LDL

LDL refers to label distribution learning. Its definition can be as follows:

Let \(\mathcal{X} = \mathbb{R}^{q}\) denote the input space and \(\mathcal{Y} = \lbrace y_i \rbrace_{i=1}^{c}\) denote the label space, where \(q\) is the dimensionality of the input space and \(c\) is the number of labels. The description degree of \(y \in \mathcal{Y}\) to \(\boldsymbol{x} \in \mathcal{X}\) is denoted by \(d_{\boldsymbol{x}}^{y}\). Then the label distribution of \(\boldsymbol{x}\) is denoted by \(\boldsymbol{d} = \lbrace d_{\boldsymbol{x}}^{y} \rbrace_{y \in \mathcal{Y}}\). It is under the constraints of probability simplex, i.e., \(\boldsymbol{d} \in \Delta^{c-1}\), where

\[\Delta^{l-1} = \lbrace \boldsymbol{d} \in \mathbb{R}^{l} \,|\, \boldsymbol{d} \geq 0,\, \boldsymbol{d}^{\top} \boldsymbol{1} = 1 \rbrace\text{.}\]

Given a training set of \(n\) samples \(\mathcal{S} = \lbrace \boldsymbol{X},\, \boldsymbol{D} \rbrace = \lbrace (\boldsymbol{x}_i,\, \boldsymbol{d}_i) \rbrace_{i=1}^{n}\), the goal of LDL is to learn a mapping function \(f: \mathcal{X} \to \Delta^{c-1}\) that minimizes the discrepancy between predicted and true label distributions. The performance of \(f\) is ultimately evaluated on a test set, typically by distance/similarity measures.

BaseLDL

class pyldl.algorithms.base.BaseLDL(**kwargs)

Base class for all LDL models in PyLDL.

RG4LDL

class pyldl.algorithms.RG4LDL(estimator=None, *, n_hidden: int = 64, **kwargs)

RG4LDL is proposed in paper [LDL-TCZ+25].

R\(k\)NN-LDL

class pyldl.algorithms.RKNN_LDL(*args, **kwargs)

RkNN-LDL is proposed in paper [LDL-WFLG25]. R\(k\)NN refers to residual \(k\)-nearest neighbor.

SNEFY-LDL

class pyldl.algorithms.SNEFY_LDL(*args, **kwargs)

SNEFY-LDL is proposed in paper [LDL-ZTS25]. SNEFY refers to squared neural family.

\(\mathcal{S}\)-LDL

class pyldl.algorithms._S_LDL(combi, t, lam)

Base class for \(\mathcal{S}\)-LDL algorithms, which are proposed in paper [LDL-WLJ25]. \(\mathcal{S}\) refers to subtasks.

\(\mathcal{S}\)-LRR

class pyldl.algorithms.S_LRR(*args, **kwargs)

\(\mathcal{S}\)-SCL

class pyldl.algorithms.S_SCL(*args, **kwargs)

\(\mathcal{S}\)-KLD

class pyldl.algorithms.S_KLD(*args, **kwargs)

\(\mathcal{S}\)-CJS

class pyldl.algorithms.S_CJS(*args, **kwargs)

\(\mathcal{S}\)-QFD\(^{2}\)

class pyldl.algorithms.S_QFD2(*args, **kwargs)

Shallow \(\mathcal{S}\)-LDL

class pyldl.algorithms.Shallow_S_LDL(estimator=None, combi=None, t=10, lam=0.2, **kwargs)

\(\delta\)-LDL

class pyldl.algorithms.Delta_LDL(*args, **kwargs)

Delta-LDL is proposed in paper [LDL-LWLJ25].

LDL-HVLC

class pyldl.algorithms.LDL_HVLC(*args, **kwargs)

LDL-HVLC is proposed in paper [LDL-LLW+24]. HVLC refers to horizontal & vertical label correlation.

LRLDL

class pyldl.algorithms._LRLDL(mode='threshold', param=None, alpha=0.001, beta=0.001, random_state=None)

Base class for pyldl.algorithms.TLRLDL and pyldl.algorithms.TKLRLDL, which are proposed in paper [LDL-KWT+24]. LR refers to low-rank.

