Dictionary learning algorithm of SPD data based on Riemannian manifold tangent space and local homeomorphism

Abstract

The problem of SPD data dictionary learning is studied. All of the SPD data do not form a linear space, and dictionary learning is essentially sparse linear coding, so that dictionary learning cannot be directly performed on the SPD data. The SPD data can form a Riemannian manifold under a certain topological structure and Riemannian metric, and the tangent space of the Riemannian manifold is a finite-dimensional Hilbert space and is isomorphic with an Euclidean space. Therefore, the invention provides another SPD data dictionary learning algorithm, the SPD data is firstly converted into the tangent space of the SPD Riemannian manifold, and dictionary learning is carried out on the tangent space. The tangent space of the SPD Riemannian manifold is a symmetric matrix space, and the symmetric matrix comprises an SPD matrix. Therefore, according to the SPD data transformation method provided by the invention, the change in data form and property is minimum. Furthermore, in the dictionary learning process, regularization constraints of local homeomorphism between dictionary learning samples and sample dictionary codes are also added.

Description

technical field [0001] The invention belongs to the field of machine learning, relates to the problem of SPD data dictionary learning, and maintains the geometric structure and category information of SPD original data to the maximum extent. Background technique [0002] In recent years, with the continuous development and in-depth research of machine learning, non-European data has become more and more common in machine learning. For example, symmetric positive definite (SPD) data is a kind of non-European data. The SPD matrix data is generally obtained by extracting the regional covariance descriptor of the original data, which provides a nonlinear representation of the original data and enjoys rich geometric characteristics. It is used in 3-D object recognition, visual surveillance, object recognition, action recognition, Fields such as medical imaging, manual detection and tracking have excellent performance. SPD matrix data is a typical non-Euclidean characteristic dat...

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Problems solved by technology

However, the linear combination of a set of SPD matrices cannot guarantee that it is still an SPD matrix, and many restrictions need to be added to it, which makes many difficulties in the dictionary learning process.

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