Two-Dimensional Canonical Correlation Analysis

Lee, Sun-Ho; Choi, Seungjin

doi:10.1109/lsp.2007.896438

Cited by 96 publications

(57 citation statements)

References 8 publications

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“…In addition, following the idea of 2DPCA, researchers have extended the classical feature extraction methods like LDA and canonical correlation analysis (CCA), and the state-of-the-art methods like ICA [45] and local preserving projection (LPP) [46], to their two-dimensional (or matrix-based) versions, respectively [47][48][49][50][51][52][53][54][55][56]. Since a matrix can be viewed as the second-order tensor, the matrix-based representation methods have been further generalized to high-order tensor based methods [57][58][59][60][61].…”

Section: Tensor-based Feature Extraction Methods and Their Generatingmentioning

confidence: 99%

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Kernel feature extraction methods observed from the viewpoint of generating-kernels

Yang

2011

Front. Electr. Electron. Eng. China

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This paper introduces an idea of generating a kernel from an arbitrary function by embedding the training samples into the function. Based on this idea, we present two nonlinear feature extraction methods: generating kernel principal component analysis (GKPCA) and generating kernel Fisher discriminant (GKFD). These two methods are shown to be equivalent to the function-mapping-space PCA (FMS-PCA) and the function-mapping-space linear discriminant analysis (FMS-LDA) methods, respectively. This equivalence reveals that the generating kernel is actually determined by the corresponding function map. From the generating kernel point of view, we can classify the current kernel Fisher discriminant (KFD) algorithms into two categories: KPCA + LDA based algorithms and straightforward KFD (SKFD) algorithms. The KPCA + LDA based algorithms directly work on the given kernel and are not suitable for non-kernel functions, while the SKFD algorithms essentially work on the generating kernel from a given symmetric function and are therefore suitable for non-kernels as well as kernels. Finally, we outline the tensor-based feature extraction methods and discuss ways of extending tensor-based methods to their generating kernel versions.

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Section: Tensor-based Feature Extraction Methods and Their Generatingmentioning

confidence: 99%

“…Eng. China 2011, 6(1): [43][44][45][46][47][48][49][50][51][52][53][54][55] sian kernel function has been modified into a new function by replacing the Euclidean distance measure with a Chi square distance measure [30] and applied with a KFD algorithm in Ref. [19].…”

Section: Introductionmentioning

confidence: 99%

Kernel feature extraction methods observed from the viewpoint of generating-kernels

Yang

2011

Front. Electr. Electron. Eng. China

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“…After applying FWM, the reduced matrix is vectorized and canonical correlation analysis (CCA) is used to further reduce the dimension of the final feature vector using discriminative criteria. Our approach is closely related to bilinear dimensionality reduction methods such as 2D-LDA [21] and 2D-CCA [22]. A notable advantage of our method is that it is a deterministic method and no iterative optimization is required.…”

Section: Two-step Dimensionality Reduction Of Part Featuresmentioning

confidence: 99%

Efficient Two-Step Middle-Level Part Feature Extraction for Fine-Grained Visual Categorization

Nakayama

Tsuda

2016

IEICE Trans. Inf. & Syst.

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SUMMARY Fine-grained visual categorization (FGVC) has drawn increasing attention as an emerging research field in recent years. In contrast to generic-domain visual recognition, FGVC is characterized by high intraclass and subtle inter-class variations. To distinguish conceptually and visually similar categories, highly discriminative visual features must be extracted. Moreover, FGVC has highly specialized and task-specific nature. It is not always easy to obtain a sufficiently large-scale training dataset. Therefore, the key to success in practical FGVC systems is to efficiently exploit discriminative features from a limited number of training examples. In this paper, we propose an efficient two-step dimensionality compression method to derive compact middle-level part-based features. To do this, we compare both space-first and feature-first convolution schemes and investigate their effectiveness. Our approach is based on simple linear algebra and analytic solutions, and is highly scalable compared with the current onevs-one or one-vs-all approach, making it possible to quickly train middlelevel features from a number of pairwise part regions. We experimentally show the effectiveness of our method using the standard Caltech-Birds and Stanford-Cars datasets.

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“…For example, the classical CCA was extended in Lee and Choi (2007) to 2D-CCA, which directly analyzes 2D images without reshaping them into vectors. Some of its extensions are local 2D-CCA Wang (2010), sparse 2D- CCA Yan et al (2012), and multilinear CCA (MCCA) Lu (2013).…”

Section: Canonical Correlation Analysis and Its Extensionsmentioning

confidence: 99%

Tensor Canonical Correlation Analysis for Multi-View Dimension Reduction

Luo

Tao

Ramamohanarao

et al. 2015

IEEE Trans. Knowl. Data Eng.

201

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Canonical correlation analysis (CCA) has proven an effective tool for two-view dimension reduction due to its profound theoretical foundation and success in practical applications. In respect of multi-view learning, however, it is limited by its capability of only handling data represented by two-view features, while in many real-world applications, the number of views is frequently many more. Although the ad hoc way of simultaneously exploring all possible pairs of features can numerically deal with multiview data, it ignores the high order statistics (correlation information) which can only be discovered by simultaneously exploring all features.Therefore, in this work, we develop tensor CCA (TCCA) which straightforwardly yet naturally generalizes CCA to handle the data of an arbitrary number of views by analyzing the covariance tensor of the different views. TCCA aims to directly maximize the canonical correlation of multiple (more than two) views. Crucially, we prove that the multi-view canonical correlation maximization problem is equivalent to finding the best rank-1 approximation of the data covariance tensor, which can be solved efficiently using the well-known alternating least squares (ALS) algorithm. As a consequence, the high order correlation information contained in the different views is explored and thus a more reliable common subspace shared by all features can be obtained. In addition, a non-linear extension of TCCA is presented. Experiments on various challenge tasks, including large scale biometric structure prediction, internet advertisement classification and web image annotation, demonstrate the effectiveness of the proposed method.

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Two-Dimensional Canonical Correlation Analysis

Cited by 96 publications

References 8 publications

Kernel feature extraction methods observed from the viewpoint of generating-kernels

Kernel feature extraction methods observed from the viewpoint of generating-kernels

Efficient Two-Step Middle-Level Part Feature Extraction for Fine-Grained Visual Categorization

Tensor Canonical Correlation Analysis for Multi-View Dimension Reduction

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