So I have a question on clustering vs. classification. I know there are tons of questions on this here and elsewhere on the Internet, but I have not found my answer so far. I think this (A clustering and classification question) is closest that I have found so far.
Let's says that we have the standard dataset on breast cancer in sklearn. There exists a target variable that is 1 if the tumor is cancerous and 0 if benign. The standard approach would be to use a classification algorithm, such as SVM. But since we know that there are only two possible outcomes (either canceours or benign), why can't we use a clustering algorithm, such as Kmeans? I now that our data is labeled, and therefore we should use a supervised algorithm, but I don't understand why we can't use an unsupervised algorithm (e.g. Kmeans) since we actually know the number of clusters (2 in this case). What am I missing? Is it that I simply assume that the data will cluster on the outcome variable, instead of at something else, and that I assume that there only will be 2 clusters?