Reports of timefyme.com feature a tag cloud representation. One of the most popular and useful ways to create a tag cloud is by calculating the logarithm of the usage for each tag. Using the logarithm rather than the original usage value results to a smooth gradation from the less to the most used tag.
In order to implement the feature, we searched for a suitable algorithm in usual resources such as stackoverflow, but couldn’t find an approach that works for every data case (e.g. with few or just one tag). So we needed to go back and refresh our memories with interpolation methods we studied in numerical analysis undergraduate courses, to build the (simple to be honest) algorithm ourselves. We offer this algorithm we used and works perfectly for us, for anyone interested in tag clouds.
Let’s assume that the tags usage is a vector ![\bf{u} = [u_1, u_2, ..., u_n]](https://s0.wp.com/latex.php?latex=%5Cbf%7Bu%7D+%3D+%5Bu_1%2C+u_2%2C+...%2C+u_n%5D&bg=ffffff&fg=555555&s=0&c=20201002)
, then the minimum and maximum usage values are 
and 
.
Using the formula:
we get a linearised value 
for each tag varying from 0 to 1. Then we can use e.g. to calculate grey (rgb) values or to multiply a cardinality of css classes.
A Python implementation of the above methodology follows, code is also available for download.
#!/usr/bin/env python
# -*- encoding: utf-8 -*-
# vi:expandtab:tabstop=4 shiftwidth=4 textwidth=79
import math
TAG_CLOUD_CSS_CLASSES = 3
"""
Let's have three separate css classes for our example
"""
TAG_CLOUD_CSS_CLASS_TEMPLATE = '.tag-cloud-%d'
"""
This can be a css template, with ".tags-cloud-1" for the less used tag and
".tags-cloud-3" for the most used tag (assuming 3 distinct classes)
"""
def get_tags_cloud(data):
"""
data should be a list containing tags items. Each item should be a
dictionary containing at least the `name` of the tag and the number of tag
occurrences named as `usage`.
Returns a list sorted by `name` plus two fields: a `css_class` and the
linear value resulting from logarithmic interpolation.
"""
if not data:
return
# Find the maximum and minimum usage
maximum = max(data, key=lambda x: x['usage'])['usage']
minimum = min(data, key=lambda x: x['usage'])['usage']
# Do the math, find the common subtractor and divider and calculate log
# value for each tag. Then, assuming that log value is linearized, find the
# integer class from 1 to TAGS_CLOUD_CSS_CLASSES
subtractor = math.log(float(minimum))
divider = math.log(float(maximum)) - subtractor or 1.0 # 1.0 if min==max
for item in data:
log_value = (math.log(float(item['usage']))-subtractor) / divider
d = int(round(log_value*(TAG_CLOUD_CSS_CLASSES-1) + 1))
item['css_class'] = TAG_CLOUD_CSS_CLASS_TEMPLATE%d
item['log_value'] = log_value
# Sort results by name for displaying tags in an alphabetical order
return sorted(data, key=lambda x: x['name'])
# An example
if __name__ == '__main__':
import pprint
TEST_SET = [
{'name': 'popular tag', 'usage': 100},
{'name': 'medium popularity tag', 'usage': 10},
{'name': 'another medium popularity tag', 'usage': 15},
{'name': 'obscure tag', 'usage': 2}
]
pprint.pprint(get_tags_cloud(TEST_SET))
# This is a potential Django application of the tag cloud. Django code is
# untested, it is just to prove the concept. Let's assume two models, first
# model represents blog posts and second models tags being used in posts.
#
# from django.db import models
# from django.db.models import Count
#
# class BlogPost(models.Model):
#
# # Several blog fields defined here...
# #
#
# tags = models.ManyToManyField("Tag", related_name='blog_posts')
#
#
# class Tag(models.Model):
#
# name = models.CharField(max_length=40)
#
# @staticmethod
# def tags_cloud_data(limit=50):
# data = (Tag.objects.
# values('name').
# annotate(usage=Count('blog_bosts')).
# order_by('-usage')[:limit])
# data = [item for item in data if item['usage']]
# return data
#
# @staticmethod
# def tags_cloud(limit=50):
# return get_tags_cloud(Tag.tags_cloud_data(limit))
By running the example above we get this result:
[{'css_class': '.tag-cloud-2',
'log_value': 0.5150539804460444,
'name': 'another medium popularity tag',
'usage': 15},
{'css_class': '.tag-cloud-2',
'log_value': 0.41140808993222105,
'name': 'medium popularity tag',
'usage': 10},
{'css_class': '.tag-cloud-1',
'log_value': 0.0,
'name': 'obscure tag',
'usage': 2},
{'css_class': '.tag-cloud-3',
'log_value': 1.0,
'name': 'popular tag',
'usage': 100}]
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