Monotonicity of the $$\chi ^2$$ χ 2 -statistic and Feature Selection

Feature selection is an important preprocessing step in analyzing large scale data. In this paper, we prove the monotonicity property of the $$\chi ^2$$ χ 2 -statistic and use it to construct a more robust feature selection method. In particular, we show that $$\chi ^2_{Y, X_1} \le \chi ^2_{Y, (X_1, X_2)}$$ χ Y , X 1 2 ≤ χ Y , ( X 1 , X 2 ) 2 . This result indicates that a new feature should be added to an existing feature set only if it increases the $$\chi ^2$$ χ 2 -statistic beyond a certain threshold. Our stepwise feature selection algorithm significantly reduces the number of features considered at each stage making it more efficient than other similar methods. In addition, the selection process has a natural stopping point thus eliminating the need for user input. Numerical experiments confirm that the proposed algorithm can significantly reduce the number of features required for classification and improve classifier accuracy.