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Power Normalizations in Fine-Grained Image, Few-Shot Image and Graph Classification.

Bibliographic Details
Title: Power Normalizations in Fine-Grained Image, Few-Shot Image and Graph Classification.
Authors: Koniusz, Piotr, Zhang, Hongguang
Source: IEEE Transactions on Pattern Analysis & Machine Intelligence; Feb2022, Vol. 44 Issue 2, p591-609, 19p
Subject Terms: Covariance matrices, Nonlinear operators, Deep learning, Laplacian matrices, Classification, Charts, diagrams, etc., Feature extraction
Abstract: Power Normalizations (PN) are useful non-linear operators which tackle feature imbalances in classification problems. We study PNs in the deep learning setup via a novel PN layer pooling feature maps. Our layer combines the feature vectors and their respective spatial locations in the feature maps produced by the last convolutional layer of CNN into a positive definite matrix with second-order statistics to which PN operators are applied, forming so-called Second-order Pooling (SOP). As the main goal of this paper is to study Power Normalizations, we investigate the role and meaning of MaxExp and Gamma, two popular PN functions. To this end, we provide probabilistic interpretations of such element-wise operators and discover surrogates with well-behaved derivatives for end-to-end training. Furthermore, we look at the spectral applicability of MaxExp and Gamma by studying Spectral Power Normalizations (SPN). We show that SPN on the autocorrelation/covariance matrix and the Heat Diffusion Process (HDP) on a graph Laplacian matrix are closely related, thus sharing their properties. Such a finding leads us to the culmination of our work, a fast spectral MaxExp which is a variant of HDP for covariances/autocorrelation matrices. We evaluate our ideas on fine-grained recognition, scene recognition, and material classification, as well as in few-shot learning and graph classification. [ABSTRACT FROM AUTHOR]
Copyright of IEEE Transactions on Pattern Analysis & Machine Intelligence is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Power Normalizations in Fine-Grained Image, Few-Shot Image and Graph Classification.
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  Data: <searchLink fieldCode="AR" term="%22Koniusz%2C+Piotr%22">Koniusz, Piotr</searchLink><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Hongguang%22">Zhang, Hongguang</searchLink>
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  Data: IEEE Transactions on Pattern Analysis & Machine Intelligence; Feb2022, Vol. 44 Issue 2, p591-609, 19p
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  Data: <searchLink fieldCode="DE" term="%22Covariance+matrices%22">Covariance matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+operators%22">Nonlinear operators</searchLink><br /><searchLink fieldCode="DE" term="%22Deep+learning%22">Deep learning</searchLink><br /><searchLink fieldCode="DE" term="%22Laplacian+matrices%22">Laplacian matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Classification%22">Classification</searchLink><br /><searchLink fieldCode="DE" term="%22Charts%2C+diagrams%2C+etc%2E%22">Charts, diagrams, etc.</searchLink><br /><searchLink fieldCode="DE" term="%22Feature+extraction%22">Feature extraction</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Power Normalizations (PN) are useful non-linear operators which tackle feature imbalances in classification problems. We study PNs in the deep learning setup via a novel PN layer pooling feature maps. Our layer combines the feature vectors and their respective spatial locations in the feature maps produced by the last convolutional layer of CNN into a positive definite matrix with second-order statistics to which PN operators are applied, forming so-called Second-order Pooling (SOP). As the main goal of this paper is to study Power Normalizations, we investigate the role and meaning of MaxExp and Gamma, two popular PN functions. To this end, we provide probabilistic interpretations of such element-wise operators and discover surrogates with well-behaved derivatives for end-to-end training. Furthermore, we look at the spectral applicability of MaxExp and Gamma by studying Spectral Power Normalizations (SPN). We show that SPN on the autocorrelation/covariance matrix and the Heat Diffusion Process (HDP) on a graph Laplacian matrix are closely related, thus sharing their properties. Such a finding leads us to the culmination of our work, a fast spectral MaxExp which is a variant of HDP for covariances/autocorrelation matrices. We evaluate our ideas on fine-grained recognition, scene recognition, and material classification, as well as in few-shot learning and graph classification. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of IEEE Transactions on Pattern Analysis & Machine Intelligence is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1109/TPAMI.2021.3107164
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 19
        StartPage: 591
    Subjects:
      – SubjectFull: Covariance matrices
        Type: general
      – SubjectFull: Nonlinear operators
        Type: general
      – SubjectFull: Deep learning
        Type: general
      – SubjectFull: Laplacian matrices
        Type: general
      – SubjectFull: Classification
        Type: general
      – SubjectFull: Charts, diagrams, etc.
        Type: general
      – SubjectFull: Feature extraction
        Type: general
    Titles:
      – TitleFull: Power Normalizations in Fine-Grained Image, Few-Shot Image and Graph Classification.
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            NameFull: Koniusz, Piotr
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            NameFull: Zhang, Hongguang
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            – D: 01
              M: 02
              Text: Feb2022
              Type: published
              Y: 2022
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            – TitleFull: IEEE Transactions on Pattern Analysis & Machine Intelligence
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