class09_similarity_R_template.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CS446/546 - Class Session 13 - Similarity and Hierarchical Clustering\n",
    "\n",
    "In this class session we are going to hierachically cluster (based on Sorensen-Dice similarity) vertices in a directed graph from a landmark paper on human gene regulation (Neph et al., Cell, volume 150, pages 1274-1286, 2012; see PDF on Canvas)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by having a look at the Neph et al. data file, `neph_gene_network.txt`.  It is in edge-list format, with no header and no \"interaction\" column.  Just two columns, first column contains the \"regulator gene\" and the second column contains the \"target gene\":\n",
    "\n",
    "    head neph_gene_network.txt\n",
    "    AHR     BCL6\n",
    "    AHR     BHLHE41\n",
    "    AHR     BPTF\n",
    "    AHR     CEBPA\n",
    "    AHR     CNOT3\n",
    "    AHR     CREB1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's load the packages that we will need for this exercise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "suppressPackageStartupMessages(library(igraph))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using `read.table`, read the file `shared/neph_gene_network.txt`; name the two columns of the resulting data frame, `regulator` and `target`.  Since there is no header, we will use `header=FALSE`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "edge_list_neph <- read.table(\"shared/neph_gene_network.txt\",\n",
    "                            header=FALSE,\n",
    "                            sep=\"\\t\",\n",
    "                            stringsAsFactors=FALSE,\n",
    "                            col.names=c(\"regulator\",\"target\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the edge-list data into a Graph object in igraph, using `graph_from_data_frame`. Make the graph undirected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IGRAPH c6d5c31 UN-- 538 47945 -- \n",
      "+ attr: name (v/c)\n"
     ]
    }
   ],
   "source": [
    "neph_graph <- graph_from_data_frame(edge_list_neph, directed=FALSE)\n",
    "summary(neph_graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the adjacency matrix for the graph, using `get.adjacency`, and assign to matrix `g_matrix`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "g_matrix <- get.adjacency(neph_graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the Sorensen-Dice similarity of this graph, and assign to similarity matrix `S`, using the igraph `similarity` function and specifying `method=\"dice\"`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute a distance matrix by calling `as.dist` on the object 1-S; assign to object `D`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perform average-linkage hierarchical clustering on this distance object, using `hclust` with `method=average`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the dendrogram using `plot` and make the labels really small using `cex=0.01`, using `plot`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
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8btek2RAe6nsQSuILMXD5wJWuFYtEFjFfh1aCkAd5QF1mvJmeUM2AnzRMBx8Jkc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\n/4At24s+PanKmJsYsB3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      "text/plain": [
       "Plot with title \"Cluster Dendrogram\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.4.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}