genetic algorithm et al

Autocorrelation.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Title: Fuzzy sequence matching with cross-correlation\n",
+    "\n",
+    "## Cross-correlation\n",
+    "\n",
+    "I am going to generate a \"random file\" - an array with values ranging between -1 and 1, and then randomly choose a \"random slice\" - a subarray portion from the \"random file\".  I'm then going to randomly mutate some of the values in teh subarray, and see if I can still find where in the \"random file\" the \"random slice\" came from."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "import random\n",
+    "import numpy as np\n",
+    "\n",
+    "FILE_SIZE = 100000\n",
+    "SLICE_SIZE = 100\n",
+    "\n",
+    "random_file = np.asarray([random.uniform(-1,1) for i in range(FILE_SIZE)])\n",
+    "random_slice_index = random.randint(0, FILE_SIZE-SLICE_SIZE)\n",
+    "random_slice = random_file[random_slice_index:random_slice_index+SLICE_SIZE]\n",
+    "\n",
+    "# Randomly change the sample by about 50% - simulating a 50% noise\n",
+    "random_slice_mutated = np.asarray([i + random.uniform(-0.5,0.5) for i in random_slice])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "So now, we are going to try to find where in `random_file` the `random_slice_mutated` came from.  We know it should be `random_slice_index`.\n",
+    "\n",
+    "### First, let's write our own cross-correlation function to find it."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "# Coding our own cross-correlation algorithm\n",
+    "\n",
+    "def find_sample_index(container, sample):\n",
+    "    best_match_index = 0\n",
+    "    largest_dot_product = 0\n",
+    "    sample_size = len(sample)\n",
+    "    for index in range(len(container) - sample_size):\n",
+    "        dot = np.dot(container[index:index+sample_size], sample)\n",
+    "        if dot > largest_dot_product:\n",
+    "            best_match_index = index\n",
+    "            largest_dot_product = dot\n",
+    "    return (best_match_index, largest_dot_product)\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(14108, 33.238798044766)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "find_sample_index(random_file, random_slice_mutated)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Actual index (should match): 14108\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"Actual index (should match):\", random_slice_index)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Now, let's use the `scipy.signal.correlate()` function instead of our own one.\n",
+    "\n",
+    "Note that the numpy implementation returns a vector of all of the correlation values, not just the largest one, so to find the largest index, we need to find the largest value."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "14108"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import scipy.signal\n",
+    "result = scipy.signal.correlate(random_file, random_slice)\n",
+    "max_correlation_index = np.argmax(result) - (SLICE_SIZE-1)\n",
+    "max_correlation_index"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Cross-correlation algorithm"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([ 3,  8, 14, 20, 26, 14,  5])"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "a = np.array([1,2,3,4,5])\n",
+    "b = np.array([1,2,3])\n",
+    "scipy.signal.correlate(a,b)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "For vectors:\n",
+    "\n",
+    "A=\n",
+    "<table>\n",
+    "<tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td></tr>\n",
+    "</table>\n",
+    "\n",
+    "B=\n",
+    "<table>\n",
+    "<tr><td>1</td><td>2</td><td>3</td></tr>\n",
+    "</table>\n",
+    "\n",
+    "The cross-correlate algorithm zero-pads each vector as such (where the blank cells represent 0):\n",
+    "\n",
+    "#### Step 1\n",
+    "<table>\n",
+    "<tr><td></td><td></td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td></tr>\n",
+    "<tr><td>1</td><td>2</td><td>3</td><td></td><td></td><td></td><td></td></tr>\n",
+    "</table>\n",
+    "\n",
+    "    0*1 + 0*2 + 1*3 + 2*0 + 3*0 + 4*0 + 5*0 = 3\n",
+    "\n",
+    "#### Step 2\n",
+    "<table>\n",
+    "<tr><td></td><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td></tr>\n",
+    "<tr><td>1</td><td>2</td><td>3</td><td></td><td></td><td></td></tr>\n",
+    "</table>\n",
+    "\n",
+    "    0*1 + 1*2 + 2*3 + 3*0 + 4*0 + 5*0 = 8\n",
+    "\n",
+    "#### Step 3\n",
+    "<table>\n",
+    "<tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td></tr>\n",
+    "<tr><td>1</td><td>2</td><td>3</td><td></td><td></td></tr>\n",
+    "</table>\n",
+    "\n",
+    "    1*1 + 2*2 + 3*3 + 4*0 + 5*0 = 14\n",
+    "\n",
+    "## ...\n",
+    "\n",
+    "#### Last step\n",
+    "<table>\n",
+    "<tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td></td><td></td></tr>\n",
+    "<tr><td></td><td></td><td></td><td></td><td>1</td><td>2</td><td>3</td></tr>\n",
+    "</table>\n",
+    "\n",
+    "So each step consists of doing the appropriate zero-padding and taking the dot product of the 2 vectors, and then moving to the right one spot."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
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