A feature cross is a synthetic feature that is obtained by combining two or more existing features, usually by taking their product or concatenation. A feature cross can help to capture the nonlinear and interaction effects between the original features, and improve the predictive performance of the model. A feature cross can be applied to different types of features, such as numeric, categorical, or geospatial features1.

For the use case of building an ML model to predict car sales in different cities around the world, the best option is to use one feature obtained as an element-wise product between binned latitude, binned longitude, and one-hot encoded car type. This option involves creating a feature cross that combines three individual features: binned latitude, binned longitude, and one-hot encoded car type. Binning is a technique that transforms a continuous numeric feature into a discrete categorical feature by dividing its range into equal intervals, or bins. One-hot encoding is a technique that transforms a categorical feature into a binary vector, where each element corresponds to a possible category, and has a value of 1 if the feature belongs to that category, and 0 otherwise. By applying binning and one-hot encoding to the latitude, longitude, and car type features, the feature cross can capture the city-specific relationships between car type and number of sales, as each combination of bins and car types can represent a different city and its preference for a certain car type. For example, the feature cross can learn that a city with a latitude bin of [40, 50], a longitude bin of [-80, -70], and a car type of SUV has a higher number of sales than a city with a latitude bin of [-10, 0], a longitude bin of [10, 20], and a car type of sedan. Therefore, using one feature obtained as an element-wise product between binned latitude, binned longitude, and one-hot encoded car type is the best option for this use case.

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Feature Crosses | Machine Learning Crash Course