Orthogonal Polynomial Approximation for Matrix Log Normalization in Global Covariance Pooling
Global Covariance Pooling (GCP) improves deep networks by capturing second-order feature statistics, and is especially effective for fine-grained recognition. Because covariance matrices live on the Symmetric Positive Definite (SPD) manifold, a normalization step is required before the Euclidean classifier. The faithful choice is the matrix logarithm (MLN-COV), which maps the SPD manifold to its tangent space; in practice it was abandoned in favour of the matrix square root because its eigendecomposition-based gradient is numerically unstable. We show that this instability is an artifact of computing the logarithm spectrally, not of the logarithm itself. Approximating the logarithm with f...
| Authors | Md Rifat Ur Rahman, Md Raihan Khan, Md Sakib Hossain Shovon et al. |
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| Primary category | cs.CV |
| Published | 19 August 2026 |
| Last updated at source | 29 August 2026 |
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