Homology groups of filtrations

Details Homology groups of filtrations Homology groups of filtrations

2011-01-11

arxiv.org/abs/1101.2008v2

Mathematics

Algebraic Topology

Scientific paper

Such modern applications of topology as data analysis and digital image analysis have to deal with noise and other uncertainty. In this environment, topological spaces often appear equipped with a real valued function. Persistence is a measure of robustness of the homology classes of the filtration of the lower level sets of this function. In this paper we introduce the homology group of filtration as the product of the kernels of the homology maps of the inclusions. This group contains all possible homology classes in all elements of the filtration so that we can later pick the features that lie within the user's choice of the acceptable level of noise.

Affiliated with

Also associated with

No associations

Rating

Homology groups of filtrations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Homology groups of filtrations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homology groups of filtrations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-152800