diff --git a/Hamming.ipynb b/Hamming.ipynb
new file mode 100644
index 0000000000000000000000000000000000000000..f407e113fa21b314950050cd67d936e34d463688
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@@ -0,0 +1,220 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Graphing a kind of \"Hamming Similarity\" of strings\n",
+ "\n",
+ "This notebook explores a slightly weird similarity measure for strings.\n",
+ "\n",
+ "## Equal characters in strings\n",
+ "\n",
+ "Given two strings, the idea is to consider the positions where their characters match:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "v = \"Wiesbaden\"\n",
+ "w = \"Potsdam\"\n",
+ "# s a – the matching characters of the two strings "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can extract those characters with a loop:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "m = [] # resulting equal characters\n",
+ "for i in range(min(map(len, [v, w]))): # loop over the shortest word's length\n",
+ " if v[i] == w[i]: # check character equality \n",
+ " m.append(v[i]) # add character\n",
+ "m"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's create a function that, given two strings, returns their equal characters:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def equal_chars(w, v):\n",
+ " m = [] # resulting equal characters\n",
+ " for i in range(min(map(len, [v, w]))): # loop over the shortest word's length\n",
+ " if v[i] == w[i]: # check character equality \n",
+ " m.append(v[i]) # add character\n",
+ " return m"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "By the way: thanks to Python's [list comprehensions](https://docs.python.org/3/howto/functional.html#generator-expressions-and-list-comprehensions) we can write the body of the function in one line:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def equal_chars(w, v):\n",
+ " return [v[i] for i in range(min(map(len, [v, w]))) if v[i] == w[i]]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Similarity \n",
+ "\n",
+ "Now the number of equal characters between two strings defines a similarity measure. For example, the similarity of our two strings is:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "len(equal_chars(v, w))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Graph\n",
+ "\n",
+ "Now given a set of strings, for example, the 16 capitals of all German states:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "capitals_de = [\"Berlin\", \"Bremen\", \"Dresden\", \"Düsseldorf\", \"Erfurt\",\n",
+ " \"Hamburg\", \"Hannover\", \"Kiel\", \"Magdeburg\", \"Mainz\", \"München\",\n",
+ " \"Potsdam\", \"Saarbrücken\", \"Schwerin\", \"Stuttgart\", \"Wiesbaden\"]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "we can create a graph with the strings as nodes by connecting strings whose similarity is larger than zero, that is, they have at least one position with equal characters:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import networkx as nx\n",
+ "\n",
+ "def sim_graph(words):\n",
+ " G = nx.Graph() # resulting graph\n",
+ "\n",
+ " for k, v in enumerate(words): # first node\n",
+ " for l, w in enumerate(words): # second node\n",
+ " if k > l: # avoid reverse duplicates\n",
+ " ec = equal_chars(v, w) # equal characters\n",
+ " sim = len(ec) # similarity\n",
+ " if sim > 0: # ignore dissimilar words\n",
+ " G.add_edge(v, w, label=\"\".join(ec), weight=sim) # add edge\n",
+ " return G"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's compute the graph for our set of capitals:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "g = sim_graph(capitals_de)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "A good way to understand a graph is to visualise it:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "from networkx.drawing.nx_agraph import graphviz_layout\n",
+ "import matplotlib.pyplot as plt\n",
+ " \n",
+ "pos = graphviz_layout(g, prog='dot')\n",
+ "nx.draw(g, pos, with_labels=True, arrows=False)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This layout is not the best but we can try to use graphviz directly:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from networkx.drawing.nx_pydot import write_dot\n",
+ "import pydot\n",
+ "from IPython.display import HTML, display\n",
+ "import random\n",
+ "\n",
+ "write_dot(g, \"graph.dot\")\n",
+ "graph = pydot.graph_from_dot_file(\"graph.dot\")\n",
+ "graph[0].write_svg(\"graph.svg\")\n",
+ " \n",
+ "display(HTML('<img src=\"graph.svg?{0}\">'.format(random.randint(0,2e9)))) "
+ ]
+ }
+ ],
+ "metadata": {
+ "language_info": {
+ "name": "python",
+ "pygments_lexer": "ipython3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/README.org b/README.org
index 0e043ed994c88dd605855a9a0dc32cdbdf5f6635..57c93a487a8ddf25d0d3ed77a2cd32eaa20775c3 100644
--- a/README.org
+++ b/README.org
@@ -30,11 +30,12 @@ their difficulty (☆ = simple, ☆☆ = advanced, ☆☆☆ = sophisticated):
data, basic statistics and visualisation (☆☆)
- [[file:crawling_a_blog.ipynb][Crawling a blog]] :: crawling web sites, basic text mining, basic
statistics and visualisation (☆☆)
-- [[file:distances.ipynb][Distances]] :: Comprehensive interactive simulation of recovering
+- [[file:distances.ipynb][Distances]] :: comprehensive interactive simulation of recovering
information from noisy data (namely, point positions given their
noisy distance matrix) (☆☆☆)
- [[file:exponential_smoothing.ipynb][Exponential smoothing]] :: using [[https://ipywidgets.readthedocs.io/en/latest/examples/Widget%2520Basics.html][Jupyter's interactive widget]] to
explore [[https://en.wikipedia.org/wiki/Exponential_smoothing][exponential smoothing]] (☆)
+- [[file:Hamming.ipynb][Hamming]] :: a graph visualising a strange type of word similarity (☆)
- [[file:Jupyter-Demo.ipynb][Jupyter demo]] :: demo of some Jupyter features useful for creating
learning material (☆)
- [[file:statistics_top50faculty.ipynb][Statistics top 50 faculty]] :: exploratory statistical analysis of the