PDF version of this entire document
According to the aforementioned definition of Specificity and Generalisation, only nearest image distances get accounted for. This prevents us from attaining a robust measure that is dependent upon the set of images as a whole. Image distances can be perceived as a graph with a network of distances between nodes. We come to consider K nearest neighbours (kNN), wherein several nearest neighbours contribute to the measure. Making use of literature in the area, it is possible to treat the problem using entropic graphs analysis, as proposed by Neemuchwala et al. [16]. Rather than dealing with two isolated yet reciprocal measures like Specificity and Generalisation, overlap between data clouds can be estimated using an approximation of Shannon's entropy. We adopt the Jensen's dissimilarity measure, which is defined thus
xxxx formula xxxx use similified one? xxxx
where...
To make the calculation even simpler we compute the entropy in the following way
xxxx formula xxxx
In our experiments we consider minimal spanning tree (MST) with just one nearest node. As Fig. /refentropy suggests, we are able to get a measure that is closely-related to both Generalisation and Specificity, only with a higher (?hopefully?) level of certainty. The results also indicate that entropy is by all means a good surrogate of Specificity and Generalisation. It is considered to be a more principled way of measuring clouds overlap and it incorporates normalisation. This means that set sizes do not play any significant role, so a variety of models can be compared regardless of these free parameters.
|
|