Locality Adaptive Discriminant Analysis

Li, Xuelong; Chen, Mulin; Nie, Feiping; Wang, Qi

doi:10.24963/ijcai.2017/306

Cited by 137 publications

(43 citation statements)

References 18 publications

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“…Examples of the mapping function include unsupervised dimensionality reductions, such as principal component analysis (PCA) (Pearson 1901;Jolliffe 1986); locality preserving projections (LPP) (He and Niyogi 2004); and supervised dimensionality reductions, such as Fisher discriminant analysis (FDA) (Fisher 1936), local FDA (LFDA) (Sugiyama 2007), semi-supervised LFDA (SELF) (Sugiyama et al 2010), locality adaptive discriminant analysis (LADA) (Li et al 2017); and complex moment-based supervised eigenmap (CMSE) (Imakura et al 2019). One can also consider a partial structure of deep neural networks.…”

Section: Fundamental Concept and Frameworkmentioning

confidence: 99%

Data Collaboration Analysis Framework Using Centralization of Individual Intermediate Representations for Distributed Data Sets

Imakura

Sakurai

2020

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

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This paper proposes a data collaboration analysis framework for distributed data sets. The proposed framework involves centralized machine learning while the original data sets and models remain distributed over a number of institutions. Recently, data has become larger and more distributed with decreasing costs of data collection. Centralizing distributed data sets and analyzing them as one data set can allow for novel insights and attainment of higher prediction performance than that of analyzing distributed data sets individually. However, it is generally difficult to centralize the original data sets because of a large data size or privacy concerns. This paper proposes a data collaboration analysis framework that does not involve sharing the original data sets to circumvent these difficulties. The proposed framework only centralizes intermediate representations constructed individually rather than the original data set. The proposed framework does not use privacy-preserving computations or model centralization. In addition, this paper proposes a practical algorithm within the framework. Numerical experiments reveal that the proposed method achieves higher recognition performance for artificial and real-world problems than individual analysis.

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Section: Fundamental Concept and Frameworkmentioning

confidence: 99%

Data Collaboration Analysis Framework Using Centralization of Individual Intermediate Representations for Distributed Data Sets

Imakura

Sakurai

2020

ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.

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“…We compare the proposed method (SFS) with previous supervised dimensionality reduction methods in terms of accuracy by numerical experiments on artificial data and practical datasets and show that the proposed method outperforms previous methods in some cases, and is more robust than the previous methods. The previous methods were kernel versions of LDA (KDA) [2,6] and LFDA (KLFDA) [25] and LADA [17]. The performance measures used for comparisons were overall accuracy (OA), average accuracy (AA), and normalized mutual information (NMI) [%] [23].…”

Section: Numerical Experimentsmentioning

confidence: 99%

Spectral Feature Scaling Method for Supervised Dimensionality Reduction

Matsuda

Morikuni

Sakurai

2018

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence

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Irregular features disrupt the desired classification. In this paper, we consider aggressively modifying scales of features in the original space according to the label information to form wellseparated clusters in low-dimensional space. The proposed method exploits spectral clustering to derive scaling factors that are used to modify the features. Specifically, we reformulate the Laplacian eigenproblem of the spectral clustering as an eigenproblem of a linear matrix pencil whose eigenvector has the scaling factors. Numerical experiments show that the proposed method outperforms well-established supervised dimensionality reduction methods for toy problems with more samples than features and real-world problems with more features than samples.

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“…A family of discriminant analysis methods are proposed for dimensionality reduction, including Fisher discriminant analysis (FDA) (Fisher 1936;Fukunaga 2013), local FDA (LFDA) (Sugiyama 2007), semi-supervised LFDA (SELF) (Sugiyama et al 2010) and locality adaptive discriminant analysis (LADA) (Li et al 2017).…”

Section: Introductionmentioning

confidence: 99%

Complex Moment-Based Supervised Eigenmap for Dimensionality Reduction

Imakura

Matsuda

et al. 2019

AAAI

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Dimensionality reduction methods that project highdimensional data to a low-dimensional space by matrix trace optimization are widely used for clustering and classification. The matrix trace optimization problem leads to an eigenvalue problem for a low-dimensional subspace construction, preserving certain properties of the original data. However, most of the existing methods use only a few eigenvectors to construct the low-dimensional space, which may lead to a loss of useful information for achieving successful classification. Herein, to overcome the deficiency of the information loss, we propose a novel complex moment-based supervised eigenmap including multiple eigenvectors for dimensionality reduction. Furthermore, the proposed method provides a general formulation for matrix trace optimization methods to incorporate with ridge regression, which models the linear dependency between covariate variables and univariate labels. To reduce the computational complexity, we also propose an efficient and parallel implementation of the proposed method. Numerical experiments indicate that the proposed method is competitive compared with the existing dimensionality reduction methods for the recognition performance. Additionally, the proposed method exhibits high parallel efficiency.

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Locality Adaptive Discriminant Analysis

Cited by 137 publications

References 18 publications

Data Collaboration Analysis Framework Using Centralization of Individual Intermediate Representations for Distributed Data Sets

Data Collaboration Analysis Framework Using Centralization of Individual Intermediate Representations for Distributed Data Sets

Spectral Feature Scaling Method for Supervised Dimensionality Reduction

Complex Moment-Based Supervised Eigenmap for Dimensionality Reduction

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