I'm interested in building an unsupervised clustering model to look at the physical activity data of a person. Below is an image of the model in the 2D space (built through t-SNE), where each data point has been labelled with its ground-truth label.
Obviously, the model isn't particularly brilliant. There is some OK-ish separability of the stair classes which can be identified e.g through DBSCAN. However, while there isn't really any separability of the flat, uphill and downhill classes, I think its still clear there is a kind of gradient-like distribution. Ideally, I'd be looking to try and construct a cluster model looking something like this:
My attempts so far to construct cluster models using K-Means or GMM has resulted in some shockingly poor NMIs (ranging from 10-20%) that resemble nothing like the "ideal" distribution. Are there any clustering models out there that could help, or am I ultimately just never going to get anywhere with this?
P.S I am aware a supervised approach is going to be better, but in this research context I'm trying to look at how the data could be handled without presence of Ground Truth Annotation for training.