categorical_vis.ipynb

categorical_vis.py

# -*- coding: utf-8 -*-
# <nbformat>3.0</nbformat>

# <markdowncell>

# Draw a co-ocurrence matrix with matplotlib.matshow (matplotlib.imshow)
# 
# https://en.wikipedia.org/wiki/Co-occurrence_matrix
# 
# * https://en.wikipedia.org/wiki/Matplotlib
# * http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.matshow
# * http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.imshow
# 
# Created with IPython notebook in an Anaconda 1.9.1 environment
# 
# * http://ipython.org/notebook.html
# * http://docs.continuum.io/anaconda/install.html
# * http://docs.continuum.io/anaconda/pkgs.html

# <codecell>

%pylab inline --no-import-all
# import numpy as np
# import matplotlib.pyplot as plt
# import pylab
import collections
from pprint import pformat

# <codecell>

DATA_CONSTRAINTS = (
    (('english',), 5),
    (('math',), 7),
    (('social studies',), 3),
    (('science',), 3),
    (('english', 'science'), 1),
    (('english', 'social studies',), 1),
    (('math', 'science'), 2),
    (('science', 'social studies',), 1)
)

def generate_data(constraints):
    """
    Args:
        constraints: ((categories_tuple,), count_int)

    Returns:
        list of category tuples satisfying constraints

    """
    def _standardize_constraints(constraints):
        return [(tuple(sorted(c[0])), c[1]) for c in constraints]

    def fits_constraints(data, constraints):
        dataset = list(data)
        counts = collections.Counter(tuple(sorted(elem)) for elem in dataset)
        _constraints = _standardize_constraints(constraints)
        return sorted(counts.iteritems()) == sorted(_constraints)

    def generate_data(constraints):
        _constraints = _standardize_constraints(constraints)
        for categories, count in _constraints:
            for n in xrange(count):
                yield categories

    data = list(generate_data(constraints))
    if fits_constraints(data, constraints):
        return data
    raise Exception("uh") # XXX
data = generate_data(DATA_CONSTRAINTS)
data

# <codecell>

def iter_adjacencies(data):
    """
    Args:
        data: iterable of categories
    Returns:
        iterable of (row, (category_x, category_y)) pairs with self edges
    """
    for row_n, row in enumerate(data):
        _len = len(row)
        for category in row:
            yield (row_n,row), (category, category)
        if _len > 1:
            for i in xrange(_len-1):
                yield (row_n,row), (row[i], row[i+1])

adj_list = list(iter_adjacencies(data))
adj_list

# <codecell>

def build_array_from_adj_list(data, adj_list):
    print(pformat(collections.Counter(data).items()))
    
    categories = collections.OrderedDict(
        (v,k) for k,v in enumerate(sorted(set(item for row in data for item in row))))
    print("Indices: %s" % categories)
    
    adjacency_dimensions = len(categories), len(categories)
    print(adjacency_dimensions)
    
    adj = np.zeros(adjacency_dimensions)
    #print(adj)
    
    for row, adjacencies in adj_list:
        x, y = categories.get(adjacencies[0]), categories.get(adjacencies[1])
        adj[x][y] += 1
        if x != y:
            adj[y][x] += 1
    print(adj)
    
    subtotal_0 = np.sum(adj, axis=0)
    subtotal_1 = np.sum(adj, axis=1)
    if not np.all(np.equal(subtotal_0, subtotal_1)):
        raise Exception("Should be the same")
    
    totals =  zip(categories.keys(), subtotal_0)
    print("Totals: %s" % totals)
    return adj, categories

adj, categories = build_array_from_adj_list(data, adj_list)

# <codecell>

def draw_co_ocurrence_diagram(adj, categories, figsize=(4,5)):
    pylab.rcParams['figure.figsize'] = figsize
    plt.matshow(adj, cmap="Greys")
    ticks = (np.arange(len(categories)), categories.keys())
    plt.xticks(*ticks, rotation=90)
    plt.yticks(*ticks)
    plt.colorbar(orientation='horizontal')

draw_co_ocurrence_diagram(adj, categories)

# <codecell>