lmcinnes / lmcinnes/umap

What does 'epochs_per_sample', 'epochs_of_next_sample' and 'epochs_per_negative_sample' mean in the`optimize_layout()` function?

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Description

Source code in `optimize_layout()` function:
![image](https://user-images.githubusercontent.com/15790176/48346071-e6792180-e6b4-11e8-9ebd-aab01384ee2f.png)

According to [this page](https://jlmelville.github.io/smallvis/theory.html). The gradient is

![image](https://user-images.githubusercontent.com/15790176/48346034-c0ec1800-e6b4-11e8-9a74-1920a46b4dd3.png)

1. Where is the term `Vij` in the the source code?
2. What does `epochs_per_sample`, `epochs_of_next_sample` and `epochs_per_negative_sample` mean in the`optimize_layout()` function?

Anyone can give some hint on this? Thanks!

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Research direction

Start at the `optimize_layout()` function and compare its calculations with the linked smallvis theory page. Trace where `Vij`, `epochs_per_sample`, `epochs_of_next_sample`, and `epochs_per_negative_sample` are used, then document explanations that answer the two questions in the issue.

Written by the indexing model from the issue text.

Assessment

Tech stack
python
Domain
machine-learning
Issue type
Documentation
Difficulty
3/5
Estimated time
1-2 days
Activity status
Stale
Clarity
Needs clarification
Newbie friendliness
35/100

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