Removing outliers before fitting convex hull

Question

I have a few datasets that I'd like to visualise with convex hull (and derive some statistics from that convex hull). However, each dataset contains some noise. Therefore, convex hull covers not only points in the main data cloud, but also all the outliers making the area of convex hull pretty large and not very different between datasets. An example of the dataset may be seen below:

The whole area is not unimodal, but we can certainly observe some outliers (especially on the left) that mess up convex hull shape. The estimated KDE looks like below:

Therefore, I'd like to remove those outliers. What algorithm could be used to fit minimal area convex hull to n - k points from the dataset, where k is set to some number respective to given percentage of observations?

Please note that pictures refer to an example and I'm in fact dealing with plenty of different datasets

Answer 1

To mark or remove outlier, you will have at least two popular libs in python language:

1. classic sklearn movelty and outlier detection .
2. Pyod

Bother offered visuallized decison boundary for reference in the reference URL. you can based on you dataset distribution to pick an approporiate algorithm.

My favorite two algorithms are: HBOS and isolated forest. They showed stable performance in large dataset. The former work well for global outliers. The later work well for local outlier.

Good luck, if you like the answer, pls vote it up.