doc/kmers-and-minhash.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# An introduction to k-mers for genome comparison and analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "k-mers provide sensitive and specific methods for comparing and analyzing genomes.\n",
    "\n",
    "This notebook provides pure Python implementations of some of the basic k-mer comparison techniques implemented in sourmash, including hash-based subsampling techniques.\n",
    "\n",
    "### Running this notebook.\n",
    "\n",
    "You can run this notebook interactively via mybinder; click on this button:\n",
    "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/dib-lab/sourmash/master?filepath=doc%2Fkmers-and-minhash.ipynb)\n",
    "\n",
    "A rendered version of this notebook is available at [sourmash.readthedocs.io](https://sourmash.readthedocs.io) under \"Tutorials and notebooks\".\n",
    "\n",
    "You can also get this notebook from the [doc/ subdirectory of the sourmash github repository](https://github.com/dib-lab/sourmash/tree/master/doc). See [binder/environment.yaml](https://github.com/dib-lab/sourmash/blob/master/binder/environment.yml) for installation dependencies.\n",
    "\n",
    "### What is this?\n",
    "\n",
    "This is a Jupyter Notebook using Python 3. If you are running this via [binder](https://mybinder.org), you can use Shift-ENTER to run cells, and double click on code cells to edit them.\n",
    "\n",
    "Contact: C. Titus Brown, ctbrown@ucdavis.edu. Please [file issues on GitHub](https://github.com/dib-lab/sourmash/issues/) if you have any questions or comments!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating Jaccard similarity and containment\n",
    "\n",
    "Given any two collections of k-mers, we can calculate similarity and containment using the union and intersection functionality in Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def jaccard_similarity(a, b):\n",
    "    a = set(a)\n",
    "    b = set(b)\n",
    "    \n",
    "    intersection = len(a.intersection(b))\n",
    "    union = len(a.union(b))\n",
    "    \n",
    "    return intersection / union"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def jaccard_containment(a, b):\n",
    "    a = set(a)\n",
    "    b = set(b)\n",
    "    \n",
    "    intersection = len(a.intersection(b))\n",
    "    \n",
    "    return intersection / len(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's try these functions out on some simple examples!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = ['ATGG', 'AACC']\n",
    "b = ['ATGG', 'CACA']\n",
    "c = ['ATGC', 'CACA']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jaccard_similarity(a, a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jaccard_containment(a, a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3333333333333333"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jaccard_similarity(b, a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jaccard_similarity(a, c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jaccard_containment(b, a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib_venn._common.VennDiagram at 0x10cb677b8>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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j8OZ73wqfPAS3l2BgAD7/M/DV/wHfc1lTjzdHpz1+5et88tQMt1fqDPzDL/P5D23gq//0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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib_venn import venn2, venn3\n",
    "\n",
    "venn2([set(a), set(b)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib_venn._common.VennDiagram at 0x111e74c18>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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I3ADcBvTZLMpBU3g92xO2C7Gp40O3QYTrgd3AoO1aLCsDB4FfGMM7bvtkn6Tx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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "venn3([set(a), set(b), set(c)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating k-mers from DNA sequences\n",
    "\n",
    "To extract k-mers from DNA sequences, we walk over the sequence with a sliding window:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_kmers(sequence, ksize):\n",
    "    kmers = []\n",
    "    n_kmers = len(sequence) - ksize + 1\n",
    "    \n",
    "    for i in range(n_kmers):\n",
    "        kmer = sequence[i:i + ksize]\n",
    "        kmers.append(kmer)\n",
    "        \n",
    "    return kmers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['ATGGACCAGATATAGGGAGAG',\n",
       " 'TGGACCAGATATAGGGAGAGC',\n",
       " 'GGACCAGATATAGGGAGAGCC',\n",
       " 'GACCAGATATAGGGAGAGCCA',\n",
       " 'ACCAGATATAGGGAGAGCCAG',\n",
       " 'CCAGATATAGGGAGAGCCAGG',\n",
       " 'CAGATATAGGGAGAGCCAGGT',\n",
       " 'AGATATAGGGAGAGCCAGGTA',\n",
       " 'GATATAGGGAGAGCCAGGTAG',\n",
       " 'ATATAGGGAGAGCCAGGTAGG',\n",
       " 'TATAGGGAGAGCCAGGTAGGA',\n",
       " 'ATAGGGAGAGCCAGGTAGGAC',\n",
       " 'TAGGGAGAGCCAGGTAGGACA']"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "build_kmers('ATGGACCAGATATAGGGAGAGCCAGGTAGGACA', 21)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the k-mers that are output, you can see how the sequence shifts to the right - look at the pattern in the middle.\n",
    "\n",
    "So, now, you can compare two sequences!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "seq1 = 'ATGGACCAGATATAGGGAGAGCCAGGTAGGACA'\n",
    "seq2 = 'ATGGACCAGATATTGGGAGAGCCGGGTAGGACA'\n",
    "# differences:       ^         ^"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 0.09090909090909091\n"
     ]
    }
   ],
   "source": [
    "K = 10\n",
