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@gbirke
Last active August 29, 2015 14:15
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Hash-Experiments
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{
"metadata": {
"name": "",
"signature": "sha256:8341380358ccde735c5824a9da156b23a2469f49073ed0708e5501af81a4552d"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import matplotlib.pylab as pylab\n",
"pylab.rcParams['figure.figsize'] = 20, 10 # Set default width and height for matplotlib figures"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 159
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib.pyplot as plt\n",
"import numpy as np"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"\n",
"import hashlib\n",
"\n",
"class ChangeHistogram(object):\n",
"\n",
" def __init__(self, width=256):\n",
" self.width = width\n",
" self.histogram = [0] * width\n",
"\n",
" def add_item(self, item):\n",
" index = int(hashlib.md5(item).hexdigest(), 16) % self.width\n",
" self.histogram[index] += 1\n",
"\n",
" def get_item_count(self):\n",
" return sum(self.histogram)\n",
"\n",
" def get_normalized_histogram(self, scale_to=100, digits=0):\n",
" count = self.get_item_count() or 1 # avoid div by 0\n",
" return [round((e / count) * scale_to, digits) for e in self.histogram]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import random\n",
"\n",
"def generate_items(num_items, mutation_probability=0):\n",
" \"\"\" Generate items for the change histogram, with a chance of a certain number of items being different in each run.\"\"\"\n",
" for i in range(0, num_items):\n",
" rnd = random.random()\n",
" if rnd < mutation_probability:\n",
" yield str(rnd * num_items)\n",
" else:\n",
" yield str(i)\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 43
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Trying to visualize how many items a ChangeHistogram with a certain width can hold and still give a meaningful \"fingerprint\" of the distribution of items."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"width = 16\n",
"histograms=[]\n",
"start_item = 2\n",
"for i in range(start_item,start_item+4):\n",
" num_items = 2**(i*2)\n",
" ch = ChangeHistogram(width)\n",
" for item in generate_items(num_items):\n",
" ch.add_item(item)\n",
" histograms.append(ch.histogram)\n",
"\n",
"fig, ax = plt.subplots(2,2)\n",
"\n",
"x = range(width)\n",
"bar_width = 0.8\n",
"\n",
"for row in range(0,2):\n",
" for col in range(0,2):\n",
" hist_index = (row * 2) + col\n",
" ax[row, col].bar(x, histograms[hist_index], width=bar_width)\n",
" ax[row, col].set_title(\"{} items\".format(sum(histograms[hist_index])))\n",
"plt.subplots_adjust(hspace=.4)\n",
"\n",
"histograms\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 116,
"text": [
"[[2, 0, 0, 3, 0, 1, 2, 0, 0, 1, 2, 1, 3, 1, 0, 0],\n",
" [6, 3, 2, 4, 4, 2, 7, 2, 3, 5, 4, 4, 7, 4, 1, 6],\n",
" [14, 11, 13, 19, 23, 16, 13, 15, 14, 13, 17, 16, 15, 20, 15, 22],\n",
" [72, 54, 56, 61, 62, 65, 61, 62, 66, 60, 52, 77, 70, 66, 71, 69]]"
]
},
{
"metadata": {},
"output_type": "display_data",
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MNQ/9T22U7A2cWVVPnOW19cC1VVVJDgROq6q9Z9muRj+raVjM8XRNEiz7dlj23dXlcz+e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\nkiRJjfgNbvOd4eNru7cAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0xa670f10>"
]
}
],
"prompt_number": 116
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Graphs above shows that when the number of items goes up, the fingerprint becomes more and more insignificant.\n",
"\n",
"Let's try and quantify the relationships between the number of items, the difference between min and max amount of items in each \"bucket\" and other figures."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"width = 500\n",
"h_max = []\n",
"h_min = []\n",
"h_avg = []\n",
"h_diff = []\n",
"h_rel_avg = []\n",
"h_rel_sum = []\n",
"w_sqr = []\n",
"steps = range(1, 51)\n",
"for i in steps:\n",
" ch = ChangeHistogram(width)\n",
" num_items = width * i\n",
" for item in generate_items(num_items):\n",
" ch.add_item(item)\n",
" i_sum = sum(ch.histogram)\n",
" i_max = max(ch.histogram)\n",
" i_diff = i_max - min(ch.histogram)\n",
" i_avg = i_sum / len(ch.histogram)\n",
" h_max.append(max(ch.histogram))\n",
" h_min.append(min(ch.histogram))\n",
" h_avg.append(i_avg)\n",
" h_diff.append(i_diff)\n",
" h_rel_avg.append((i_diff * 100) /i_avg)\n",
" h_rel_sum.append(i_diff / i_sum)\n",
"\n",
"fig, ax = plt.subplots(2,2)\n",
"ax[1,0].set_title(\"Base values\")\n",
"p_min, = ax[0,0].plot(steps, h_min, label=\"min\")\n",
"p_max, = ax[0,0].plot(steps, h_max, label=\"max\")\n",
"p_avg, = ax[0,0].plot(steps, h_avg, label=\"avg\")\n",
"p_diff, = ax[0,0].plot(steps, h_diff, label=\"diff\")\n",
"ax[0,0].legend(handles=[p_min, p_max, p_avg, p_diff])\n",
"\n",
"ax[0,1].set_title(\"Difference/average\")\n",
"ax[0,1].grid(True)\n",
"ax[0,1].plot(steps, h_rel_avg)\n",
"\n",
"ax[1,0].set_title(\"Difference/sum\")\n",
"ax[1,0].plot(steps, h_rel_sum)\n",
"\n",
"ax[1,1].plot(steps, h_diff, 'c', label=\"diff\")\n",
"plt.subplots_adjust(hspace=.4)\n",
"\n",
"print h_diff, sum(h_diff)/len(h_diff)\n",
