Your experiment is most similar to those in categorization research. For example, Wills et al (2013)* argued that single-dimension classification (one-feature analysis) is less effortful, than multidimensional with more than one dimension, and omni-dimensional, where you process and categorize the stimuli as a whole. They used the match-to-standard procedure, where each stimuli is classified by participants as members of categories. This task was first used by Regehr and Brooks (1995) and basically means that you map each the stimuli features and each stimuli feature that you categorize.
For example, you have Stimulus A (dark, square), Stimulus B (light, triangle) and Stimulus C (dark, triangle). The dimensions are shape and colour.
Dimensions colour shape
Stimulus A 1 0
Stimulus B 0 1
Stimulus C 1 1
Of course you have to have to set up rules for stimuli structures in category learning or learning in general and fit the stimuli into those structures.
If you instruct them to pay attention to the first dimension only, you would pay attention only to the first dimension in the data analysis. But that would be supervised learning, and that would defeat the purpose of your experiment. If you are curious to whether they learn by single-dimensions or through omni-dimension, you must not supervise the learningand should not provide feedback, because feedback will likely become superior to simple observational learning (see Wills, Milton & Edmunds, 2015).
A very good example is Nosofsky et al. (1994) replicating Shepard et al. (1961). That one is the closest to what you described you want to do. You can find the data and look at the categorisational structure in catlearn (Wills et al., 2016), so you can see how they handled their stimuli dimensions and data.
Hope this helps. I might have not been too coherent, but I think the gist is there.
Nosofsky, R. M., Gluck, M. A., Palmeri, T. J., McKinley, S. C., & Glauthier, P. (1994). Comparing modes of rule-based classification learning: A replication and extension of Shepard, Hovland, and Jenkins (1961). Memory & Cognition, 22(3), 352–369.
Regehr, G., & Brooks, L. R. (1995). Category organization in free classification: The organizing effect of an array of stimuli. Journal of Experimental Psychology: Learning, Memory, and Cognition, 21(2), 347–363.
Shepard, R. N., Hovland, C. I., & Jenkins, H. M. (1961). Learning and memorization of classifications. Psychological Monographs: General and Applied, 75(13), 1.
Wills, A. J., Connell, G. O., Edmunds, C. E. R., & Inkster, A. B. (2016). Progress in modeling through distributed collaboration: Concepts, tools, and category-learning examples. Psychology of Learning and Motivation, 1–23.
Wills, A. J., Milton, F., & Edmunds, C. E. R. (2015). Feedback can be superior to observational training for both rule-based and information-integration category structures. Retrieved from https://pearl.plymouth.ac.uk/handle/10026.1/3064
Wills, A.J., Milton, F., Longmore, C.A., Hester, S., & Robinson, J. (2013). Is overall similarity classification less effortful than single-dimension classification?. Quarterly Journal of Experimental Psychology, 66, 299-318.
* You can visit the authors' website to get the data and how the analysed that data.