Dimensionality Reduction in Multiple Ordinal Regression

Conditional Uncorrelation and Efficient Subset Selection in Sparse Regression

Given m d -dimensional responsors and n d -dimensional predictors, sparse regression finds at most k predictors for each responsor for linear approximation, 1 ≤ k ≤ d-1 . The key problem in sparse regression is subset selection, which usually suffers from high computational cost. In recent years, many improved approximate methods of subset selection have been published. However, less attention has been paid to the nonapproximate method of subset selection, which is very necessary for many questions in data analysis. Here, we consider sparse regression from the view of correlation and propose the formula of conditional uncorrelation. Then, an efficient nonapproximate method of subset selection is proposed in which we do not need to calculate any coefficients in the regression equation for candidate predictors. By the proposed method, the computational complexity is reduced from O([1/6]k³+(m+1)k²+mkd) to O([1/6]k³+[1/2](m+1)k²) for each candidate subset in sparse regression. Because the dimension d is generally the number of observations or experiments and large enough, the proposed method can greatly improve the efficiency of nonapproximate subset selection. We also apply the proposed method in real scenarios of dental age assessment and sparse coding to validate the efficiency of the proposed method.

Multilabel Distribution Learning Based on Multioutput Regression and Manifold Learning

Real-world multilabel data are high dimensional, and directly using them for label distribution learning (LDL) will incur extensive computational costs. We propose a multilabel distribution learning algorithm based on multioutput regression through manifold learning, referred to as MDLRML. By exploiting smooth, similar spaces' information provided by the samples' manifold learning and LDL, we link the two spaces' manifolds. This facilitates using the topological relationship of the manifolds in the feature space to guide the manifold construction of the label space. The smoothest regression function is used to fit the manifold data, and a locally constrained multioutput regression is designed to improve the data's local fitting. Based on the regression results, we enhance the logical labels into the label distributions, thereby mining and revealing the label's hidden information regarding importance or significance. Extensive experimental results using real-world multilabel datasets show that the proposed MDLRML algorithm significantly improves the multilabel distribution learning accuracy and efficiency over several existing state-of-the-art schemes.