Speed-up and multi-view extensions to subclass discriminant analysis

Chumachenko, Kateryna; Raitoharju, Jenni; Iosifidis, Alexandros; Gabbouj, Moncef

doi:10.1016/j.patcog.2020.107660

Cited by 15 publications

(3 citation statements)

References 32 publications

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“…After the DR step, a K-Nearest Neighbor classifier (k-NN) [50] is used with k = 5. For comparative purposes, we also add the performance of SVM [51], Decision Tree classifier [52], TRPCAA [53], K-Nearest Neighbor [54], RSLDA [55], and fastSDA [56], [57].…”

Section: Image Classificationmentioning

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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Section: Image Classificationmentioning

confidence: 99%

Non-Linear Spectral Dimensionality Reduction Under Uncertainty

Laakom¹,

Raitoharju²,

Passalis³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

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“…Secondly, in classical LDA, the number of extracted features is limited to the number of classes minus one, which means a severe and inappropriate reduction in the dimensionality of data [9,10,11]. The general remedy to this limitation is to use a clustering algorithm and incorporate the subclass structure into the LDA analysis [12,13,14,15] and to choose all eigenvectors with nonzero eigenvalues for feature extraction 1 . In this paper, we assume that LDA is applied to subclasses and C stands for the number of clusters.…”

Section: Introductionmentioning

confidence: 99%

Revisiting Classical Multiclass Linear Discriminant Analysis with a Novel Prototype-based Interpretable Solution

Ghiasi-Shirazi¹

2022

Preprint

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Linear discriminant analysis (LDA) is a fundamental method for feature extraction and dimensionality reduction. Despite having many variants, classical LDA has its importance, as it is a keystone in human knowledge about pattern recognition. For a dataset containing C clusters, the classical solution to LDA extracts at most C − 1 features. In this paper, we introduce a novel solution to classical LDA, called LDA++, that yields C features, each one interpretable as measuring similarity to one cluster. This novel solution bridges between dimensionality reduction and multiclass classification. Specifically, we prove that, under some mild conditions, the optimal weights of a linear multiclass classifier for homoscedastic Gaussian data also make an optimal solution to LDA. In addition, this novel interpretable solution reveals some new facts about LDA and its relation with PCA. We provide a complete numerical solution for our novel method, covering the cases 1) when the scatter matrices can be constructed explicitly, 2) when constructing the scatter matrices is infeasible, and 3) the kernel extension. The code is available at https://github.com/ k-ghiasi/LDA-plus-plus.

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“…This method is a powerful tool for developing a statistical prediction algorithm (Raudys and Young, 2004) . It has proven very successful in a variety of tasks, including recognizing, assessment of risk, identi cation, diagnosis, or classifying (Vranckx et al, 2021;Chumachenko et al, 2021;Bari and Fattah, 2020;Wang et al, 2018). This method has several models, such as Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), and Fisher Discriminant Analysis (FDA).…”

Section: Introductionmentioning

confidence: 99%

Prediction of Plastic-Type for Sorting System using Fisher Discriminant Analysis

Yani

Resti

Burlian

et al. 2021

Sci. Technol. Indones

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Recycling is a more environmentally friendly method of managing and reducing plastic waste that can significantly reduce land degradation, pollution, and greenhouse gas emissions. According to its composition, an essential first step in the recycling process is sorting out plastic waste. However, inadequate sorting of plastic types can result in cross-contamination and increasing industrial operating costs. A low-cost automated plastic sorting system can be developed by using digital image data in the red, green, and blue (RGB) color space as the dataset and predicting the type using learning datasets. The purpose of this paper is to demonstrate how to use Fisher Discriminant Analysis (FDA) to predict the plastic type from a digital image of the RGB model and then evaluate the performance using cross-validation. This work has four main steps: collecting plastic digital image data, forming statistical tests, predicting plastic types, and evaluating prediction performance. FDA is quite effective for predicting the type of plastic. Performance measures the accuracy of 87.11 %, the recall-micro of 91.67 %, the recall-micro of 80.97 %, the specificity-micro of 90.33 %, and the specificity-macro of 90.38 %, respectively. The micro is determined by the number of decisions made for each object. In comparison, the macro is calculated based on the average decision made by each class.

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Speed-up and multi-view extensions to subclass discriminant analysis

Cited by 15 publications

References 32 publications

Non-Linear Spectral Dimensionality Reduction Under Uncertainty

Non-Linear Spectral Dimensionality Reduction Under Uncertainty

Revisiting Classical Multiclass Linear Discriminant Analysis with a Novel Prototype-based Interpretable Solution

Prediction of Plastic-Type for Sorting System using Fisher Discriminant Analysis

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