Some methods related to manifold-learning are commonly stated as good-for-visualization, such as T-SNE and self-organizing-maps (SOM).
I understand that when referring specifically to "visualization" means that the non-linear dimensionality reduction can provide good insights of data in its low-dimensional projection, but that most commonly this low-dimensional projection cannot be used in machine learning algorithms, since some of information of the high-dimensional structure is lost (roughly).
However, and here the question, If "clusters" are being observed in the visualization is it acceptable to apply a clustering algorithm to the low-dimensional transformed data and analyze the clusters or groups separately?
For example, I'm applying T-SNE to rather-high dimensional data (40 features) and obtaining this representation:
Disregarding the colors you observe in the picture, I would like to apply a clustering algorithm and separate the data from the found clusters (let's say 6 or 7 clusters), and then analyze the characteristics of each cluster using the high-dimensional representation of each point.
This is in synthesis: using the low dimensional to find clusters, and analyze (exploration) each cluster separately using the high dimensional representation. If I'm not able to do this, I don't see the actual point of visualizing in the low-dimensional space, in a practical sense.
I understand T-SNE preserves well local structures and less accurately global structures, is this a drawback to do why I want? Is this low-dim clustering approach more suitable for other manifold learning methods?
EDIT: Probably a more direct way of asking this is: Can I use observed clusters in low dimensional representation to label or tag examples, and use these labels for discrimination using the original high dimensional representation?