The importance of gene expression data in cancer diagnosis and treatment by now has been widely recognized by cancer researchers in recent years. However, one of the major challenges in the computational analysis of such data is the curse of dimensionality, due to the overwhelming number of measures of gene expression levels versus the small number of samples. Here, we use a two-step method to reduce the dimension of gene expression data. At first, we extract a subset of genes based on the statistical characteristics of their corresponding gene expression measurements. For further dimensionality reduction, we then apply diffusion maps, which interpret the eigenfunctions of Markov matrices as a system of coordinates on the original data set in order to obtain efficient representation of data geometric descriptions, to the reduced data. A neural network clustering theory, Fuzzy ART, is applied to the resulting data to generate clusters of cancer samples. Experimental results on the small round blue-cell tumor (SRBCT) data set, compared with other widely-used clustering algorithms, demonstrate the effectiveness of our proposed method in addressing multidimensional gene expression data.