I don’t think that this solution gives you everything that you want from semantic categories. Assume for example that you have a multidimensional cluster with heavy tails (for simplicity, assume symmetry under rotation). You measure some of the features, and determine that the given example belongs to the cluster almost surely. You want to use this fact to predict the other features. knowing the deviation of the known features is still relevant for your uncertainty about the other features. You may think about this extra property as measuring “typicality”, or as measuring “how much does it really belong in the cluster.
I don’t think that this solution gives you everything that you want from semantic categories. Assume for example that you have a multidimensional cluster with heavy tails (for simplicity, assume symmetry under rotation). You measure some of the features, and determine that the given example belongs to the cluster almost surely. You want to use this fact to predict the other features. knowing the deviation of the known features is still relevant for your uncertainty about the other features. You may think about this extra property as measuring “typicality”, or as measuring “how much does it really belong in the cluster.