"print [round(a, 2) for a in h_rel_avg], sum(h_rel_avg)/len(h_rel_avg)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[5, 7, 8, 10, 11, 14, 14, 14, 16, 17, 17, 19, 19, 21, 22, 23, 22, 23, 22, 24, 25, 25, 26, 26, 27, 27, 30, 31, 30, 31, 31, 31, 32, 31, 33, 32, 32, 32, 32, 32, 32, 32, 35, 38, 39, 39, 39, 38, 39, 40] 25.9\n",
"[500.0, 350.0, 266.67, 250.0, 220.0, 233.33, 200.0, 175.0, 177.78, 170.0, 154.55, 158.33, 146.15, 150.0, 146.67, 143.75, 129.41, 127.78, 115.79, 120.0, 119.05, 113.64, 113.04, 108.33, 108.0, 103.85, 111.11, 110.71, 103.45, 103.33, 100.0, 96.88, 96.97, 91.18, 94.29, 88.89, 86.49, 84.21, 82.05, 80.0, 78.05, 76.19, 81.4, 86.36, 86.67, 84.78, 82.98, 79.17, 79.59, 80.0] 134.916977168\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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sA2aoan4959m0NWPMMeUcyuGxjx/jr1/9letGXsdPx/2U3p17h7pZpr07ehQ2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EoeiYhIt3D0aEgiVVWljo3LgQPhtaZK8hkIyY9Bg0IyKf3Y+Dy9JJMm6dcDB4bkzfFwDwm0995r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\n",
"text": [
"<matplotlib.figure.Figure at 0xcabc190>"
]
}
],
"prompt_number": 134
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The graphs show that when the difference between highest and lowest value in the buckets gets too close to the average value in the buckets, the difference does not change very much any more. There is a \"tipping point\" between `items*10` and `items*20` where there is no longer enough variation.\n",
"\n",
"The next step is to visualize how the histogram looks when it is generated multiple times and 1% of the items are changed in each run."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"rows = range(3)\n",
"histograms=[]\n",
"width = 64\n",
"items = [2, 5, 10, 20]\n",
"for r in rows:\n",
" histograms.append([])\n",
" for i in items:\n",
" num_items = width * i\n",
" ch = ChangeHistogram(width)\n",
" for item in generate_items(num_items, .01):\n",
" ch.add_item(item)\n",
" histograms[r].append(ch.histogram)\n",
"\n",
"bar_width = 0.5\n",
"fig, ax = plt.subplots(len(items))\n",
"\n",
"cols = range(len(items))\n",
"\n",
"row_colors = ['b', 'g', 'm']\n",
"\n",
"for col in cols:\n",
" for row in rows:\n",
" x = [w+.1*row for w in range(width)]\n",
" ax[col].bar(x, histograms[row][col], width=bar_width, alpha=0.5, color=row_colors[row], label=\"Run %d\" % row)\n",
" ax[col].set_title(\"width x {}\".format(items[col]))\n",
" ax[col].grid(True)\n",
"#plt.subplots_adjust(hspace=.4) \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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S/Ykvqj3xSfUnvqj2pJ1UNfhjZp3ALmArcAVw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"text": [
"<matplotlib.figure.Figure at 0x15173fd0>"
]
}
],
"prompt_number": 182
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see in the above graph, that even for a large number of items, well above our threshold, the changes between each run are clearly visible. This is unexpected. Now let's try to write a function that quantifies the amount of change between two runs."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def count_differences(hist1, hist2):\n",
" diff = 0\n",
" for i in range(len(hist1)):\n",
" diff += abs(hist1[i] - hist2[i])\n",
" return diff \n",
"\n",
"\n",
"width = 256\n",
"items = [1, 2, 5, 10, 20]\n",
"items = range(1,20)\n",
"\n",
"def get_change_amount(width, mutation_probability):\n",
" change_counts = []\n",
"\n",
" for i in items:\n",
" num_items = width * i\n",
" ch = [ChangeHistogram(width), ChangeHistogram(width)] \n",
" for j in range(2):\n",
" for item in generate_items(num_items, mutation_probability):\n",
" ch[j].add_item(item)\n",
" diff = count_differences(ch[0].histogram, ch[1].histogram)\n",
" change_counts.append((diff * 100) / num_items)\n",
" return change_counts\n",
"\n",
"# base line - equal histograms - should be 0\n",
"assert(sum(get_change_amount(width, 0)) == 0)\n",
"stages = [x/100 for x in range(10,105,20)]\n",
"\n",
"plots = []\n",
"for stage in stages:\n",
" heights = get_change_amount(width, stage)\n",
" p, = plt.plot(items, heights,label=\"%d%% random\" % (stage*100))\n",
" plots.append(p)\n",
"plt.legend(handles=plots)\n",
"plt.grid(True)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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OnKjZs2fLbrdr8ODBmjBhgsvc5cuXKyQkRIMGDdK4ceP06KOPasaMGTeM5WbP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+oJ9OgH+3+gbc3bdKL7hG7dcKu2btyq1TWr0/gZAhhTOCydOpU6MGppkRYtSh0YNTZK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\nnEU6tvuY3A63Lr36U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"text": [
"<matplotlib.figure.Figure at 0x14478cd0>"
]
}
],
"prompt_number": 253
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This graph shows: The more changes the items have, the more \"smoothed over\" (unable to detect the correct number of changes) the graph becomes when you have a large number of items.\n",
"\n",
"There may be several solutions: \n",
"- Use a width that's equal to item numbers, count every difference as 1 (instead of abs). Problem: Uses more memory, lines must be counted or all hashes stored (uses even more memory)\n",
"- Amplify differences when number of items is high (eg diff * (average_value / 2). This must be tested as the next step."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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