ]]\n",
    "N10e2 = zeros(Int,length(ks))\n",
    "\n",
    "ds = Systems.henon()\n",
    "data = trajectory(ds,N;dt=1)\n",
    "x = data[:,1]\n",
    "\n",
    "for k in eachindex(ks)\n",
    "    N10e2[k] = estimate_delay(x,\"mutual_inf\"; k=ks[k])\n",
    "end\n",
    "\n",
    "dfN10e2 = DataFrame(k = ks, N10e2 = N10e2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>k</th><th>N10e3</th></tr></thead><tbody><tr><th>1</th><td>1</td><td>22</td></tr><tr><th>2</th><td>2</td><td>24</td></tr><tr><th>3</th><td>3</td><td>25</td></tr><tr><th>4</th><td>4</td><td>18</td></tr><tr><th>5</th><td>5</td><td>19</td></tr><tr><th>6</th><td>1000</td><td>8</td></tr><tr><th>7</th><td>2500</td><td>3</td></tr><tr><th>8</th><td>5000</td><td>1</td></tr></tbody></table>"
      ],
      "text/plain": [
       "8×2 DataFrames.DataFrame\n",
       "│ Row │ k    │ N10e3 │\n",
       "├─────┼──────┼───────┤\n",
       "│ 1   │ 1    │ 22    │\n",
       "│ 2   │ 2    │ 24    │\n",
       "│ 3   │ 3    │ 25    │\n",
       "│ 4   │ 4    │ 18    │\n",
       "│ 5   │ 5    │ 19    │\n",
       "│ 6   │ 1000 │ 8     │\n",
       "│ 7   │ 2500 │ 3     │\n",
       "│ 8   │ 5000 │ 1     │"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 10e3\n",
    "\n",
    "ks = [ collect(1:5); [ Int(N*0.1), Int(N*0.25), Int(N*0.5) ]]\n",
    "N10e3 = zeros(Int,length(ks))\n",
    "\n",
    "ds = Systems.henon()\n",
    "data = trajectory(ds,N;dt=1)\n",
    "x = data[:,1]\n",
    "\n",
    "for k in eachindex(ks)\n",
    "    N10e3[k] = estimate_delay(x,\"mutual_inf\"; k=ks[k])\n",
    "end\n",
    "\n",
    "dfN10e3 = DataFrame(k = ks, N10e3 = N10e3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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