What does the phrase "spread crossing" mean?

Question

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.

Answer 1

In various financial markets, an instrument has two listed prices -- the bid, the current amount that someone is willing to pay to buy the instrument from someone wishing to sell it, and the ask, the current amount that someone is willing to accept to sell the instrument to someone wishing to buy it. For obvious reasons, the bid is less than the ask. The difference between the bid and the ask is called the spread.

A trader crosses the spread when he offers to buy at the ask, i.e., he offers to pay the sellers' price, which is above what other buyers are willing to pay. The trick is that the trader does this on only one exchange, say Chicago. This pushes up the price on the other exchanges, which will recognize that someone is offering more than the instrument is nominally worth. If the trader is fast enough, he can sell a lot of the shares of the instrument in New York at the higher prices before anyone realizes that he engineered the higher price.