Plans for lattice reduction?

[jboynyc]

Many thanks for your work on this! After playing around with this for a while I inevitably wound up with some messy lattices, so I was wondering whether you have any plans to include simple lattice reduction techniques based on stability, support and the like in concepts.

I came across this repository with an MIT-licensed Python implementation of lattice reduction, and if it's of interest I could try to integrate that in this library.

[xflr6]

Thanks for the feedback (happy if this is useful to anyone).

lattice reduction

I think I am not familiar. Do you mean this method?

https://github.com/simplerick/nn_fca/blob/master/local/fca.py#L244-L249

Not sure if it uses the stability currently:

https://github.com/simplerick/nn_fca/blob/master/local/fca.py#L198-L203

Would this be for removing (omitting) arbitrary nodes from the graph when rendering for visualization or rather for keeping the reduced graph structure for further usage? Both Context and Lattice instances are treated as immutable in this library (and they point to each other); so the latter might require introducing a new type for a mutable graph detached from a context/lattice, but maybe there are other options.

[jboynyc]

I must admit I'm a novice, all I know about reduction/clarification is from this unit of the Coursera course on FCA. The basic idea, as I understand it, is that you set a cutoff point for stability, support or probability of concepts and eliminate them from the line graph to make it less noisy.

I'm mainly interested in this for the purposes of visualizing overall lattice structure, so mutating the data structures probably wouldn't be necessary.

[xflr6]

Thanks for the link. IIUC both clarification and reduction are applied to the context (rather than its lattice) creating a new clarified/reduced context. So the reduced_lattice()-method mentioned above looks like a different kind of operation.

Adding e.g. Context.clarified() (or Definition.clarified()) seems straightforward (not sure if you have identical objects/attributes); I suspect .clarified(reduced=True) might require to dig in a bit into possible algorithms.

When it comes to removing nodes from the lattice graph (only for visualization or creating a new graph), I am wondering about the exact semantics: Say we have A < {B, C} < D, then removing B means removing the node and its edges (A, B) and (B, D). Removing C afterwards would additionally involve adding an edge (A, D) to keep the former transitive relations, right? Not sure if reduced_lattice() does that.

[jboynyc]

I think I need to do some more reading in this area. Since my original question was based on a misunderstanding, I'm going to close this issue. I'll come back to it when I have a better understanding.