In this section, we demonstrate that the imposition of linearity on our error model E leads to a richer theory of persistence. ... Put R = dE(f, g) and S = dE(g, h) and fix a point x a X. Then using the triangle inequality for the standard metric in IR, we find |f(x) a h(x)| ... Persistent Homology under Non-uniform Error 21 Linear Error.
|Title||:||Mathematical Foundations of Computer Science 2010|
|Author||:||Petr Hlineny, Antonin Kucera|
|Publisher||:||Springer - 2010-08-14|