eigenvectors.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import json\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Load the NeuroTree distance file.  \n",
    "with open('dist_mtx.txt','rb') as f:\n",
    "    dist_data = json.loads(f.read().decode('latin1'))\n",
    "    \n",
    "# Load the NeuroTree fingerprint file.  \n",
    "with open('fingerprint_mtx.txt','rb') as f:\n",
    "    fp_data = json.loads(f.read().decode('latin1'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Parse the NeuroTree distance file into a matrix.  \n",
    "ancestors = list(set([x['p0'] for x in dist_data])) # Extract ancestor list\n",
    "regulars = list(set([x['p1'] for x in dist_data]).union(set([x['p2'] for x in dist_data]))) # Extract regular list.  \n",
    "n_regulars = len(regulars) # Number of regulars.\n",
    "dist_matrix = -1.0 * np.ones((n_regulars,n_regulars)) # Matrix of distances, filled with -1 (no path).  \n",
    "for entry in dist_data: # Iterate over entries in the distance data.  \n",
    "    p0,p1,p2,d = [entry[i] for i in ['p0','p1','p2','d']]\n",
    "    d = np.inf if d=='-1' else int(d)\n",
    "    x1 = regulars.index(p1) # Matrix index of individual with id p1.  \n",
    "    x2 = regulars.index(p2) # Matrix index of individual with id p2.  \n",
    "    dist_matrix[x1,x2] = d # Set forward distance to d.  \n",
    "    dist_matrix[x2,x1] = d # Set reverse distance to d (for symmetry).  \n",
    "for i in range(n_regulars): # For each individual.  \n",
    "    dist_matrix[i,i] = 0 # Set the diagonal entry (self distance) to 0.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create an adjacency matrix from the distance matrix  \n",
    "adj_matrix = (dist_matrix==1).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Compute its eigenvalues and eigenvectors\n",
    "evls,evcts = np.linalg.eigh(adj_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b72ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot eigenvalues in ascending order\n",
    "plt.plot(evls);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZZ2HlykOnMwvtf++9YZs47bSwDT7+eKjLXXeFHkvSGz333FDfj30s/+efrHK5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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b72898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DO+wwc4D45jdL/wEtLcBFFwH//u+mH/Ggg4oPxj73nPlfxm++aaYxHnmkee0P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\nCMD/B0YOQ60ihJxBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x106b72eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot node weights for the last eigenvector (corresponding to the most positive eigenvalue)\n",
    "plt.plot(evcts[:,-1])\n",
    "plt.figure()\n",
    "# Plot node weights for the second to last eigenvector (corresponding to the second most positive eigenvalue)\n",
    "plt.plot(evcts[:,-2]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(58, 437)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# How many ancestors among the nodes we have in the matrix, vs ancestors overall?\n",
    "len(set(regulars).intersection(ancestors)),len(ancestors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# A node name extraction function.  \n",
    "from neurotree_api import get_neurotree_node_info\n",
    "def node2name(node):\n",
    "    node = int(node)\n",
    "    info = get_neurotree_node_info(node)\n",
    "    return '%s %s' % (info['firstname'],info['lastname'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvector 0:\n",
      "\t1) Bert Sakmann\n",
      "\t2) Andreas Draguhn\n",
      "\t3) Peter Jonas\n",
      "\t4) Jason Kerr\n",
      "\t5) Greg Stuart\n",
      "Eigenvector 1:\n",
      "\t1) David Prince\n",
      "\t2) Phillip Schwartzkroin\n",
      "\t3) Barry Connors\n",
      "\t4) John Huguenard\n",
      "\t5) Tom Brown\n",
      "Eigenvector 2:\n",
      "\t1) Jean Rossier\n",
      "\t2) Rodolfo Llinu00e1s\n",
      "\t3) Serge Charpak\n",
      "\t4) Etienne Audinat\n",
