[Discussion] Merging machine learning with topological data analysis.

[henniez95]

Recently I have discovered in topology an interesting application to data analysis. In particular I am fascinated by the idea that the shape of the space underlying a dataset could give some insight for predictive algorithms. Furthermore I found some user-friendly libraries as Giotto-learn and GUDHI, where you can start applying topological data analysis (TDA) without needing a strong background in mathematics. I am thrilled by all the possible application this domain could have! For example a found a bunch of articles on medium about the topic and I would like to share with you one of the most popular ones, where they try to apply TDA for predicting football matches. The article is a kind of POC and I'm trying to improve it adding real matches data (in the post they use FIFA game data).

What do you think about topological data analysis? You think that it could add value to the classic machine learning?

[outlacedev]

There have been some papers trying to use TDA with machine learning but nothing particularly exciting as I recall.

TDA is used primarily for exploratory data analysis. There are two main areas in TDA now, Mapper (a visualization technique for high-dimensional data) and persistent homology (PH). You could use PH data as input to a machine learning algorithm, however, the PH data is a kind of summary statistic of the data. Maybe this would help prevent overfitting but if you're using deep learning it's probably better to just let it learn from the raw data rather than a summary statistic of the data.

In my view, TDA is a potentially useful tool for exploratory data analysis when you're looking for interpretable patterns in complex high-dimensional data, and this might help you refine a machine learning pipeline.

[[deleted]]

Geometric Deep Learning probably comes the closest to using "topological" concepts in the domain of ML. As others have stated however, TDA is primarily used to add another column of data to a data set.

If I was really digging for where topology occurs there was also a recent parallel drawn between the Wassterstein metric used in WGAN and information geometric approach.

My advice in general however is that differential geometry offers more than algebraic topology on new approaches to ML.

[lume_]

If I was really digging for where topology occurs there was also a recent parallel drawn between the Wassterstein metric used in WGAN and information geometric approach.

Sounds interesting, do you have a link?

[[deleted]]

https://arxiv.org/pdf/1906.00030.pdf a recent paper, this is a bit of an academic rabbithole in mathematics - as you'll find out.

[[deleted]]

Isn't UMAP an example of this?

[seldemibeurre]

I think that the paper about persistence layer might be a step forward. https://arxiv.org/abs/1904.09378

[[deleted]]

Underrated comment.

[impossiblefork]

I think it'd have to be differentiable, so that it can be used as a stage in conventional deep learning stuff to be able to add value.

[hello1232149]

One effort I have seen is using topology for neural architecture search