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A nominal association matrix with feature selection for categorical data |
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| Authors: | Wenxue Huang Yong Shi Xiaogang Wang |
| Institution: | 1. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong, P.R. China;2. Research Center on Fictitious Economy and Data Science, University of Chinese Academy of Sciences, and Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, P. R. China;3. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada |
| Abstract: | An intrinsic association matrix is introduced to measure category-to-variable association based on proportional reduction of prediction error by an explanatory variable. The normalization of the diagonal gives rise to the expected rates of error-reduction and the off-diagonal yields expected distributions of the rates of error for all response categories. A general framework of association measures based on the proposed matrix is established using an application-specific weight vector. A hierarchy of equivalence relations defined by the association matrix and vector is shown. Applications to financial and survey data together with simulation results are presented. |
| Keywords: | Association matrixl Association vector Categorical data Feature selection Proportional prediction The GK-tau |