I have a dataset that is completely binary and labeled. I would like to be able to use machine learning for one of the columns. I have read that unsupervised models, such as K-Means, do not work with the data in binary form since the distance measures are only between 0 and 1, and therefore, unable to provide valid clusters. Are there other models that would work adequately? The dataset is comprised of medical diagnoses, and they are broad characteristics with hundreds of columns. Any tips would be helpful!
You can use any instance-based classifier, such as $k$-Nearest Neighbour, equipped with a similarity metric (e.g., Euclidean distance) to assign the class to a new instance; that is, find the $k$ most similar examples of your labelled dataset and give the majority class of such cases to that (new) instance.
Moreover, claiming that $k$-means does not work on binary data is false. From a theoretical point of view, it works, but, from a practical point of view, it should be avoided, as explained in this post.