A nominal association matrix with feature selection for categorical data

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

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H20
• 62F07
• 68T30

Funding

The research of the first named author was partially supported by NSFC [grant number 11171202], Guangzhou University [grant number Hwx1-2001]. The research of the second named author was partially supported by NSFC [grant number 71501175], [grant number 71110107026], [grant number 71331005]. The research of the third named author was partially supported by an NSERC grant.