Experimental Results regarding multiple Machine Learning via Quaternions
- URL: http://arxiv.org/abs/2308.01946v1
- Date: Thu, 3 Aug 2023 08:14:07 GMT
- Title: Experimental Results regarding multiple Machine Learning via Quaternions
- Authors: Tianlei Zhu, Renzhe Zhu
- Abstract summary: This paper presents an experimental study on the application of quaternions in several machine learning algorithms.
Based on quaternions and multiple machine learning algorithms, it has shown higher accuracy and significantly improved performance in prediction tasks.
- Score: 1.2183405753834562
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This paper presents an experimental study on the application of quaternions
in several machine learning algorithms. Quaternion is a mathematical
representation of rotation in three-dimensional space, which can be used to
represent complex data transformations. In this study, we explore the use of
quaternions to represent and classify rotation data, using randomly generated
quaternion data and corresponding labels, converting quaternions to rotation
matrices, and using them as input features. Based on quaternions and multiple
machine learning algorithms, it has shown higher accuracy and significantly
improved performance in prediction tasks. Overall, this study provides an
empirical basis for exploiting quaternions for machine learning tasks.
Related papers
- Inferring Kernel $ε$-Machines: Discovering Structure in Complex Systems [49.1574468325115]
We introduce causal diffusion components that encode the kernel causal-state estimates as a set of coordinates in a reduced dimension space.
We show how each component extracts predictive features from data and demonstrate their application on four examples.
arXiv Detail & Related papers (2024-10-01T21:14:06Z) - The HR-Calculus: Enabling Information Processing with Quaternion Algebra [23.004932995116054]
quaternions and their division algebra have proven to be advantageous in modelling rotation/orientation in three-dimensional spaces.
adaptive information processing techniques specifically designed for quaternion-valued signals have only recently come to the attention of the machine learning, signal processing, and control communities.
arXiv Detail & Related papers (2023-11-28T13:25:34Z) - Dual Quaternion Rotational and Translational Equivariance in 3D Rigid
Motion Modelling [6.130606305848124]
We propose a dual quaternion representation of rigid motions in the 3D space that jointly describes rotations and translations of point sets.
Our approach is translation and rotation equivariant, so it does not suffer from shifts in the data.
Models endowed with this formulation outperform previous approaches in a human pose forecasting application.
arXiv Detail & Related papers (2023-10-11T16:06:14Z) - Geometry-Informed Neural Operator for Large-Scale 3D PDEs [76.06115572844882]
We propose the geometry-informed neural operator (GINO) to learn the solution operator of large-scale partial differential equations.
We successfully trained GINO to predict the pressure on car surfaces using only five hundred data points.
arXiv Detail & Related papers (2023-09-01T16:59:21Z) - Accelerated Discovery of Machine-Learned Symmetries: Deriving the
Exceptional Lie Groups G2, F4 and E6 [55.41644538483948]
This letter introduces two improved algorithms that significantly speed up the discovery of symmetry transformations.
Given the significant complexity of the exceptional Lie groups, our results demonstrate that this machine-learning method for discovering symmetries is completely general and can be applied to a wide variety of labeled datasets.
arXiv Detail & Related papers (2023-07-10T20:25:44Z) - Learning 4DVAR inversion directly from observations [0.0]
We design a hybrid architecture learning the assimilation task directly from partial and noisy observations.
We show in an experiment that the proposed method was able to learn the desired inversion with interesting regularizing properties.
arXiv Detail & Related papers (2022-11-17T18:05:41Z) - Quaternion-based machine learning on topological quantum systems [0.0]
In this work, we incorporate quaternion algebras into data analysis to classify two-dimensional Chern insulators.
For the unsupervised-learning aspect, we apply the principal component analysis (PCA) on the quaternion-transformed eigenstates.
We construct our machine by adding one quaternion convolutional layer on top of a conventional convolutional neural network.
arXiv Detail & Related papers (2022-09-29T05:02:20Z) - Exploring the Adjugate Matrix Approach to Quaternion Pose Extraction [0.0]
Quaternions are important for a wide variety of rotation-related problems in computer graphics, machine vision, and robotics.
We study the nontrivial geometry of the relationship between quaternions and rotation matrices by exploiting the adjugate matrix of the characteristic equation of a related eigenvalue problem.
We find an exact solution to the 3D orthographic least squares pose extraction problem, and apply it successfully also to the perspective pose extraction problem with results that improve on existing methods.
arXiv Detail & Related papers (2022-05-17T23:20:55Z) - GENEOnet: A new machine learning paradigm based on Group Equivariant
Non-Expansive Operators. An application to protein pocket detection [97.5153823429076]
We introduce a new computational paradigm based on Group Equivariant Non-Expansive Operators.
We test our method, called GENEOnet, on a key problem in drug design: detecting pockets on the surface of proteins that can host.
arXiv Detail & Related papers (2022-01-31T11:14:51Z) - An Analysis of SVD for Deep Rotation Estimation [63.97835949897361]
We present a theoretical analysis that shows SVD is the natural choice for projecting onto the rotation group.
Our analysis shows simply replacing existing representations with the SVD orthogonalization procedure obtains state of the art performance in many deep learning applications.
arXiv Detail & Related papers (2020-06-25T17:58:28Z) - Quaternion Equivariant Capsule Networks for 3D Point Clouds [58.566467950463306]
We present a 3D capsule module for processing point clouds that is equivariant to 3D rotations and translations.
We connect dynamic routing between capsules to the well-known Weiszfeld algorithm.
Based on our operator, we build a capsule network that disentangles geometry from pose.
arXiv Detail & Related papers (2019-12-27T13:51:17Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.