The research discussed in this paper documents a comparative analysis of two nonlinear dimensionality reduction techniques for the classification of facial expressions at varying degrees of intensity. These nonlinear dimensionality reduction techniques are Kernel Principal Component Analysis (KPCA) and Locally Linear Embedding (LLE). The approaches presented in this paper employ psychological tools, computer vision techniques and machine learning algorithms. In this paper we concentrate on comparing the performance of these two techniques when combined with Support Vector Machines (SVMs) at the task of classifying facial expressions across the full expression intensity range from near-neutral to extreme facial expression. Receiver Operating Characteristic (ROC) curve analysis is employed as a means of comprehensively comparing the results of these techniques.