| Abstract |
Hamiltonian time-series data are observations derived from a Hamiltonian dynamical
system. Our goal is to analyze the time-series data using the topological information of Hamiltonian
dynamical systems. Exact Multi-parameter Persistent Homology is one aspect of this analysis, in this
case, the Hamiltonian system is composed of uncoupled one-dimensional harmonic oscillators. This
is a very simple model. However, we can induce the exact persistence barcode formula from it.
From this formula, we can obtain a calculable and interpretable analysis. Filtration is necessary to
extract the topological information of data and to define persistent homology. However, in many
cases, we use static filtrations, such as the Vietoris-Rips filtration. My ongoing research is on
topological optimization, which involves finding a filtration in Exact Multi-parameter Persistent
Homology that minimizes the cross-entropy loss function for the classification of time-series data. |
