Robust Fast Subclass Discriminant Analysis

Chumachenko, Kateryna; Iosifidis, Alexandros; Gabbouj, Moncef

doi:10.23919/eusipco47968.2020.9287557

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…Next, to address the small sample size problem of the FDA, various works have been done on sparse FDA [14]- [17]. Another group of FDA variants is for FDA with imbalanced data [18]- [20]. To deal with multimodal data, Sugiyama et al [21] presented Local Fisher Discriminant Analysis, and Kim et al [22] introduced kernel MFDA.…”

Section: Denotes Equal Contributionmentioning

confidence: 99%

“…Another group of FDA variants consists of the FDA variants for imbalanced data [18]- [20]. Fast Subclass Discriminant Analysis and Subclass Discriminant Analysis [18] allow one to put more attention on under-represented classes or classes that are likely to be confused with each other. [19] focused on Uncorrelated Linear Discriminant Analysis for imbalanced data.…”

Section: Related Workmentioning

confidence: 99%

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Unequal Covariance Awareness for Fisher Discriminant Analysis and Its Variants in Classification

Nguyen¹,

Le²,

Tu³

et al. 2022

Preprint

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Fisher Discriminant Analysis (FDA) is one of the essential tools for feature extraction and classification. In addition, it motivates the development of many improved techniques based on the FDA to adapt to different problems or data types. However, none of these approaches make use of the fact that the assumption of equal covariance matrices in FDA is usually not satisfied in practical situations. Therefore, we propose a novel classification rule for the FDA that accounts for this fact, mitigating the effect of unequal covariance matrices in the FDA. Furthermore, since we only modify the classification rule, the same can be applied to many FDA variants, improving these algorithms further. Theoretical analysis reveals that the new classification rule allows the implicit use of the class covariance matrices while increasing the number of parameters to be estimated by a small amount compared to going from FDA to Quadratic Discriminant Analysis. We illustrate our idea via experiments, which shows the superior performance of the modified algorithms based on our new classification rule compared to the original ones.

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Section: Denotes Equal Contributionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Unequal Covariance Awareness for Fisher Discriminant Analysis and Its Variants in Classification

Nguyen¹,

Le²,

Tu³

et al. 2022

Preprint

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“…Thus, they need to be discarded and not used to learn the low-dimensional embedding [16]. Various DR methods have been extended based on this assumption, for examples the approaches in [17], [18], [19], [20] for Linear Discriminant Analysis (LDA) [21] and the approaches in [22], [23], [24], [25] for Principal Component Analysis (PCA) [26].…”

Section: Introductionmentioning

confidence: 99%

Non-Linear Spectral Dimensionality Reduction Under Uncertainty

Laakom¹,

Raitoharju²,

Passalis³

et al. 2022

Preprint

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In this paper, we consider the problem of non-linear dimensionality reduction under uncertainty, both from a theoretical and algorithmic perspectives. Since real-world data usually contain measurements with uncertainties and artifacts, the input space in the proposed framework consists of probability distributions to model the uncertainties associated with each sample. We propose a new dimensionality reduction framework, called NGEU, which leverages uncertainty information and directly extends several traditional approaches, e.g., KPCA, MDA/KMFA, to receive as inputs the probability distributions instead of the original data. We show that the proposed NGEU formulation exhibits a global closed-form solution, and we analyze, based on the Rademacher complexity, how the underlying uncertainties theoretically affect the generalization ability of the framework. Empirical results on different datasets show the effectiveness of the proposed framework.

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