## Landmarks
As the name shows, the landmarks act like some kind of indicator for the system. Consider a very complex chemical system, gives experimental/simulation data, and generates high-dimensional descriptions. How can we apply them? See the following workflow:
>[!Note]
>The procedure of selecting a small number of representative landmark structures to analyze makes it possible to have an out-of-sample algorithm that allows you to construct a representation for any configuration that is outside the initial training set, and adopt some kind of workflow.
>Namely, perform initial analysis in small amount of data.
![[Drawing 2024-08-30 18.30.56.excalidraw.svg]]
So a big question is, how to select landmark and sample the system. Sampling depends on what knowledge/results one wants to extract!
- random sampling.
- farthest point sampling → find a further point from the current one .
problem: not following $P(x)$ distribution
- well-tempered FPS (farthest point sampling)
\- First, use FPS
\- After FPS, give each point different weight.
\- Under the weight, use random sampling. (big $\gamma$, closer to $P(x)$ ( i.e., random), smaller $P(x)$, closer to FPS.)
>[!Info]
>Make sure to check the slides for detailed information.
>As for FPS, check some api examples or docs like https://docs.dgl.ai/en/1.1.x/api/python/dgl.geometry.html.
>See similar chapters for more on data processing and sampling: [[Data representation]], [[Reweighting and enhanced sampling techniques]], [[Dimensionality reduction]].