This study adopts the Isomap algorithm that uses the variation of modal frequencies caused by stiffness damage to classify damage locations in a structure. The Isomap algorithm belongs to a nonlinear generalization of classical multidimensional scaling, which makes a new coordinate system for high-dimensional data. And this coordinate system provides good observations for the extraction of the data pattern and for the classification of their nonlinear characteristics. Thus, the Isomap can easily find globally meaningful coordinates and identify the nonlinear structure of complex data sets for many cases, whereas neither the principal component analysis (PCA) nor multidimensional scaling has been successful. This study compares the performances of the PCA and the Isomap algorithm in classifying damage locations in terms of modal frequency changes. The article also investigates the benefits of incorporating the concept of sensitivity enhancing control in the Isomap-based damage classification to improve the level of resolution of a modal frequency shift. It is demonstrated that the Isomap algorithm successfully enhances the quality of patterns and classifications related to damage locations through simulation examples.