A number of studies have been conducted on the nonlinear dimension reduction for manifold learning in the literature. Among them, the isometric sliced inverse regression (ISOSIR), a semi-supervised learning algorithm, has been proposed and shown to be useful for exploring the embedded geometric structure of the nonlinear manifold data set such as the Swiss roll. ISOSIR applied K-means as a base clustering method to the pre-calculated isometric distance matrix of the data set. However, the ordering information of response both within and between the resulting clusters was ignored where the ordering structure was one of the most important characteristics of a nonlinear manifold data set. On the other hand, the construction of the isometric distance matrix did not consider the class labels of data if they were available. In this study, we are motivated to settle these two defects and propose the supervised extensions of ISOSIR and isometric cumulative slicing mean estimation. We conducted the simulation studies and real data analysis and shown that the proposed method can reveal the geometric structure of a nonlinear manifold data set and the results were comparable to the supervised ISOSIR. We further investigated the applications of the found features for the classification and regression problems to the real world data sets.