How to normalize a Counter and combine 2 normalized Counters? - python

Question

Firstly, I have two list of strings:

['abc','abc','def','jkl']
['abc','def','def','pqr', 'pr', 'foo', 'bar']

And then I need counters of the lists that are normalized such that the sum of the values in each counter equals 1:

Counter({'abc': 0.8164965809277261, 'jkl': 0.4082482904638631, 'def': 0.4082482904638631})
Counter({'abc': 1.1498299142610595, 'def': 1.0749149571305296, 'jkl': 0.4082482904638631, 'pr': 0.3333333333333333, 'bar': 0.3333333333333333, 'pqr': 0.3333333333333333, 'foo': 0.3333333333333333})

The normalizing factor is

math.sqrt(sum(i*i for i in counter.values()))

I've tried the following by iterating throw the counter keys but is there any other way of achieving the say x+y Counter?

>>> from collections import Counter
>>> import math
>>> x = Counter(['abc','abc','def','jkl'])
>>> denominator = 1/math.sqrt(sum(math.pow(i,2) for i in x.values()))
>>> for i in x:
...     x[i]*=denominator
... 
>>> x
Counter({'abc': 0.8164965809277261, 'jkl': 0.4082482904638631, 'def': 0.4082482904638631})
>>> y = Counter(['abc','def','def','pqr', 'pr', 'foo', 'bar'])
>>> denominator2 = 1/math.sqrt(sum(math.pow(i,2) for i in y.values()))
>>> for i in y:
...     y[i]*=denominator2
... 
>>> y
Counter({'def': 0.6666666666666666, 'pr': 0.3333333333333333, 'abc': 0.3333333333333333, 'bar': 0.3333333333333333, 'pqr': 0.3333333333333333, 'foo': 0.3333333333333333})
>>> x+y
Counter({'abc': 1.1498299142610595, 'def': 1.0749149571305296, 'jkl': 0.4082482904638631, 'pr': 0.3333333333333333, 'bar': 0.3333333333333333, 'pqr': 0.3333333333333333, 'foo': 0.3333333333333333})

Answer 1

You need to sum the values, then divide each count by the sum:

total = sum(x.values(), 0.0)
for key in x:
    x[key] /= total

By starting the sum with 0.0 we make sure total is a floating point value, avoiding the Python 2 floor division behaviour of / with integer operands.

Demo:

>>> from collections import Counter
>>> x = Counter(['abc','abc','def','jkl'])
>>> total = sum(x.values(), 0.0)
>>> for key in x:
...     x[key] /= total
... 
>>> x
Counter({'abc': 0.5, 'jkl': 0.25, 'def': 0.25})
>>> y = Counter(['abc','def','def','pqr', 'pr', 'foo', 'bar'])
>>> total = sum(y.values(), 0.0)
>>> for key in y:
...     y[key] /= total
... 
>>> y
Counter({'def': 0.2857142857142857, 'pr': 0.14285714285714285, 'abc': 0.14285714285714285, 'bar': 0.14285714285714285, 'pqr': 0.14285714285714285, 'foo': 0.14285714285714285})

If you need to sum the counters, you'd need to re-normalize the resulting counter separately; summing two normalized counters means you have a new counter whole values sum to 2, for example.