ADMM is used as optimization algorithm.

_update_V()

Please note that Eq. (11) in paper [LDL-KWT+24] should be corrected to:

\[\boldsymbol{\Gamma}_1 \leftarrow \boldsymbol{\Gamma}_1 + \mu \left(\boldsymbol{W}\boldsymbol{X}^{\top}\boldsymbol{O} - \boldsymbol{G}\right)\text{.}\]

_update_W()

Please note that Eq. (8) in paper [LDL-KWT+24] should be corrected to:

\[\begin{split}\begin{aligned} \boldsymbol{W} \leftarrow & \left(\left(\mu \boldsymbol{G} + \boldsymbol{\Gamma}_1 + \boldsymbol{L}\right) \boldsymbol{O}^{\top} \boldsymbol{X} + \boldsymbol{D}\boldsymbol{X} \right) \\ & \left( \boldsymbol{X}^{\top}\boldsymbol{X} + 2 \lambda \boldsymbol{I} + (1+\mu) \boldsymbol{X}^{\top}\boldsymbol{O}\boldsymbol{O}^{\top}\boldsymbol{X} \right)^{-1}\text{,} \end{aligned}\end{split}\]

where \(\\boldsymbol{I}\) is the identity matrix.

And Eq. (10) should be corrected to:

\[\begin{split}\begin{aligned} \boldsymbol{O} \leftarrow & \left( (1+\mu) \boldsymbol{X}\boldsymbol{W}^{\top} \left( \boldsymbol{X}\boldsymbol{W}^{\top} \right)^{\top} + 2 \lambda \boldsymbol{I} \right)^{-1} \\ & \boldsymbol{X}\boldsymbol{W}^{\top} \left(\boldsymbol{L} + \mu \boldsymbol{G} - \boldsymbol{\Gamma}_1\right)\text{.} \end{aligned}\end{split}\]

TKLRLDL

class pyldl.algorithms.TKLRLDL(**kwargs)

TKLRLDL is proposed in paper [LDL-KWT+24]. TK refers to top-\(k\) (a top-\(k\) binaryzation method is used to generate the logical label matrix).

TLRLDL

class pyldl.algorithms.TLRLDL(**kwargs)

TLRLDL is proposed in paper [LDL-KWT+24]. T refers to threshold (a threshold-based binaryzation method is used to generate the logical label matrix).

LDL-DPA

class pyldl.algorithms.LDL_DPA(*args, **kwargs)

LDL-DPA is proposed in paper [LDL-JQLL24]. DPA refers to description-degree percentile average.

BFGS is used as the optimization algorithm.

LDL-LRR

class pyldl.algorithms.LDL_LRR(*args, **kwargs)

LDL-LRR is proposed in paper [LDL-JSL+23]. LRR refers to label ranking relation.

BFGS is used as the optimization algorithm.

DF-LDL

class pyldl.algorithms.DF_LDL(estimator=None, *, k: int = 5, **kwargs)

DF-LDL is proposed in paper [LDL-GGAT+21].

LDL-SCL

class pyldl.algorithms.LDL_SCL(*args, **kwargs)

LDL-SCL is proposed in paper [LDL-ZJL18].

Adam is used as optimizer.

See also:

[LDL-SCL-JLZ+21]

Xiuyi Jia, Zechao Li, Xiang Zheng, Weiwei Li, and Sheng-Jun Huang. Label distribution learning with label correlations on local samples. IEEE Transactions on Knowledge and Data Engineering, 33(4):1619–1631, 2021. URL: https://doi.org/10.1109/TKDE.2019.2943337.

Duo-LDL

class pyldl.algorithms.Duo_LDL(*args, **kwargs)

Duo-LDL is proposed in paper [LDL-ZM21].

BD-LDL

class pyldl.algorithms.BD_LDL(*, alpha: float = 0.001, beta: float = 0.01, **kwargs)

BD-LDL is proposed in paper [LDL-LZZ+21].

