Jensen-Bregman LogDet Divergence with Application to Efficient Similarity Search for Covariance Matrices

Cherian, Anoop; Sra, Suvrit; Banerjee, Arindam; Papanikolopoulos, N.

doi:10.1109/tpami.2012.259

Cited by 150 publications

(112 citation statements)

References 42 publications

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“…The advantages offered by this generalized distance measure (which is not a true metric) are similar to those by S JS (more precisely, by δ S ): it has many of the properties of the geodesic distance δ R but its calculation does not require matrix eigenvalue computations, or logarithms, see [4]. It can be easily seen that for any A, B ∈ P n we have…”

Section: Introduction and Statement Of The Resultsmentioning

confidence: 97%

Transformations on positive definite matrices preserving generalized distance measures

Molnár

Szokol

2015

Linear Algebra and its Applications

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Abstract. We substantially extend and unify former results on the structure of surjective isometries of spaces of positive definite matrices obtained in the paper [14]. The isometries there correspond to certain geodesic distances in Finsler-type structures and to a recently defined interesting metric which also follows a nonEuclidean geometry. The novelty in our present paper is that here we consider not only true metrics but so-called generalized distance measures which are parameterized by unitarily invariant norms and continuous real functions satisfying certain conditions. Among the many possible applications, we shall see that using our new result it is easy to describe the surjective maps of the set of positive definite matrices that preserve the Stein's loss or several other types of divergences. We also present results concerning similar preserver transformations defined on the subset of all complex positive definite matrices with unit determinant.

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Section: Introduction and Statement Of The Resultsmentioning

confidence: 97%

Transformations on positive definite matrices preserving generalized distance measures

Molnár

Szokol

2015

Linear Algebra and its Applications

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“…Among possible choices, we make use of the Stein divergence (Cherian et al, 2013) in this work. Hence,…”

Section: Discriminative Lossmentioning

confidence: 99%

Learning an Invariant Hilbert Space for Domain Adaptation

Herath

Harandi

Porikli

2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

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This paper introduces a learning scheme to construct a Hilbert space (i.e., a vector space along its inner product) to address both unsupervised and semi-supervised domain adaptation problems. This is achieved by learning projections from each domain to a latent space along the Mahalanobis metric of the latent space to simultaneously minimizing a notion of domain variance while maximizing a measure of discriminatory power. In particular, we make use of the Riemannian optimization techniques to match statistical properties (e.g., first and second order statistics) between samples projected into the latent space from different domains. Upon availability of class labels, we further deem samples sharing the same label to form more compact clusters while pulling away samples coming from different classes.We extensively evaluate and contrast our proposal against state-of-the-art methods for the task of visual domain adaptation using both handcrafted and deepnet features. Our experiments show that even with a simple nearest neighbor classifier, the proposed method can outperform several state-of-the-art methods benefitting from more involved classification schemes.

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“…As mentioned by Lee [3], polarimetric SAR images of different bands can be considered as statistically independent if the radar frequencies are sufficiently separated. Our objective is to minimize the following optimization function Equation (22).…”

Section: Multi-band Merged Polarimetric Sar Classification Based On Smentioning

confidence: 99%

“…Let v i represent the i-th row of the matrix, meaning that v i = v Li v P i v Ci . Then, Equation (22) can be relaxed to a new form as follows.…”

Section: Multi-band Merged Polarimetric Sar Classification Based On Smentioning

confidence: 99%

“…It is noteworthy that Stein divergence is also named Jensen-Bregman logdet divergence in [22] and introduced by Song [11] to polarimetric SAR classification. In addition, it has the same mathematical form as Bartlett distance, and it is consistent with the logarithm of likelihood-ratio test statistic Q proposed by Conradsen [23], which is defined to measure the similarity between two regions in polarimetric SAR image.…”

Section: Introduction Of the Riemannian Manifold And Stein Kernelmentioning

confidence: 99%

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Multi-Frequency Polarimetric SAR Classification Based on Riemannian Manifold and Simultaneous Sparse Representation

Yang

Gao

et al. 2015

Remote Sensing

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Normally, polarimetric SAR classification is a high-dimensional nonlinear mapping problem. In the realm of pattern recognition, sparse representation is a very efficacious and powerful approach. As classical descriptors of polarimetric SAR, covariance and coherency matrices are Hermitian semidefinite and form a Riemannian manifold. Conventional Euclidean metrics are not suitable for a Riemannian manifold, and hence, normal sparse representation classification cannot be applied to polarimetric SAR directly. This paper proposes a new land cover classification approach for polarimetric SAR. There are two principal novelties in this paper. First, a Stein kernel on a Riemannian manifold instead of Euclidean metrics, combined with sparse representation, is employed for polarimetric SAR land cover classification. This approach is named Stein-sparse representation-based classification (SRC). Second, using simultaneous sparse representation and reasonable assumptions of the correlation of representation among different frequency bands, Stein-SRC is generalized to simultaneous Stein-SRC for multi-frequency polarimetric SAR classification. These classifiers are assessed using polarimetric SAR images from the Airborne Synthetic Aperture Radar (AIRSAR) sensor of the Jet Propulsion Laboratory (JPL) and the Electromagnetics Institute Synthetic Aperture Radar (EMISAR) sensor of the Technical University of Denmark (DTU). Experiments on single-band and multi-band data both show that these approaches acquire more accurate classification results in comparison to many conventional and advanced classifiers.Remote Sens. 2015, 7 8470

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Jensen-Bregman LogDet Divergence with Application to Efficient Similarity Search for Covariance Matrices

Cited by 150 publications

References 42 publications

Transformations on positive definite matrices preserving generalized distance measures

Transformations on positive definite matrices preserving generalized distance measures

Learning an Invariant Hilbert Space for Domain Adaptation

Multi-Frequency Polarimetric SAR Classification Based on Riemannian Manifold and Simultaneous Sparse Representation

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