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Facial expression recognition is a topic of interest both in industry and academia. Recent approaches to facial expression recognition are based on mapping expressions to low dimensional manifolds. In this paper we revisit various dimensionality reduction algorithms using a graph-based paradigm. We compare eight dimensionality reduction algorithms on a facial expression recognition task. For this task, experimental results show that although Linear Discriminant Analysis (LDA) is the simplest and oldest supervised approach, its results are comparable to more flexible recent algorithms. LDA, on the other hand, is much simpler to tune, since it only depends on one parameter.