Applications of Diffusion Maps in Gene Expression Data-Based Cancer Diagnosis Analysis

Rui Xu, Missouri University of Science and Technology
Donald C. Wunsch, Missouri University of Science and Technology
Steven Damelin

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Early detection of a tumor's site of origin is particularly important for cancer diagnosis and treatment. The employment of gene expression profiles for different cancer types or subtypes has already shown significant advantages over traditional cancer classification methods. One of the major problems in cancer type recognition-oriented gene expression data analysis is the overwhelming number of measures of gene expression levels versus the small number of samples, which causes the curse of dimension issue. Here, we use 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, for dimensionality reduction. The derived data are then clustered with Fuzzy ART to form the division of the cancer samples. Experimental results on the small round blue-cell tumor data set demonstrate the effectiveness of our proposed method in addressing multidimensional gene expression data and identifying different types of tumors.