How Long to Read Covariances in Computer Vision and Machine Learning

How Long Does it Take to Read Covariances in Computer Vision and Machine Learning?

It takes the average reader 2 hours and 53 minutes to read Covariances in Computer Vision and Machine Learning by Hà Quang Minh

Assuming a reading speed of 250 words per minute. Learn more

Description

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.

How long is Covariances in Computer Vision and Machine Learning?

Covariances in Computer Vision and Machine Learning by Hà Quang Minh is 172 pages long, and a total of 43,344 words.

This makes it 58% the length of the average book. It also has 53% more words than the average book.

How Long Does it Take to Read Covariances in Computer Vision and Machine Learning Aloud?

The average oral reading speed is 183 words per minute. This means it takes 3 hours and 56 minutes to read Covariances in Computer Vision and Machine Learning aloud.

What Reading Level is Covariances in Computer Vision and Machine Learning?

Covariances in Computer Vision and Machine Learning is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Covariances in Computer Vision and Machine Learning?

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