Covariances in Computer Vision and Machine Learning is popular PDF and ePub book, written by Hà Quang Minh in 2022-05-31, it is a fantastic choice for those who relish reading online the Computers genre. Let's immerse ourselves in this engaging Computers book by exploring the summary and details provided below. Remember, Covariances in Computer Vision and Machine Learning can be Read Online from any device for your convenience.
Covariances in Computer Vision and Machine Learning Book PDF Summary
Covariance matrices play important roles in many areas of mathematics, statistics, and machine learning, as well as their applications. In computer vision and image processing, they give rise to a powerful data representation, namely the covariance descriptor, with numerous practical applications. In this book, we begin by presenting an overview of the {\it finite-dimensional covariance matrix} representation approach of images, along with its statistical interpretation. In particular, we discuss the various distances and divergences that arise from the intrinsic geometrical structures of the set of Symmetric Positive Definite (SPD) matrices, namely Riemannian manifold and convex cone structures. Computationally, we focus on kernel methods on covariance matrices, especially using the Log-Euclidean distance. We then show some of the latest developments in the generalization of the finite-dimensional covariance matrix representation to the {\it infinite-dimensional covariance operator} representation via positive definite kernels. We present the generalization of the affine-invariant Riemannian metric and the Log-Hilbert-Schmidt metric, which generalizes the Log-Euclidean distance. Computationally, we focus on kernel methods on covariance operators, especially using the Log-Hilbert-Schmidt distance. Specifically, we present a two-layer kernel machine, using the Log-Hilbert-Schmidt distance and its finite-dimensional approximation, which reduces the computational complexity of the exact formulation while largely preserving its capability. Theoretical analysis shows that, mathematically, the approximate Log-Hilbert-Schmidt distance should be preferred over the approximate Log-Hilbert-Schmidt inner product and, computationally, it should be preferred over the approximate affine-invariant Riemannian distance. Numerical experiments on image classification demonstrate significant improvements of the infinite-dimensional formulation over the finite-dimensional counterpart. Given the numerous applications of covariance matrices in many areas of mathematics, statistics, and machine learning, just to name a few, we expect that the infinite-dimensional covariance operator formulation presented here will have many more applications beyond those in computer vision.
Detail Book of Covariances in Computer Vision and Machine Learning PDF
- Author : Hà Quang Minh
- Release : 31 May 2022
- Publisher : Springer Nature
- ISBN : 9783031018206
- Genre : Computers
- Total Page : 156 pages
- Language : English
- PDF File Size : 18,5 Mb
If you're still pondering over how to secure a PDF or EPUB version of the book Covariances in Computer Vision and Machine Learning by Hà Quang Minh, don't worry! All you have to do is click the 'Get Book' buttons below to kick off your Download or Read Online journey. Just a friendly reminder: we don't upload or host the files ourselves.