Applying diffusion distance for multi-scale analysis of an experience space

Diffusion distance has been shown to be significantly more effective than Euclidean distance in multi-scale recognition of similar experiences in RecognitionPrimed Decision making (Fan and Su 2010). In this paper, we first examine the experience data set used in the previous study. The visualization of the data set (using the first three dominant eigenvectors of the diffusion space) suggests the applicability of the diffusion approach. Second, we investigate two approaches to the computation of diffusion distance: Spectrum based and Probability-Matching based. Specifically, by 'Spectrum based' approach we refer to the one derived in terms of the eigenvalues/eigenvectors of the normalized diffusion matrix (Coifman and Lafon 2006). We use the term 'Probability-Matching' to refer to the use of various probability distances, where the original L² diffusion distance is treated as a special case. Our preliminary result indicates that the performance of using L ² diffusion distance at least is tied with the use of Spectrum based distance. Furthermore, when spectrum based approach is applied, we have to use the embedding and extending techniques for labeling new experience data (Lieu and Saito 2009), while such re-computation is not necessary when the L ² diffusion distance is used. We do not need to re-compute the diffusion matrix, hence the diffusion map each time when adding a new data. It is more natural and robust especially for labeling new single experience data. The numerical examples also show the improvement on the performance. We are currently working on several other Probability-Matching approaches (e.g. the Earth-Mover's Distance).