Two-Directional Two-Dimensional Kernel Canonical Correlation Analysis

Gao, Xizhan; Niu, Sijie; Sun, Quansen

doi:10.1109/lsp.2019.2939986

Cited by 14 publications

(9 citation statements)

References 28 publications

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“…This is substantially less than 40, the number of classes. Next, these samples are utilized to construct the first view data set and the twice wavelet transform [34] is performed on each sample in the first data set to generate the corresponding second data set. Moreover, two experimental settings are adopted, front-left and front-right.…”

Section: Experimental Results and Analysismentioning

confidence: 99%

ODMTCNet: An Interpretable Multi-view Deep Neural Network Architecture for Image Feature Representation

Gao¹,

Guo²,

Guan³

2021

Preprint

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Recently, deep cascade architecture-based algorithms have attracted wide interest and have been applied to various application domains successfully. However, the longstanding challenge of interpretability, is still considered as an Achilles' heel of such algorithms. Moreover, due to its data-driven nature, the deep cascade architecture likely causes over-fitting problems when there is no sufficient data available. To address these pressing issues, this work proposes an interpretable multi-view deep neural network architecture, namely optimal discriminant multi-view tensor convolutional network (ODMTCNet), by integrating statistical machine learning (SML) principles with the deep neural network (DNN) architecture. Benefiting from the joint strength of SML and DNN, we demonstrate that ODMTCNet is analytically interpretable for multi-view image feature representation. Specifically, a discriminant multi-view tensor convolution strategy is proposed and integrated with the desired deep cascade architecture to generate high quality feature representations. Different from the traditional DNN models, the parameters of the convolutional layers in ODMTCNet are determined by analytically solving a SML-based optimization problem in each convolutional layer independently. This work demonstrates that, in ODMTCNet, the relation between the optimal performance and parameters (e.g., the number of convolutional filters) can be predicted, with each layer generating justified knowledge representations, leading to an interpretable multi-view based convolutional network. In addition, an information theoretic based descriptor, information quality (IQ), is utilized for feature representation of the given multi-view data sets. Because of its unique design, ODMTCNet is able to handle image data sets of different scales, large or small, effectively addressing the data hungry nature of DNN in image representation and forming a generic platform for multi-view image feature representation. To validate the effectiveness and the generic nature of the proposed ODMTCNet, we conducted experiments on four image data sets of different scales: The Olivetti Research Lab (ORL) database, Facial Recognition Technology (FERET) database, ETH-80 database and Caltech 256 database. The results show the superiority of the proposed solution compared to state-of-the-art.

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Section: Experimental Results and Analysismentioning

confidence: 99%

ODMTCNet: An Interpretable Multi-view Deep Neural Network Architecture for Image Feature Representation

Gao¹,

Guo²,

Guan³

2021

Preprint

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show abstract

“…Each subject provides three samples with a size of 20 × 20 pixels according to three different poses (front, left and right). Then, all 600 samples are utilized to construct the 2D data set X and the wavelet transform [10] is performed twice on each sample in the data set X to generate the corresponding 2D data set Y . Moreover, two experimental settings are adopted, front-left and front-right.…”

Section: B Experiments Under Different Poses On the Feret Databasementioning

confidence: 99%

“…Assume we have N two dimensional samples with a size of m × n. Then the computational complexity of the traditional CCA is on the order O((mn) 3 ) while 2DCCA only requires a computational complexity of O((m) 3 ) or O((n) 3 ). Moreover, local two-dimensional canonical correlation analysis (L2DCCA) [17] and two-directional two-dimensional kernel canonical correlation analysis ((2D) 2 KCCA) [10] are proposed as an extension of 2DCCA. In L2DCCA, the local structural information is introduced to the 2DCCA space, revealing more useful representations between 2D data sets with the computational complexity on the order of O((m…”

Section: Introductionmentioning

confidence: 99%

A Complete Discriminative Tensor Representation Learning for Two-Dimensional Correlation Analysis

Gao

Guan

2020

IEEE Signal Process. Lett.

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As an effective tool for two-dimensional data analysis, two-dimensional canonical correlation analysis (2DCCA) is not only capable of preserving the intrinsic structural information of original two-dimensional (2D) data, but also reduces the computational complexity effectively. However, due to the unsupervised nature, 2DCCA is incapable of extracting sufficient discriminatory representations, resulting in an unsatisfying performance. In this letter, we propose a complete discriminative tensor representation learning (CDTRL) method based on linear correlation analysis for analyzing 2D signals (e.g. images). This letter shows that the introduction of the complete discriminatory tensor representation strategy provides an effective vehicle for revealing and extracting the discriminant representations across the 2D data sets, leading to improved results. Experimental results show that the proposed CDTRL outperforms state-ofthe-art methods on the evaluated data sets.

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“…In pattern recognition and machine learning, canonical correlation analysis (CCA) is a typical method used to analyze correlations between two or more types of feature views of a given dataset [1], [2], and is widely adopted to extract related representations from individual views and fuse them together for pattern classification tasks [3], [4], [5], [6], [7]. Specially, given two (or more) views of feature representation of interested data, traditional CCA aims to find corresponding projection directions for individual views, along which the correlations of the views are maximized.…”

Section: Introductionmentioning

confidence: 99%

A Convex Discriminant Semantic Correlation Analysis for Cross-View Recognition

Qiu

Cao

et al. 2022

IEEE Trans. Cybern.

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Canonical correlation analysis (CCA) is a typical statistical model used to analyze the correlation components between different view representations of the same objects. When the label information is available with the data representations, CCA can be extended to its discriminative counterparts by incorporating supervision in the analysis. Although most discriminative variants of CCA have achieved improved results, nearly all of their objective functions are nonconvex, implying that optimal solutions are difficult to obtain. More importantly, that crossview representations from the same sample should be consistent, i.e., the cross-view semantic consistency, has however not been modelled. To overcome these drawbacks, in this paper we propose a Discriminant Semantic Correlation Analysis (DSCA) model by modelling the cross-view semantic consistency for each object in the sample space rather than in the commonly used feature space. To boost the nonlinear discriminating capability of DSCA, we extend it from the Euclidean to the geodesic space by transforming the metric and incorporating both the cross-view semantic and representation correlation information and consequently obtain our final model with convex objective, namely Convex DSCA (C-DSCA). Finally, with extensive experiments and comparisons we validate the effectiveness and superiority of the proposed method.

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Two-Directional Two-Dimensional Kernel Canonical Correlation Analysis

Cited by 14 publications

References 28 publications

ODMTCNet: An Interpretable Multi-view Deep Neural Network Architecture for Image Feature Representation

ODMTCNet: An Interpretable Multi-view Deep Neural Network Architecture for Image Feature Representation

A Complete Discriminative Tensor Representation Learning for Two-Dimensional Correlation Analysis

A Convex Discriminant Semantic Correlation Analysis for Cross-View Recognition

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