      "\t5) Jacques Glowinski\n",
      "Eigenvector 3:\n",
      "\t1) Phillip Schwartzkroin\n",
      "\t2) Paul Buckmaster\n",
      "\t3) Barry Connors\n",
      "\t4) Scott Baraban\n",
      "\t5) F Dudek\n",
      "Eigenvector 4:\n",
      "\t1) Rodolfo Llinu00e1s\n",
      "\t2) Jean Rossier\n",
      "\t3) Anthony Grace\n",
      "\t4) Etienne Audinat\n",
      "\t5) Brian Macvicar\n",
      "Eigenvector 5:\n",
      "\t1) Peter Somogyi\n",
      "\t2) Eberhard Buhl\n",
      "\t3) Dominique Engel\n",
      "\t4) Zoltan Nusser\n",
      "\t5) Stuart Cobb\n",
      "Eigenvector 6:\n",
      "\t1) Stephen Kitai\n",
      "\t2) Barry Connors\n",
      "\t3) Gerald Finnerty\n",
      "\t4) John Jefferys\n",
      "\t5) Charles Wilson\n",
      "Eigenvector 7:\n",
      "\t1) Stephen Kitai\n",
      "\t2) Charles Wilson\n",
      "\t3) Dietmar Plenz\n",
      "\t4) Yasuo Kawaguchi\n",
      "\t5) John Jefferys\n",
      "Eigenvector 8:\n",
      "\t1) F Dudek\n",
      "\t2) Scott Baraban\n",
      "\t3) Sanjay Kumar\n",
      "\t4) Paul Buckmaster\n",
      "\t5) John Huguenard\n",
      "Eigenvector 9:\n",
      "\t1) German Barrionuevo\n",
      "\t2) Tom Brown\n",
      "\t3) Sven Kroener\n",
      "\t4) Nathan Urban\n",
      "\t5) John Jefferys\n"
     ]
    }
   ],
   "source": [
    "# Print important nodes in each eigenvector.  \n",
    "# The nodes within an eigenvector are not necessarily related (although they often will be).\n",
    "# In some cases they can be opposing forces (i.e. together they are informative about lineage).\n",
    "\n",
    "for rank in range(10):\n",
    "    eigenvector = np.abs(evcts[:,-1-rank]) # Take absolute value so we can find most important values \n",
    "                                           # and not worry about sign.  \n",
    "    results = sorted(zip(eigenvector,regulars),key=lambda x:x[0],reverse=True) # Sort nodes by weight in eigenvector.\n",
    "    print(\"Eigenvector %d:\" % rank)\n",
    "    for depth in range(5): # Print the top 5 nodes in each eigenvector.  \n",
    "        print(\"\\t%d) %s\" % (depth+1,node2name(results[depth][1])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Parse the NeuroTree fingerprint file into a matrix.  \n",
    "ancestors = list(set([x['p0'] for x in fp_data])) # Extract ancestor list\n",
    "regulars = list(set([x['p1'] for x in fp_data])) # Extract list of key nodes\n",
    "key_nodes = list(set([x['p2'] for x in fp_data])) # Extract list of key nodes\n",
    "n_regulars = len(regulars) # Number of regulars\n",
    "n_key_nodes = len(key_nodes) # Number of key nodes\n",
    "fp_matrix = np.inf * np.ones((n_regulars,n_key_nodes)) # Matrix of distances, filled with -1 (no path).  \n",
    "for entry in fp_data: # Iterate over entries in the distance data.  \n",
    "    p0,p1,p2,d = [entry[i] for i in ['p0','p1','p2','d']]\n",
    "    d = np.inf if d=='-1' else int(d)\n",
    "    x1 = regulars.index(p1) # Matrix index of individual with id p1.  \n",
    "    x2 = key_nodes.index(p2) # Matrix index of individual with id p2.  \n",
    "    fp_matrix[x1,x2] = d # Set distance to d.  \n",
    "fp_matrix[np.isinf(fp_matrix)] = 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x10dd07898>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8QfbKSKipTnwTseOLCOFZxYl0Cg/sOoe2zVvxSOHxeMZ5gKxtoygyPVSjP7gD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\nicQkRwr6RCKRmORIQZ9IJBKTHP8/lr7Wp4wHdrgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dd875f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pcolor(fp_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Compute its eigenvalues and eigenvectors\n",
    "from sklearn.decomposition import PCA,NMF\n",
    "pca = PCA(n_components=25)\n",
    "nmf = NMF(n_components=25)\n",
    "components = pca.fit_transform(fp_matrix.T)\n",
    "components = nmf.fit_transform(fp_matrix.T)\n",
    "components = components[:,1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pca_err = np.zeros(50)\n",
