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Clustering is an effective approach for computing analysis of gene expression data. Various of clustering algorithms have been developed to give reasonable interpretations of biological data and discover biological meaningful patterns of cellular functions. Based on the manifold structure of gene expression data analyzed under the framework of geometric representation, a novel clustering approach is presented to reveal the nonlinear expression patterns. The novel clustering approach can be divided into the following computing steps. The first step is to construct a neighborhood graph for gene expression points through which the approximate geodesic distances between each two points can be obtained. Then, instead of Euclidean distance, approximate geodesic distance is exploited to reveal the similarity between gene profiles. Finally, via defining the geodesic distance between a cluster and a gene expression point, new clusters can be generated after essential iterative processes. Application of the approach to the yeast cell-cycle dataset validates its rationality and efficiency.