Extrinsic Kernel Ridge Regression Classifier for Planar Kendall Shape Space

12/17/2019
by   Hwiyoung Lee, et al.
0

Kernel methods have had great success in the statistics and machine learning community. Despite their growing popularity, however, less effort has been drawn towards developing kernel based classification methods on manifold due to the non-Euclidean geometry. In this paper, motivated by the extrinsic framework of manifold-valued data analysis, we propose two types of new kernels on planar Kendall shape space Σ_2^k, called extrinsic Veronese Whitney Gaussian kernel and extrinsic complex Gaussian kernel. We show that our approach can be extended to develop Gaussian like kernels on any embedded manifold. Furthermore, kernel ridge regression classifier (KRRC) is implemented to address the shape classification problem on Σ_2^k, and their promising performances are illustrated through the real dataset.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/13/2014

A Framework for Shape Analysis via Hilbert Space Embedding

We propose a framework for 2D shape analysis using positive definite ker...
research
10/04/2021

A manifold learning approach for gesture identification from micro-Doppler radar measurements

A recent paper (Neural Networks, 132 (2020), 253-268) introduces a strai...
research
09/17/2018

Statistically and Computationally Efficient Variance Estimator for Kernel Ridge Regression

In this paper, we propose a random projection approach to estimate varia...
research
11/26/2021

Neural Fields as Learnable Kernels for 3D Reconstruction

We present Neural Kernel Fields: a novel method for reconstructing impli...
research
06/03/2022

Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics

This paper introduces algorithms to select/design kernels in Gaussian pr...
research
05/28/2020

Hyperbolic Manifold Regression

Geometric representation learning has recently shown great promise in se...
research
02/01/2016

A Spectral Series Approach to High-Dimensional Nonparametric Regression

A key question in modern statistics is how to make fast and reliable inf...

Please sign up or login with your details

Forgot password? Click here to reset