Angle-Based Hierarchical Classification Using Exact Label Embedding

Fan, Yiwei; Lü, Xiaoling; Liu, Yufeng; Zhao, Junwei

doi:10.1080/01621459.2020.1801450

Cited by 3 publications

(10 citation statements)

References 26 publications

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“…A desired embedding approach is to embed nodes into points in a low-dimensional space while keeping the hierarchical properties exactly. To achieve these two goals, Fan et al [9] proposed a new label embedding method, which is summarized as follows.…”

Section: L(a)mentioning

confidence: 99%

“…To construct points in hierarchical classification, Fan et al [9] first introduced an algorithm to embed nodes in a standard q-class multicategory classification problem. Algorithm S1 in the Appendix gives the detailed procedure.…”

Section: L(a)mentioning

confidence: 99%

“…To satisfy H. S. properties, it is required that δ 2 ≥ 2 √ 2 + 2 in Proposition S1. We set L (1) = 1 and δ = √ 5 as suggested by Fan et al [9]. For the example shown in FIG 1, we begin from the second layer and construct two points −1 and 1 by Algorithm S1 given L (1) = 1.…”

Section: L(a)mentioning

confidence: 99%

“…Besides the methods mentioned above, several methods on label embedding have been developed for hierarchical classification [3,29], which map nodes into a set of points in the Euclidean space, such that the Euclidean distances among these points mimic the dissimilarities among the nodes. Recently, Fan et al [9] has pointed out that the classical label embedding fails to keep the hierarchy well and can be inefficient because of the high dimension of the embedded space. To overcome these drawbacks, Fan et al [9] proposed a label embedding method, which keeps the hierarchy exactly and reduces the dimension of the embedded space to m leaf −1 with m leaf being the number of leaf nodes.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Fan et al [9] has pointed out that the classical label embedding fails to keep the hierarchy well and can be inefficient because of the high dimension of the embedded space. To overcome these drawbacks, Fan et al [9] proposed a label embedding method, which keeps the hierarchy exactly and reduces the dimension of the embedded space to m leaf −1 with m leaf being the number of leaf nodes. Despite this method has great advantages in hierarchical classification, how to utilize it in OWL to estimate ITRs for hierarchical treatments remains unclear.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Estimating individualized treatment rules for treatments with hierarchical structure

Fan

Lü

Zhao

et al. 2022

Electron. J. Statist.

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Precision medicine is an increasingly important area of research. Due to the heterogeneity of individual characteristics, patients may respond differently to treatments. One of the most important goals for precision medicine is to develop individualized treatment rules (ITRs) involving patients' characteristics directly. As an interesting topic in clinical research, many statistical methods have been developed in recent years to find optimal ITRs. For binary treatments, outcome weighted learning (OWL) was proposed to find a decision function of patient characteristics maximizing the expected clinical outcome. Treatments with hierarchical structure are commonly seen in practice. In hierarchical scenarios, how to estimate ITRs is still unclear. We propose a new framework named hierarchical outcome-weighted angle-based learning (HOAL) to estimate ITRs for treatments with hierarchical structure. Statistical properties including Fisher consistency and convergence rates of the proposed method are presented. Simulations and an application to a type 2 diabetes study under linear and nonlinear learning show the highly competitive performance of our proposed procedure in both numerical accuracy and computational efficiency.

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Section: L(a)mentioning

confidence: 99%

Section: L(a)mentioning

confidence: 99%

Section: L(a)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimating individualized treatment rules for treatments with hierarchical structure

Fan

Lü

Zhao

et al. 2022

Electron. J. Statist.

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Safe sample screening rules for multicategory angle-based support vector machines

Fan

Zhao

2022

Computational Statistics & Data Analysis

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Simplex-Based Proximal Multicategory Support Vector Machine

Chen

2023

IEEE Trans. Inform. Theory

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The multicategory support vector machine (MSVM) has been widely used for multicategory classification. Despite its widespread popularity, regular MSVM cannot provide direct probabilistic results and suffers from excessive computational cost, as it is formulated on the hinge loss function and it solves a sum-to-zero constrained quadratic programming problem. In this study, we propose a general refinement of regular MSVM, termed as the simplex-based proximal MSVM (SPMSVM). Our SPMSVM uses a novel family of squared error loss functions in place of the hinge loss and it removes the explicit sum-to-zero constraint by the simplex structure. Consequently, the SPMSVM only requires solving an unconstrained linear system, leading to closed-form solutions. In addition, the SPMSVM can be cast into a weighted regression problem so that it is scalable for largescale applications. Moreover, the SPMSVM naturally yields an estimate of the conditional category probability, which is more informative than regular MSVM. Theoretically, the SPMSVM is shown to include many existing MSVMs as its special cases, and its asymptotic and finite-sample statistical properties are well established. Simulations and real examples show that the proposed SPMSVM is a stable, scalable and competitive classifier.

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Angle-Based Hierarchical Classification Using Exact Label Embedding

Cited by 3 publications

References 26 publications

Estimating individualized treatment rules for treatments with hierarchical structure

Estimating individualized treatment rules for treatments with hierarchical structure

Safe sample screening rules for multicategory angle-based support vector machines

Simplex-Based Proximal Multicategory Support Vector Machine

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