von Sachs, Rainer
[UCL]
Timmermans, Catherine
[UCL]
The BAGIDIS (semi-) distance of Timmermans and von Sachs
(BAGIDIS: statistically investigating curves with sharp local patterns using a new
functional measure of dissimilarity. Under revision. http://www.uclouvain.be/en-
369695.html. ISBA Discussion Paper 2013-31, Université catholique de Louvain,
2013) is the central building block of a nonparametric method for comparing curves
with sharp local features, with the subsequent goal of classification or prediction.
This semi-distance is data-driven and highly adaptive to the curves being studied.
Its main originality is its ability to consider simultaneously horizontal and vertical
variations of patterns. As such it can handle curves with sharp patterns which
are possibly not well-aligned from one curve to another. The distance is based
on the signature of the curves in the domain of a generalised wavelet basis, the
Unbalanced Haar basis. In this note we give insights on the problem of stability
of our proposed algorithm, in the presence of observational noise. For this we use
theoretical investigations from Timmermans, Delsol and von Sachs (JMultivar Anal
115:421–444, 2013) on properties of the fractal topology behind our distance-based
method. Our results are general enough to be applicable to any method using a
distance which relies on a fractal topology.
| Bibliographic reference |
von Sachs, Rainer ; Timmermans, Catherine. The BAGIDIS distance: about a fractal topology, with applications to functional classification and prediction. In: Anestis Antoniadis, Jean-Michel Poggi, Xavier Brossat, Modeling and Stochastic Learning for Forecasting in High Dimensions, Springer New York LLC : (United States) New York 2015, p.319-339 |
| Permanent URL |
http://hdl.handle.net/2078.1/146393 |
