Manifold Kernel Rank Reduced Regression
Primary Area: metric learning, kernel learning, and sparse coding
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: Reproducing kernel hilbert space, Manifold kernel reduced rank regression, Shape analysis, Mandibular point cloud reconstruction
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
Abstract: The Kernel Rank Reduced Regression (KRRR) technique works well on highly dependent dataset with a latent variable structure.
When we extended the KRRR to the Reproducing Kernel Hilbert Space (RKHS), the powerful kernel presentation and reproducing ability can enhance the regression ability. But previous research always work on Euclidean space with vector data presentation, which omit the intrinsic geometric shape of the data distribution. If the whole dataset can be thought as a manifold, the regression result will only rely on the intrinsic data distribution instead of the extrinsic frame. So we present the manifold kernel rank reduced regression model (MKRRR).
We fist give the definition of the MKRRR model. Then with leveraging Kendall shape space for representing sample manifold data, we derive the closed-form solution of the regression model and prediction result. Moreover, we discuss the convergent and robust ability of the model, with presenting the robustness proof. At last, the we present a skull repair application by the MKRRR model for 3D mandibular reconstruction. The experiment result validate effective of our model even on the data with high-level noise.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 1217
Loading