Kindly explain the term spread crossing or crossing the spread. I know that it is connected with stock terminology, but I can't find a definition.
Figure 4 reveals that, broadly speaking, we have learned momentum-based strategies: for instance, for each of the four features that contain directional information (Price, Smart Price, Trade Sign, Bid-Ask Volume Imbalance, and Signed Transaction Volume), higher values of the feature (which all indicate either rising execution prices, rising midpoints, or buying pressure in the form of spread-crossing) are accompanied by greater frequency of buying in the learned policies.
From the paper "Machine Learning for Market Microstructure and High Frequency Trading" by Michael Kearns and Yuriy Nevmyvaka.