A diffusion process associated with Fréchet means

Fréchet Means for Distributions of Persistence Diagrams

Given a distribution ρ on persistence diagrams and observations X1, ...Xn iid ∼ ρ we introduce an algorithm in this paper that estimates a Fréchet mean from the set of diagrams X1, ...Xn. If the underlying measure ρ is a combination of Dirac masses ρ = 1 m ∑m i=1 δZi then we prove the algorithm converges to a local minimum and a law of large numbers result for a Fréchet mean computed by the alg...

Probabilistic Fréchet Means and Statistics on Vineyards

In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [21], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (Dp,Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a f...

Fréchet Means of Curves for Signal

Integration of the Decisions Associated with Maintenance Management and Process Control for a Series Production System

This paper studies a series production system through the integration of the decisions associated with Maintenance Management (MM) and Statistical Process Control (SPC). Hence, the primary question of the paper can be stated as follows: In a series production system, how can the decisions of MM and SPC be coordinated? To this end, an integrated mathematical model of MM and SPC is developed. Usi...

Fréchet distance with speed limits

In this paper, we introduce a new generalization of the well-known Fréchet distance between two polygonal curves, and provide an efficient algorithm for computing it. The classical Fréchet distance between two polygonal curves corresponds to the maximum distance between two point objects that traverse the curves with arbitrary non-negative speeds. Here, we consider a problem instance in which t...