# Feature crosses

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

â€śFeature crossâ€ť, â€śfeature cross productâ€ť and â€śsynthetic featureâ€ť are synonymous. A feature cross is the cross product of two features. The nonlinearity sub-section states â€śThe term cross comes from cross product.â€ť Thinking of it as a Cartessian product, which the glossary mentions, helps me grok whatâ€™s going on, and why itâ€™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 â€śLinear learners use linear modelsâ€ť. What is a â€ślinear modelâ€ť? Given â€śmodelâ€ť is synonymous with â€śequationâ€ť or â€śfunctionâ€ť, a â€ślinear modelâ€ť is a linear equation. For example, Brilliantâ€™s wiki states: â€śA linear model is an equation …â€ť What is a â€ślinear learnerâ€ť? The video might just be stating a fact: something that learns using a linear model is a â€ślinear learnerâ€ť. For example, Amazon SageMakerâ€™s Linear Learner docs states â€śThe algorithm learns a linear functionâ€ť.

A â€ślinear problemâ€ť describes a relationship that can be expressed using a straight line (to divide the input data). â€śNonlinear problemsâ€ť 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 â€śRepresents multi-hot representation of given categorical column.â€ť