If there is a limited amount of similarity groups that you know in advance you can frame this as a multiclass problem. You may put images in folders by their group and zip them into one archive that will be used by DataRobot, or add additional features as described here
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You will have 2 features, one for each image, and a target equal to 1 if the same, or 0 otherwise. Both features will have a path to the respective folder of their respective images
@km2 DataRobot allows Clustering of images and one can attend the DataRobot University Visual AI class (link below) to find out more about how to incorporate images into their machine learning process.
A key capability is DataRobot's ability to use images along with other structured and unstructured data for modeling and discovery.
A short answer to the question is to zip one's images into a directory and feed it into DataRobot and then select Clustering for the task if it only had images.
However, if there were other features one could create a feature list that only contained images and then cluster on that or include all the features.
On top of that, as my colleagues have mentioned one can also take the supervised training route which is also covered in the course above.