Calculating the similarity of two lists

Question

I have two lists:

eg. a = [1,8,3,9,4,9,3,8,1,2,3] and b = [1,8,1,3,9,4,9,3,8,1,2,3]

Both contain ints. There is no meaning behind the ints (eg. 1 is not \'cl

Answer 1

One way to tackle this is to utilize histogram. As an example (demonstration with numpy):

In []: a= array([1,8,3,9,4,9,3,8,1,2,3])
In []: b= array([1,8,1,3,9,4,9,3,8,1,2,3])

In []: a_c, _= histogram(a, arange(9)+ 1)
In []: a_c
Out[]: array([2, 1, 3, 1, 0, 0, 0, 4])

In []: b_c, _= histogram(b, arange(9)+ 1)
In []: b_c
Out[]: array([3, 1, 3, 1, 0, 0, 0, 4])

In []: (a_c- b_c).sum()
Out[]: -1

There exist now plethora of ways to harness a_c and b_c.

Where the (seemingly) simplest similarity measure is:

In []: 1- abs(-1/ 9.)
Out[]: 0.8888888888888888

Followed by:

In []: norm(a_c)/ norm(b_c)
Out[]: 0.92796072713833688

and:

In []: a_n= (a_c/ norm(a_c))[:, None]
In []: 1- norm(b_c- dot(dot(a_n, a_n.T), b_c))/ norm(b_c)
Out[]: 0.84445724579043624

Thus, you need to be much more specific to find out most suitable similarity measure suitable for your purposes.