Similarity measure based on multiple classes from a hierarchical taxonomy?
While I don't have enough expertise to advise you on selection of the best similarity measure, I've seen a number of them in various papers. The following collection of research papers hopefully will be useful to you in determining the optimal measure for your research. Please note that I intentionally included papers, using both frequentist and Bayesian approaches to hierarchical classification, including class information, for the sake of more comprehensive coverage.

Frequentist approach:


Semantic similarity based on corpus statistics and lexical taxonomy
Can’t see the forest for the leaves: Similarity and distance measures for hierarchical taxonomies with a patent classification example (also see additional results and data)
Learning hierarchical similarity metrics
A new similarity measure for taxonomy based on edge counting
Hierarchical classification of real life documents
Hierarchical document classification using automatically generated hierarchy
Split-Order distance for clustering and classification hierarchies
A hierarchical k-NN classifier for textual data


Bayesian approach:


Improving classification when a class hierarchy is available using a hierarchy-based prior
Bayesian aggregation for hierarchical genre classification
Hierarchical classification for multiple, distributed web databases