Moving Window Regression: A Novel Approach to Ordinal Regression

A novel ordinal regression algorithm, called moving window regression (MWR), is proposed in this paper. First, we propose the notion of relative rank ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\rho$</tex> -rank), which is a new order representation scheme for input and reference instances. Second, we develop global and local relative regressors ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\rho$</tex> -regressors) to predict <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\rho$</tex> -ranks within entire and specific rank ranges, respectively. Third, we refine an initial rank estimate iteratively by selecting two reference instances to form a search window and then estimating the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\rho$</tex> -rank within the window. Extensive experiments results show that the proposed algorithm achieves the state-of-the-art performances on various benchmark datasets for facial age estimation and historical color image classification. The codes are available at https://github.com/nhshin-mcl/MWR.