In one of my last blog posts, I have introduced a data set of shapes which I use to extract similarity spaces for the shape domain. As stated at the end of that blog post, I want to analyze these similarity spaces based on three predictions of the conceptual spaces framework: The representation of dissimilarities as distances, the presence of small, non-overlapping convex regions, and the presence of interpretable directions. Today, I will focus on the first of these predictions. More specifically, we will compute the correlation between distances in the MDS-spaces to the original dissimilarities and compare this to three baselines. This will help us to see how efficiently the similarity spaces represent shape similarity.
As already mentioned earlier, I want to validate my hybrid proposal for obtaining the dimensions of a conceptual space in a second study, which focuses on the domain of shapes. Today I will start reporting on joint work with Margit Scheibel on obtaining a similarity space for the shape domain based on psychological data. This is the first step of the proposed hybrid procedure and will be followed by training a neural network. But for now, let’s focus on obtaining the similarity spaces.
This blog post closes the “A Hybrid Way: Reloaded” mini-series. So far, I have analyzed the MDS solutions in part 1 and investigated first regression results in part 2 (with respect to the effects of feature space, correct vs. shuffled targets, and regularization). Today, I want to analyze what happens if we use different MDS algorithms for constructing the similarity spaces and to what extent our regression results depend on the number of dimensions in the similarity space.
In my last blog post, I analyzed the differences of metric vs. nonmetric MDS when applied to the NOUN data base. Today, I want to continue with showing some machine learning results, updating the ones from our 2018 AIC paper (see these two blog posts: part 1 and part 2).
Some time ago, I wrote two blog posts about a hybrid way for obtaining the dimensions of a conceptual space (see here and here). Currently, I’m rerunning these experiments in a more detailed way and today I want to share both the motivation for doing this as well as some first results.