In the field of data mining, there is one big open problem: the optimization subject to binary constraints. Binary constraints make data mining results interpretable and definite. Is this picture showing a cat? Should this movie be recommended to this user? Should the next chess move be this one? Binary results give a definite answer to questions like these. There are a lot of methods which are able to solve binary constrained problems, however, they mostly work under one condition: exclusivity. That is, if a picture shows a cat, then it can not show a dog, if a movie is recommended to one user, then it can't be recommended to the other, and there should only be one next chess move which is the optimal one. Depending on the application, this assumption is is more or less justified. The field of clustering is an area in which the optimization subject to binary constraints is explicitly studied. In this talk, we will discuss the broad spectrum of tasks where a matrix factorization approximation error in Frobenius norm is minimized subject to binary constraints. We will unveil under which circumstances this optimization task defines the clustering objectives of k-means, spectral clustering and subspace clustering, but we will also make connections to methods like deep learning. We will also see how bridging those disciplines under the umbrella of matrix factorization establishes novel research ideas and insights, providing inspiration to tackle pending research questions of adversarial learning, computing meaningful embeddings and to learn sensible similarity metrics.