Bregman Divergences for Infinite Dimensional Covariance Matrices

By Mehrtash Harandi, Mathieu Salzmann, Fatih Murat Porikli. 2014

112 citations recorded by the source corpus.

We introduce an approach to computing and comparing Covariance Descriptors (CovDs) in infinite-dimensional spaces. CovDs have become increasingly popular to address classification problems in computer vision. While CovDs offer some robustness to measurement variations, they also throw away part of the information contained in the original data by only retaining the second-order statistics over the measurements. Here, we propose to overcome this limitation by first mapping the original data to a high-dimensional Hilbert space, and only then compute the CovDs. We show that several Bregman divergences can be computed between the resulting CovDs in Hilbert space via the use of kernels. We then exploit these divergences for classification purpose. Our experiments demonstrate the benefits of our approach on several tasks, such as material and texture recognition, person re-identification, and action recognition from motion capture data.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

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Citations in the corpus

When Kernel Methods Meet Feature Learning: Log-Covariance Network for Action Recognition From Skeletal Data (2017, methodology): “In addition to Bregman-divergence of the infinite covariance representation [11] and the fast region covariance descriptor of [34], we included the trial-specific encoding of an action with a Gram matrix [37] reporting both Ker-RP-POL and Ker-RP-RBF (polynomial vs.”
Tensor Representations via Kernel Linearization for Action Recognition from 3D Skeletons (2016, methodology): “Such constraints have been used to model actions; examples include but not limited to using Lie Alge-bra [27], positive deﬁnite matrices [3, 5], using a torus manifold [2], Hanklet representations [11], among several others.”
Kernelized covariance for action recognition (2016, methodology): “Precisely, the following algorithms were compared in our experiments: RegionCOV [23] (covariance region descriptor), temporal pyramid of covariance descriptors (Hierarchy of COVs) [16] and, finally, an infinite covariance operator which exploits Bregman divergence, namely COV-JH-SVM [29].”
Beyond Covariance: Feature Representation with Nonlinear Kernel Matrices (2015, methodology): “Cov-JH-SVM is the method in [7] which uses an infinite-dimensional covariance matrix in a kernel-induced feature space as representation.”
Log-Hilbert-Schmidt metric between positive definite operators on Hilbert spaces (2014, methodology): “(30)”
Efficient Temporal Sequence Comparison and Classification Using Gram Matrix Embeddings on a Riemannian Manifold (2016, methodology): “5s the protocol in [16], which included 14 different actions and used 4 joints corresponding to arms and legs.”
Approximate Log-Hilbert-Schmidt Distances between Covariance Operators for Image Classification (2016, methodology): “8% over the state-of-the-art [14].”
Distribution Consistency Based Covariance Metric Networks for Few-Shot Learning (2019, methodology): “…has been widely used as a region descriptor (Tuzel, Porikli, and Meer 2006; 2007; Tabia et al. 2014) or a general representation (Wang et al. 2012; Harandi, Salzmann, and Porikli 2014; Wang et al. 2015b; 2015a; Huang et al. 2015; Wang et al. 2017), due to its favorable properties, e.g. ,…”