Homogeneity
Means are usually homogeneous, but for most functions, the f-mean is not. Indeed, the only homogeneous quasi-arithmetic means are the power means and the geometric mean; see Hardy–Littlewood–Pólya, page 68.
The homogeneity property can be achieved by normalizing the input values by some (homogeneous) mean .
However this modification may violate monotonicity and the partitioning property of the mean.
Read more about this topic: Quasi-arithmetic Mean
Famous quotes containing the word homogeneity:
“Dissonance between family and school, therefore, is not only inevitable in a changing society; it also helps to make children more malleable and responsive to a changing world. By the same token, one could say that absolute homogeneity between family and school would reflect a static, authoritarian society and discourage creative, adaptive development in children.”
—Sara Lawrence Lightfoot (20th century)
“Seems fairly clear that you fix a breed by LIMITING the amount of alien infiltration. You make a race by homogeneity and by avoiding INbreeding.... No argument has ever been sprouted against it. You like it in dogs and horses.”
—Ezra Pound (1885–1972)