    "kmers1 = build_kmers(seq1, K)\n",
    "kmers2 = build_kmers(seq2, K)\n",
    "\n",
    "print(K, jaccard_similarity(kmers1, kmers2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reading k-mers in from a file\n",
    "\n",
    "In practice, we often need to work with 100s of thousands of k-mers, and this means loading them in from sequences in files.\n",
    "\n",
    "There are three cut-down genome files in the `genomes/` directory that we will use below:\n",
    "\n",
    "```\n",
    "akkermansia.fa\n",
    "shew_os185.fa\n",
    "shew_os223.fa\n",
    "```\n",
    "The latter two are two strains of *Shewanella baltica*, and the first one is an unrelated genome *Akkermansia muciniphila*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import screed # a library for reading in FASTA/FASTQ\n",
    "\n",
    "def read_kmers_from_file(filename, ksize):\n",
    "    all_kmers = []\n",
    "    for record in screed.open(filename):\n",
    "        sequence = record.sequence\n",
    "        \n",
    "        kmers = build_kmers(sequence, ksize)\n",
    "        all_kmers += kmers\n",
    "\n",
    "    return all_kmers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "akker_kmers = read_kmers_from_file('genomes/akkermansia.fa', 31)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['AAATCTTATAAAATAACCACATAACTTAAAA',\n",
       " 'AATCTTATAAAATAACCACATAACTTAAAAA',\n",
       " 'ATCTTATAAAATAACCACATAACTTAAAAAG',\n",
       " 'TCTTATAAAATAACCACATAACTTAAAAAGA',\n",
       " 'CTTATAAAATAACCACATAACTTAAAAAGAA']"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "akker_kmers[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "499970\n"
     ]
    }
   ],
   "source": [
    "print(len(akker_kmers))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "shew1_kmers = read_kmers_from_file('genomes/shew_os185.fa', 31)\n",
    "shew2_kmers = read_kmers_from_file('genomes/shew_os223.fa', 31)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see the relationship between these three like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "akker vs shew1 0.0\n",
      "akker vs shew2 0.0\n",
      "shew1 vs shew2 0.23675152210020398\n"
     ]
    }
   ],
   "source": [
    "print('akker vs shew1', jaccard_similarity(akker_kmers, shew1_kmers))\n",
    "print('akker vs shew2', jaccard_similarity(akker_kmers, shew2_kmers))\n",
    "print('shew1 vs shew2', jaccard_similarity(shew1_kmers, shew2_kmers))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "akker vs shew1 0.0\n",
      "akker vs shew2 0.0\n",
      "shew1 vs shew2 0.38397187523995907\n"
     ]
    }
   ],
   "source": [
    "print('akker vs shew1', jaccard_containment(akker_kmers, shew1_kmers))\n",
    "print('akker vs shew2', jaccard_containment(akker_kmers, shew2_kmers))\n",
    "print('shew1 vs shew2', jaccard_containment(shew1_kmers, shew2_kmers))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib_venn._common.VennDiagram at 0x11a2e7b00>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IbXHOTrX6/FYWH5VrtxkW8rZSluWJv4MJMziBD1DKEUWJHCO6qlSFgdcA506/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\nRK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "venn3([set(akker_kmers), set(shew1_kmers), set(shew2_kmers)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's hash!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Choose a hash function!\n",
    "\n",
    "We need to pick a hash function that takes DNA k-mers and converts them into numbers.\n",
    "\n",
    "Both the [mash](https://mash.readthedocs.io/en/latest/) software for MinHash, and the [sourmash](https://sourmash.readthedocs.io) software for modulo and MinHash, use MurmurHash:\n",
    "\n",
    "https://en.wikipedia.org/wiki/MurmurHash\n",
    "\n",
    "this is implemented in the 'mmh3' library in Python.\n",
    "\n",
    "The other thing we need to do here is take into account the fact that DNA is double stranded, and so\n",
    "\n",
    "```\n",
    "hash_kmer('ATGG')\n",
    "```\n",
    "should be equivalent to\n",
    "```\n",
    "hash_kmer('CCAT')\n",
    "```\n",
    "Following mash's lead, for every input k-mer we will choose a *canonical* k-mer that is the lesser of the k-mer and its reverse complement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mmh3\n",
    "\n",
    "def hash_kmer(kmer):\n",
    "    # calculate the reverse complement\n",
    "    rc_kmer = screed.rc(kmer)\n",
    "    \n",
    "    # determine whether original k-mer or reverse complement is lesser\n",
    "    if kmer < rc_kmer:\n",
    "        canonical_kmer = kmer\n",
    "    else:\n",
    "        canonical_kmer = rc_kmer\n",
    "        \n",
    "    # calculate murmurhash using a hash seed of 42\n",
    "    hash = mmh3.hash64(canonical_kmer, 42)[0]\n",
    "    if hash < 0: hash += 2**64\n",
    "        \n",
    "    # done\n",
    "    return hash"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is now a function that we can use to turn any DNA \"word\" into a number:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13663093258475204077"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hash_kmer('ATGGC')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same input word always returns the same number:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13663093258475204077"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hash_kmer('ATGGC')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "as does its reverse complement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13663093258475204077"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hash_kmer('GCCAT')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and nearby words return very different numbers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1777382721305265773"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hash_kmer('GCCAA')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Note that hashing collections of k-mers doesn't change Jaccard calculations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hash_kmers(kmers):\n",
