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 with no clear extension to out-of-sample points. Furthermore

since MDS is based on Euclidean distance

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 (CMDS). In contrast with MDS where the mapping between the input and reduced spaces is implicit

CMDS employs an explicit nonlinear mapping between the both. As a result

CMDS can directly provide predictions for new samples.Correlation is a similarity measure

so the 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 the feature space. The effectiveness of our approach is demonstrated by extensive experiments on various data sets

in comparison with existing dimensionality reduction algorithms.