Log-Hilbert-Schmidt metric between positive definite operators on Hilbert spaces

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Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Quang et al. (2014) proposes a Log-Hilbert-Schmidt metric between positive definite operators on a Hilbert space.”
A Riemannian Network for SPD Matrix Learning (2016, background): “…Porikli, and Meer 2008; Tosato et al. 2010; Carreira et al. 2012; Fathy, Alavi, and Chellappa 2016), or map them into re-producing kernel Hilbert spaces (Harandi et al. 2012; Wang et al. 2012; Sanin et al. 2013; Quang, Biagio, and Murino 2014; Faraki, Harandi, and Porikli 2015; Zhang et al. 2015).”
Approximate Log-Hilbert-Schmidt Distances between Covariance Operators for Image Classification (2016, methodology): “The form of regularization (A + γI), γ > 0, which is often empirically necessary to ensure positive definiteness in the case dim(H) < ∞, is always necessary, both theoretically and empirically, when dim(H) = ∞, since in this case log(A), with A being a covariance operator, is always unbounded (see [”
Kernelized covariance for action recognition (2016, methodology): “The usage of the covariance Ŝ to produce descriptors for classification tasks has been intensively studied [23], [24], [25], [26], [27], [28], [29], [17].”