Let's say I want to perform a clustering analysis of paintings based on the their use of colour. This gives me three levels of analysis:
- L1: Individual paintings
- L2: Individual colours present
- L3:Individual aspects of colour use
Thus, Mondrian's Composition in Red, Blue and Yellow (L1) uses 3 colours (L2) in a linear style using primary hues (L3).
Let's assume further that L2 always has the same entries (say, the colours of the visual spectrum) and that I have numerical measures for every metric in L3, which are also fixed in number (say, hue, area and saturation).
My problem is that I can't seem to find out the best clustering algorithm for this type of data. K-means and spherical k-means require that each painting be representable as a vector of m features; my data further decomposes each of the m features into n further features. So, my questions are:
Does this matter? Given that L2 is constant, do I need to worry about it all, so long as the order of components is the same?
If it does matter, are there are any clustering algorithms that will naturally deal with three-level data like this? (Note that I might at some point like to take colour rather than painting as my superordinate category.)