# MLCC: Feature crosses

I am working through Google’s Machine Learning Crash Course. The notes in this post cover the “Feature Crosses” section.

“Feature cross”, “feature cross product” and “synthetic feature” are synonymous. A feature cross is the cross product of two features. The nonlinearity sub-section states “The term cross comes from cross product.” Thinking of it as a Cartessian product, which the glossary mentions, helps me grok what’s going on, and why it’s helpful for the example problem where examples are clustered by quarter (to consider x-y pairs), and esp the exercise involving latitude and longitude pairs.

The video states “Linear learners use linear models”. What is a “linear model”? Given “model” is synonymous with “equation” or “function”, a “linear model” is a linear equation. For example, Brilliant’s wiki states: “A linear model is an equation …” What is a “linear learner”? The video might just be stating a fact: something that learns using a linear model is a “linear learner”. For example, Amazon SageMaker’s Linear Learner docs states “The algorithm learns a linear function”.

A “linear problem” describes a relationship that can be expressed using a straight line (to divide the input data). “Nonlinear problems” cannot be expressed this way.

While trying to figure out why the exercise used an indicator_column, I found some nice TensorFlow tutorials, eg for feature crosses. In retrospect, I see the indicator_column docs state simply “Represents multi-hot representation of given categorical column.”