CORRELATION-BASED MULTIDIMENSIONAL SCALING FOR UNSUPERVISED SUBSPACE LEARNING
Guanghui He, Lingfeng Zhang, Zhaowei Shang · International Journal of Wavelets Multiresolution and Information Processing · 2012
Multidimensional scaling (MDS) has been applied in many applications such as dimensionality reduction and data mining. However, one of the drawbacks of MDS is that it is only defined on "training" data without clear extension to out-of-sample points. Furthermore, since that MDS is based on Euclidean distance (which is a dissimilarity measure), it is not suitable for detecting the nonlinear manifold structure embedded in the similarities between data points. In this paper, we extend MDS to the correlation measure space, named correlation MDS (CMDS). CMDS employs an explicit nonlinear mapping between the input and reduced space while MDS using an implicit mapping. As a result, CMDS can directly provide prediction for new samples. In addition, correlation is a similarity measure, CMDS method can effectively capture the nonlinear manifold structure of data embedded in the similarities between the data points. Theoretical analysis also shows that CMDS has some properties similar to kernel methods and can be extended to feature space. The effectiveness of the approach provided in this paper are demonstrated by extensive experiments on various datasets, in comparison with serval existing algorithms.