    "    hashes = []\n",
    "    for kmer in kmers:\n",
    "        hashes.append(hash_kmer(kmer))\n",
    "    return hashes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "shew1_hashes = hash_kmers(shew1_kmers)\n",
    "shew2_hashes = hash_kmers(shew2_kmers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.23675152210020398\n"
     ]
    }
   ],
   "source": [
    "print(jaccard_similarity(shew1_kmers, shew2_kmers))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2371520123045373\n"
     ]
    }
   ],
   "source": [
    "print(jaccard_similarity(shew1_hashes, shew2_hashes))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(ok, it changes it a little, because of the canonical k-mer calculation!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementing subsampling with modulo hashing\n",
    "\n",
    "We are now ready to implement k-mer subsampling with modulo hash.\n",
    "\n",
    "We need to pick a sampling rate, and know the maximum possible hash value.\n",
    "\n",
    "For a sampling rate, let's start with 1000.\n",
    "\n",
    "The MurmurHash function turns k-mers into numbers between 0 and `2**64 - 1` (the maximum 64-bit number).\n",
    "\n",
    "Let's define these as variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaled = 1000\n",
    "MAX_HASH = 2**64"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, choose the range of hash values that we'll keep."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.844674407370955e+16\n"
     ]
    }
   ],
   "source": [
    "keep_below = MAX_HASH / scaled\n",
    "print(keep_below)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and write a filter function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def subsample_modulo(kmers):\n",
    "    keep = []\n",
    "    for kmer in kmers:\n",
    "        if hash_kmer(kmer) < keep_below:\n",
    "            keep.append(kmer)\n",
    "        # otherwise, discard\n",
    "        \n",
    "    return keep"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now let's apply this to our big collections of k-mers!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "akker_sub = subsample_modulo(akker_kmers)\n",
    "shew1_sub = subsample_modulo(shew1_kmers)\n",
    "shew2_sub = subsample_modulo(shew2_kmers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "499970 502\n",
      "499970 513\n",
      "499970 503\n"
     ]
    }
   ],
   "source": [
    "print(len(akker_kmers), len(akker_sub))\n",
    "print(len(shew1_kmers), len(shew1_sub))\n",
    "print(len(shew2_kmers), len(shew2_sub))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we go from ~500,000 k-mers to ~500 hashes! Do the Jaccard calculations change??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "akker vs akker, total 1.0\n",
      "akker vs akker, sub 1.0\n"
     ]
    }
   ],
   "source": [
    "print('akker vs akker, total', jaccard_similarity(akker_kmers, akker_kmers))\n",
    "print('akker vs akker, sub', jaccard_similarity(akker_sub, akker_sub))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "akker vs shew1, total 0.0\n",
      "akker vs shew1, sub 0.0\n"
     ]
    }
   ],
   "source": [
    "print('akker vs shew1, total', jaccard_similarity(akker_kmers, shew1_kmers))\n",
    "print('akker vs shew1, sub', jaccard_similarity(akker_sub, shew1_sub))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shew1 vs shew2, total 0.23675152210020398\n",
      "shew1 vs shew2, sub 0.2281795511221945\n"
     ]
    }
   ],
   "source": [
    "print('shew1 vs shew2, total', jaccard_similarity(shew1_kmers, shew2_kmers))\n",
    "print('shew1 vs shew2, sub', jaccard_similarity(shew1_sub, shew2_sub))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And you can see that the numbers are different, but not very much - the Jaccard similarity is being *estimated*, so it is not exact but it is close."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's visualize --"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib_venn._common.VennDiagram at 0x123ede358>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7K566gJFnvcj4r69ixZNHsuqvFzDyrPsAyO27ga/877/bFg0L656/lBN//Cv6HLGLl675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\nRK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "venn3([set(akker_kmers), set(shew1_kmers), set(shew2_kmers)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib_venn._common.VennDiagram at 0x1252f0e48>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+n7ZCk5LmKhhyLCDDTjWHY79Y5HWY911YCfBdWLkO5gP8F3NSMgD/Gd4+bqG+1SKBnlcb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\nPB6PRf4/9BK4ugTvf7IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "venn3([set(akker_sub), set(shew1_sub), set(shew2_sub)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A full list of notebooks\n",
    "\n",
    "[An introduction to k-mers for genome comparison and analysis](kmers-and-minhash.ipynb)\n",
    "\n",
    "[Some sourmash command line examples!](sourmash-examples.ipynb)\n",
    "\n",
    "[Working with private collections of signatures.](sourmash-collections.ipynb)"
   ]
  }
 ],
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