LDL-LCLR

class pyldl.algorithms.LDL_LCLR(n_clusters=4, alpha=0.0001, beta=0.0001, gamma=0.0001, delta=0.0001, **kwargs)

LDL-LCLR is proposed in paper [LDL-RJLZ19].

ADMM is used as the optimization algorithm.

_update_W()

Please note that Eq. (9) in paper [LDL-RJLZ19] should be corrected to:

\[\begin{split}\begin{aligned} \nabla_\boldsymbol{W} = & \boldsymbol{X}^{\top} \left(\hat{\boldsymbol{D}} - \boldsymbol{D}\right) + 2 \lambda_1 \boldsymbol{W} - \boldsymbol{X}^{\top} \left(\left(\hat{\boldsymbol{D}} - \hat{\boldsymbol{D}}^2\right) \odot \boldsymbol{\Gamma}_1\right) \boldsymbol{S}^{\top} \\ - & \rho \boldsymbol{X}^{\top} \left(\left(\hat{\boldsymbol{D}} - \hat{\boldsymbol{D}}^2\right) \odot \left(\boldsymbol{D} - \hat{\boldsymbol{D}}\boldsymbol{S} - \boldsymbol{E}\right)\right) \boldsymbol{S}^{\top}\text{,} \end{aligned}\end{split}\]

where \(\odot\) denotes element-wise multiplication.

LDLSF

class pyldl.algorithms.LDLSF(alpha=0.0001, beta=0.01, gamma=0.001, **kwargs)

LDLSF is proposed in paper [LDL-RJL+19]. SF refers to specific features.

ADMM is used as optimization algorithm.

LDLLC

class pyldl.algorithms.LDLLC(*args, **kwargs)

LDLLC is proposed in paper [LDL-JLLZ18].

BFGS is used as optimization algorithm.

LALOT

class pyldl.algorithms.LALOT(*, alpha: float = 0.2, beta: float = 200.0, **kwargs)

LALOT is proposed in paper [LDL-ZZ18].

StructRF

class pyldl.algorithms.StructRF(estimator=None, n_estimators=20, sampling_ratio=0.8, **kwargs)

StructRF is proposed in paper [LDL-CWFL18].

class StructTree(max_depth=20, min_to_split=5, alpha=0.25, beta=8.0, **kwargs)

StructTree is proposed in paper [LDL-CWFL18].

BCPNN

class pyldl.algorithms.BCPNN(*args, **kwargs)

BCPNN is proposed in paper [LDL-YSS17].

RProp is used as the optimizer.

This algorithm is based on CPNN. See also:

[BCPNN-GYZ13]

Xin Geng, Chao Yin, and Zhi-Hua Zhou. Facial age estimation by learning from label distributions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(10):2401–2412, 2013. URL: https://doi.org/10.1109/TPAMI.2013.51.

ACPNN

class pyldl.algorithms.ACPNN(*args, **kwargs)

ACPNN is proposed in paper [LDL-YSS17].

RProp is used as the optimizer.

This algorithm is based on CPNN. See also:

[ACPNN-GYZ13]

Xin Geng, Chao Yin, and Zhi-Hua Zhou. Facial age estimation by learning from label distributions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(10):2401–2412, 2013. URL: https://doi.org/10.1109/TPAMI.2013.51.

LDLF

class pyldl.algorithms.LDLF(*args, **kwargs)

LDLF is proposed in paper [LDL-SZGY17].

Adam is used as the optimizer.

This algorithm employs deep neural decision forests. See also:

[LDLF-KFCB15]

Peter Kontschieder, Madalina Fiterau, Antonio Criminisi, and Samuel Rota Bulo. Deep neural decision forests. In Proceedings of the IEEE/CVF International Conference on Computer Vision, 1467–1475. 2015. URL: https://doi.org/10.1109/ICCV.2015.172.

LDLogitBoost

class pyldl.algorithms.LDLogitBoost(estimator=None, n_estimators=100, **kwargs)

LDLogitBoost is proposed in paper [LDL-XGX16].

SA

class pyldl.algorithms._SA(**kwargs)

Base class for pyldl.algorithms.SA_IIS and pyldl.algorithms.SA_BFGS.

