# Time Series Averaging under Dynamic Time Warping

## Problem:
Find an optimizer which minimizes the Fréchet function “as good as possible” for samples from many datasets.

## ToDo

- [ ] Alternative Optimizer suchen
- == Frechet function minimizer
- reine nonsmooth analysis?
- geeignet für Frechet?
- gibt es eine Veröffentlichung dazu?
- öffentliche Implementation verfügbar?
- [ ] Benchmark designen
- [ ] Paper schreiben

## Sources

### Paper

#### Highly relevant
- [original paper] https://arxiv.org/abs/1701.06393
- https://link.springer.com/article/10.1007/s10618-018-0604-8 (also written by D. Schultz)
- stochastic gradient optimization
- accelerated gradient method
- variance reduction methods
- simulated aili (?)

#### Slightly relevant
- https://papers.nips.cc/paper/9338-dtwnet-a-dynamic-time-warping-network
- https://www.semanticscholar.org/paper/FastDTW-is-approximate-and-Generally-Slower-than-it-Wu-Keogh/676b5ad60c615186df7f691fb2db4ddd7d21b4ba (FastDTW buuuuh)

#### Not sure
- https://arxiv.org/pdf/1909.13541.pdf (also written by D. Schultz)
- https://dl.acm.org/doi/10.5555/3305381.3305474 (SoftDTW)
- http://sites.labic.icmc.usp.br/dfs/pdf/SDM_PrunedDTW.pdf (PrunedDTW)
- https://arxiv.org/abs/1201.2969 (SparseDTW)
- https://www.audiolabs-erlangen.de/content/05-fau/professor/00-mueller/03-publications/2006_MuellerMattesKurth_MultiscaleAudioSynchronization_ISMIR.pdf (MsDTW)

#### Irrelevant (since they're already considered in the original paper)
- Subgradient Mean Algorithm (SG)
- Majorize-Minimize Mean Algorithm
- DTW Barycenter Averaging (seems to be equivalent to MM ??? )

### Source code
- https://www.akt.tu-berlin.de/menue/software/
- https://pypi.org/project/fastdtw/ (FastDTW)