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Nonparametric logistic regression based on sparse triangulation over a compact domain
Communications for Statistical Applications and Methods 2024;31:557-569
Published online September 30, 2024
© 2024 Korean Statistical Society.

Seoyeon Kima, Kwan-Young Bak1,b

aDepartment of Statistics, Sungshin Women’s University, Korea;
bSchool of Mathematics, Statistics and Data Science, Sungshin Women’s University, Korea
Correspondence to: 1 School of Mathematics, Statistics and Data Science, Sungshin Women’s University, 2 Bomun-ro 34 Da-gil, Seongbuk-gu, Seoul 02844, Korea. E-mail: kybak@sungshin.ac.kr
This research was supported by National Research Foundation (NRF) of Korea, RS-2022-00165581.
Received February 21, 2024; Revised April 22, 2024; Accepted April 26, 2024.
 Abstract
Based on the investigation of logistic regression models utilizing sparse triangulation within a compact domain in ℝ2, this study addresses the limited research extending the triogram model to logistic regression. A primary challenge arises from the potential instability induced by a large number of vertices, hindering the effective modeling of complex relationships. To mitigate this challenge, we propose introducing sparsity to boundary vertices of the triangulation based on the Ramer-Douglas-Peucker algorithm and employing the K-means algorithm for adaptive vertex initialization. A second order coordinate-wise descent algorithm is adopted to implement the proposed method. Validation of the proposed algorithm’s stability and performance assessment are conducted using synthetic and handwritten digit data (LeCun et al., 1989). Results demonstrate the advantages of our method over existing methodologies, particularly when dealing with non-rectangular data domains.
Keywords : barycentric coordinates, coordinate descent algorithm, logistic regression, RDP algorithm, triangulation