SA refers to specialized algorithms, where MaxEnt is employed as model.

SA-BFGS

class pyldl.algorithms.SA_BFGS(**kwargs)

SA-BFGS is proposed in paper [LDL-Gen16].

BFGS is used as optimization algorithm.

SA-IIS

class pyldl.algorithms.SA_IIS(**kwargs)

SA-IIS is proposed in paper [LDL-Gen16].

IIS is used as optimization algorithm.

IIS-LLD is the early version of SA-IIS. See also:

[SA-IIS-GYZ13]

Xin Geng, Chao Yin, and Zhi-Hua Zhou. Facial age estimation by learning from label distributions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(10):2401–2412, 2013. URL: https://doi.org/10.1109/TPAMI.2013.51.

[SA-IIS-GSMZ10]

Xin Geng, Kate Smith-Miles, and Zhi-Hua Zhou. Facial age estimation by learning from label distributions. In Proceedings of the AAAI Conference on Artificial Intelligence, 451–456. 2010. URL: https://doi.org/10.1609/aaai.v24i1.7657.

[SA-IIS-ZWG15]

Zhaoxiang Zhang, Mo Wang, and Xin Geng. Crowd counting in public video surveillance by label distribution learning. Neurocomputing, 166:151–163, 2015. URL: https://doi.org/10.1016/j.neucom.2015.03.083.

AA

AA refers to algorithm adaptation.

AA-\(k\)NN

class pyldl.algorithms.AA_KNN(*, k: int = 5, **kwargs)

AA-kNN is proposed in paper [LDL-Gen16].

AA-BP

class pyldl.algorithms.AA_BP(*args, **kwargs)

AA-BP is proposed in paper [LDL-Gen16].

PT

class pyldl.algorithms._PT(**kwargs)

Base class for pyldl.algorithms.PT_Bayes and pyldl.algorithms.PT_SVM.

PT refers to problem transformation.

PT-Bayes

class pyldl.algorithms.PT_Bayes(var_smoothing: float = 0.1, **kwargs)

PT-Bayes is proposed in paper [LDL-Gen16].

PT-SVM

class pyldl.algorithms.PT_SVM(**kwargs)

PT-SVM is proposed in paper [LDL-Gen16].

LDSVR

class pyldl.algorithms.LDSVR(**kwargs)

LDSVR is proposed in paper [LDL-GH15].

CPNN

class pyldl.algorithms.CPNN(*args, **kwargs)

CPNN is proposed in paper [LDL-GYZ13].

RProp is used as the optimizer.

cad

pyldl.algorithms.loss_function_engineering.cad(D, D_pred)

This loss function is proposed in paper [LDL-WZYY23].

cjs

pyldl.algorithms.loss_function_engineering.cjs(D, D_pred)

This loss function is proposed in paper [LDL-WZYY23].

concentrated_loss

pyldl.algorithms.loss_function_engineering.concentrated_loss(y, D_pred)

This loss function is proposed in paper [LDL-LWY+22].

qfd2

pyldl.algorithms.loss_function_engineering.qfd2(D, D_pred)

This loss function is proposed in paper [LDL-WZYY23].

unimodal_loss

pyldl.algorithms.loss_function_engineering.unimodal_loss(y, D_pred)

This loss function is proposed in paper [LDL-LWY+22].

References

[LDL-TCZ+25]

Chao Tan, Sheng Chen, Jiaxi Zhang, Zilong Xu, Xin Geng, and Genlin Ji. RG4LDL: renormalization group for label distribution learning. Knowledge-Based Systems, 320:113666, 2025. URL: https://doi.org/10.1016/j.knosys.2025.113666.

[LDL-WFLG25]

Jing Wang, Fu Feng, Jianhui Lv, and Xin Geng. Residual k-nearest neighbors label distribution learning. Pattern Recognition, 158:111006, 2025. URL: https://doi.org/10.1016/j.patcog.2024.111006.

