Fuzzy Diffusion Distance Learning for Cartoon Similarity Estimation

In this paper, a novel method called fuzzy diffusion maps (FDM) is proposed to evaluate cartoon similarity, which is critical to the applications of cartoon recognition, cartoon clustering and cartoon reusing. We find that the features from heterogeneous sources have different influence on cartoon similarity estimation. In order to take all the features into consideration, a fuzzy consistent relation is presented to convert the preference order of the features into preference degree, from which the weights are calculated. Based on the features and weights, the sum of the squared differences (L2) can be calculated between any cartoon data. However, it has been demonstrated in some research work that the cartoon dataset lies in a low-dimensional manifold, in which the L2 distance cannot evaluate the similarity directly. Unlike the global geodesic distance preserved in Isomap, the local neighboring relationship preserved in Locally Linear Embedding, and the local similarities of neighboring points preserved in Laplacian Eigenmaps, the diffusion maps we adopt preserve diffusion distance summing over all paths of length connecting the two data. As a consequence, this diffusion distance is very robust to noise perturbation. Our experiment in cartoon classification using Receiver Operating Curves shows fuzzy consistent relation's excellent performance on weights assignment. The FDM's performance on cartoon similarity evaluation is tested on the experiments of cartoon recognition and clustering. The results show that FDM can evaluate the cartoon similarity more precisely and stably compared with other methods.