Non-linear feature extraction methods, neighborhood preserving embedding (NPE) and supervised NPE (SNPE), were employed to effectively represent the IR spectral features of stomach and colon biopsy tissues for classification, and improve the classification accuracy for diagnosis of malignancy. The motivation was to utilize the NPE and SNPE's capability of capturing non-linear spectral behaviors by simultaneously preserving local relationships in order that minute spectral differences among classes would be effectively recognized. NPE and SNPE derive an optimal embedding feature such that the local neighborhood structure can be preserved in reduced spaces (variables). The IR spectra collected from stomach and colon tissues were represented by several new variables through NPE and SNPE, and also by using the principal component analysis (PCA). Then, the feature-extracted variables were subsequently classified into normal, adenoma and cancer tissues by using both k-nearest neighbor (k-NN) and support vector machine (SVM), and the resulting accuracies were compared with each other. In both cases, the combination of SNPE-SVM provided the best classification performance, and the accuracy was substantially improved compared to when PCA-SVM was used. Overall results demonstrate that NPE and SNPE could be potential feature-representation strategies useful in biomedical diagnosis based on vibrational spectroscopy where effective recognition of minute spectral differences is critical.