Spherical Regression under Mismatch Corruption with Application to Automated Knowledge Translation

Understand

Motivated by a series of applications in data integration, language translation, bioinformatics, and computer vision, we consider spherical regression with two sets of unit-length vectors when the data are corrupted by a small fraction of mismatch in the response-predictor pairs.

• We propose a three-step algorithm in which we initialize the parameters by solving an orthogonal Procrustes problem to estimate a translation matrix $\mathbb{W}$ ignoring the mismatch.
• We then estimate a mapping matrix aiming to correct the mismatch using hard-thresholding to induce sparsity, while incorporating potential group information.
• We eventually obtain a refined estimate for $\mathbb{W}$ by removing the estimated mismatched pairs.