    "nmf_err = np.zeros(50)\n",
    "for n in range(1,51):\n",
    "    pca.n_components = n\n",
    "    nmf.n_components = n\n",
    "    pca.fit_transform(fp_matrix.T)\n",
    "    nmf.fit_transform(fp_matrix.T)\n",
    "    nmf_err[n-1] = nmf.reconstruction_err_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x118aa6da0>"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Lif6/OePJXl1sqf4KYGbvAz4DvM3dN0bGELlV+JfAyqpe9w7A19z9/1Q52FVmdjzdff2O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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1187d0080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.pcolor(components,vmax=20)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Component 1:\n",
      "1) Alois Kornmu00fcller\n",
      "2) David Prince\n",
      "3) Johann von Goethe\n",
      "4) Johann von Gudden\n",
      "5) Jacob Reinbold Spielmann\n",
      "6) Julius Axelrod\n",
      "Component 2:\n",
      "1) John Langley\n",
      "2) Archibald Hill\n",
      "3) Edgar Adrian\n",
      "4) Sir Michael Foster\n",
      "5) Thomas Huxley\n",
      "Component 3:\n",
      "1) Franz Nissl\n",
      "2) Julius Axelrod\n",
      "3) Otto Creutzfeldt\n",
      "4) Johann von Gudden\n",
      "Component 4:\n",
      "1) Claude Bernard\n",
      "2) Jacob Reinbold Spielmann\n",
      "3) Franz Nissl\n",
      "Component 5:\n",
      "Component 6:\n",
      "1) Julius Axelrod\n",
      "Component 7:\n",
      "1) Oswald Schmiedeberg\n",
      "2) Ernst Weber\n",
      "Component 8:\n",
      "1) Claude Bernard\n",
      "2) Julius Axelrod\n",
      "3) Philip Bard\n",
      "Component 9:\n",
      "1) Arnold Sommerfeld\n",
      "2) Niels Bohr\n",
      "3) Julius Axelrod\n",
      "Component 10:\n",
      "Component 11:\n",
      "1) Alois Kornmu00fcller\n",
      "2) Johann von Goethe\n",
      "3) Johann von Gudden\n",
      "Component 12:\n",
      "1) Jacob Reinbold Spielmann\n",
      "Component 13:\n",
      "Component 14:\n",
      "Component 15:\n",
      "1) Rudolf Wagner\n",
      "2) Wilhelm Ostwald\n",
      "3) Karl Lashley\n",
      "4) Julius Axelrod\n",
      "5) Donald Hebb\n",
      "Component 16:\n",
      "1) Thomas Huxley\n",
      "Component 17:\n",
      "1) Niels Bohr\n",
      "Component 18:\n",
      "1) Philip Bard\n",
      "2) Walter Cannon\n",
      "3) Haldan Hartline\n",
      "Component 19:\n",
      "1) Julius Axelrod\n",
      "2) Rodolfo Llinu00e1s\n",
      "3) Johann von Gudden\n",
      "4) Harvey Carr\n",
      "5) Johann von Goethe\n",
      "6) James Angell\n",
      "7) William James\n",
      "8) Karl Lashley\n",
      "9) Louis Agassiz\n",
      "10) Stephen Kuffler\n",
      "11) Roger Nicoll\n",
      "12) Alois Kornmu00fcller\n",
      "13) Sir John Eccles\n",
      "14) Bernard Katz\n",
      "Component 20:\n",
      "Component 21:\n",
      "1) Franz Nissl\n",
      "Component 22:\n",
      "Component 23:\n",
      "1) David Prince\n",
      "Component 24:\n",
      "1) Harvey Carr\n",
      "2) James Angell\n",
      "3) Karl Lashley\n",
      "4) William James\n",
      "5) Louis Agassiz\n",
      "6) Philip Bard\n",
      "7) Walter Cannon\n",
      "8) Donald Hebb\n"
     ]
    }
   ],
   "source": [
    "for i,component in enumerate(components.T):\n",
    "    print(\"Component %d:\" % (i+1))\n",
    "    component = np.abs(component)\n",
    "    maxx = np.amax(component)\n",
    "    ranked = sorted(range(len(component)),key=lambda x:component[x],reverse=True)\n",
    "    for j,val in enumerate(ranked):\n",
    "        if component[val] > 2:#maxx/2:\n",
    "            node = key_nodes[val]\n",
    "            name = node2name(node)\n",
    "            print(\"%d) %s\" % (j+1,name))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Heinz Beck'"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "node2name(15771)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.4.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}