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:
“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)
“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)