Multi attribute multi class classification

1

Say I have 2 attributes which is color and direction.

In color we have blue, red, green,
In direction we have left, right, front, back.

So How to design a classifier to make it work output 2 attributes and according class?

I know that we using 3x3=9 classes to classify is a solution, but that not very good seems. Does there any better way to do this?

2

You could use two classification “heads” and return two outputs.
These outputs would separately compute the losses, which you could sum and backward together.