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Ratio Sum Versus Sum Ratio for Linear Discriminant Analysis

Dimension reduction is a critical technology for high-dimensional data processing, where Linear Discriminant Analysis (LDA) and its variants are effective supervised methods. However, LDA prefers to feature with smaller variance, which causes feature with weak discriminative ability retained. In this paper, we propose a novel Ratio Sum for Linear Discriminant Analysis (RSLDA), which aims at maximizing discriminative ability of each feature in subspace. To be specific, it maximizes the sum of ratio of the between-class distance to the within-class distance in each dimension of subspace. Since the original RSLDA problem is difficult to obtain the closed solution, an equivalent problem is developed which can be solved by an alternative optimization algorithm. For solving the equivalent problem, it is transformed into two sub-problems, one of which can be solved directly, the other is changed into a convex optimization problem, where singular value decomposition is employed instead of matrix inversion. Consequently, performance of algorithm cannot be affected by the non-singularity of covariance matrix. Furthermore, Kernel RSLDA (KRSLDA) is presented to improve the robustness of RSLDA. Additionally, time complexity of RSLDA and KRSLDA are analyzed. Extensive experiments show that RSLDA and KRSLDA outperforms other comparison methods on toy datasets and multiple public datasets.

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Informasi Detail

Judul Seri

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE; Vol.44 No.12 Part 3 December 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 10171-10185

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

LINEAR DISCRIMINANT ANALYSIS
SUPERVISED LEARNING
DIMENSIONALITY REDUCTION
SUBSPACE LEARNING
RATIO SUM PROBLEM
KERNEL TECHNIQUE

Info Detail Spesifik

10.1109/TPAMI.2021.3133351

Pernyataan Tanggungjawab

Jingyu Wang, Hongmei Wang, Feiping Nie, Xuelong Li

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