—As for massive multidimensional data are being generated in a wide range of emerging applications, this paper introduces two new methods of dimension reduction to conduct small-sample size and high-dimensional data processing and modeling. Through combining the support vector machine (SVM) and recursive feature elimination (RFE), SVM-RFE algorithm is proposed to select features, and further, adding the higher order singular value decomposition (HOSVD) to the feature extraction which involves successfully organizing the data into high order tensor pattern. The validation of simulation experiment data shows that the proposed novel feature selection and feature extraction methods can be effectively applied to the research work for analyzing and modeling the data of atmospheric corrosion. The feature selection method pledges that the remaining feature subset is optimal; feature extraction method reserves the original structure, discriminate information, and the integrity of data, etc. Finally, this paper proposes a complete data dimensionality reduction solution that can effectively solve the high-dimensional small sample data problem, and code programming for this solution has been implemented.
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