Fuzzy Dissimilarity based Multidimensional Scaling and its Application to Collaborative Learning Data

Recently, the elucidation of learning activity for human learning systems has gained tremendous interests in many areas including neuroscience, brain sciences, behavioral sciences, and education. The main problems of these data are noise and the large amount data (big data). Multidimensional scaling (MDS) is well known method to capture the similarity of objects in lower dimensional configuration space and latent cognitive factors as the dimensions. How- ever, ordinary MDS is based on the Euclidean distance which often fails to capture the similarity relationship in the lower dimensional space. The main reason for this fault is that data usually does not have significant variance to be captured by the MDS. Therefore, in this study, we exploit the latent classification structure of variables to the distance and propose a new dissimilarity and a new multidimensional scaling based on this dissimilarity. We show a better performance of the proposed method by using a time series log data of mobile learning with the collaboration of several students.