8.2 Background Preparation for Integrated Analysis
Similarity Measures
Given two vectors, and
= (x1, x2, ..., xn)T
= (y1, y2, ..., yn)T
where n is the number of elements in a vector, the similarity between and , g( , ) ³ 0 , can be defined by
1) dot product,
=
where M > 0 and M ³ ·
2) angular cosine
3) correlation coefficient
where xm = , ym =
4) exponential similarity
where Sk is a positive number determined by the user.
5) Non-parametric method
Let x'k = xk - xm , y'k = yk - ym and xm and ym
are the same as in 3)
n+ = the number of elements which are greater than 0 is
n- = the number of elements which are less than 0 in the same set, then g( , ) is
6) minimum - maximum ratio
7) minimum arithmetic average
8) minimum geometric average
9) sum of absolute differences, or city-bock distances, Manhattan distances
(i) e
(ii)
where M is selected such that 0 ² g( , ) ² 1
10) Euclidian distances
where M is selected such that 0 ² g( , ) ² 1