[LDL-ZTS25]

Daokun Zhang, Russell Tsuchida, and Dino Sejdinovic. Label distribution learning using the squared neural family on the probability simplex. In Proceedings of the Conference on Uncertainty in Artificial Intelligence, 4872–4888. 2025.

[LDL-WLJ25]

Haitao Wu, Weiwei Li, and Xiuyi Jia. Divide and conquer: learning label distribution with subtasks. In Proceedings of the International Conference on Machine Learning, 67408–67426. 2025. URL: https://proceedings.mlr.press/v267/wu25p.html.

[LDL-LWLJ25]

Weiwei Li, Haitao Wu, Yunan Lu, and Xiuyi Jia. Approximately correct label distribution learning. In Proceedings of the International Conference on Machine Learning, 36298–36309. 2025.

[LDL-LLW+24]

Yaojin Lin, Yulin Li, Chenxi Wang, Lei Guo, and Jinkun Chen. Label distribution learning based on horizontal and vertical mining of label correlations. IEEE Transactions on Big Data, 10(3):275–287, 2024. URL: https://doi.org/10.1109/TBDATA.2023.3338023.

[LDL-KWT+24] (1,2,3,4,5)

Zhiqiang Kou, Jing Wang, Jiawei Tang, Yuheng Jia, Boyu Shi, and Xin Geng. Exploiting multi-label correlation in label distribution learning. In Proceedings of the International Joint Conference on Artificial Intelligence, 4326–4334. 2024. URL: https://doi.org/10.24963/ijcai.2024/478.

[LDL-JQLL24]

Xiuyi Jia, Tian Qin, Yunan Lu, and Weiwei Li. Adaptive weighted ranking-oriented label distribution learning. IEEE Transactions on Neural Networks and Learning Systems, 35(8):11302–11316, 2024. URL: https://doi.org/10.1109/TNNLS.2023.3258976.

[LDL-JSL+23]

Xiuyi Jia, Xiaoxia Shen, Weiwei Li, Yunan Lu, and Jihua Zhu. Label distribution learning by maintaining label ranking relation. IEEE Transactions on Knowledge and Data Engineering, 35(2):1695–1707, 2023. URL: https://doi.org/10.1109/TKDE.2021.3099294.

[LDL-GGAT+21]

Manuel González, Germán González-Almagro, Isaac Triguero, José-Ramón Cano, and Salvador García. Decomposition-fusion for label distribution learning. Information Fusion, 66:64–75, 2021. URL: https://doi.org/10.1016/j.inffus.2020.08.024.

[LDL-ZJL18]

Xiang Zheng, Xiuyi Jia, and Weiwei Li. Label distribution learning by exploiting sample correlations locally. In Proceedings of the AAAI Conference on Artificial Intelligence, 4556–4563. 2018. URL: https://doi.org/10.1609/aaai.v32i1.11693.

[LDL-ZM21]

Adam Żychowski and Jacek Mańdziuk. Duo-ldl method for label distribution learning based on pairwise class dependencies. Applied Soft Computing, 110:107585, 2021. URL: https://doi.org/10.1016/j.asoc.2021.107585.

[LDL-LZZ+21]

Xinyuan Liu, Jihua Zhu, Qinghai Zheng, Zhongyu Li, Ruixin Liu, and Jun Wang. Bidirectional loss function for label enhancement and distribution learning. Knowledge-Based Systems, 213:106690, 2021. URL: https://doi.org/10.1016/j.knosys.2020.106690.

[LDL-RJLZ19] (1,2)

Tingting Ren, Xiuyi Jia, Weiwei Li, and Shu Zhao. Label distribution learning with label correlations via low-rank approximation. In Proceedings of the International Joint Conference on Artificial Intelligence, 3325–3331. 2019. URL: https://doi.org/10.24963/ijcai.2019/461.

[LDL-RJL+19]

Tingting Ren, Xiuyi Jia, Weiwei Li, Lei Chen, and Zechao Li. Label distribution learning with label-specific features. In Proceedings of the International Joint Conference on Artificial Intelligence, 3318–3324. 2019. URL: https://doi.org/10.24963/ijcai.2019/460.

[LDL-JLLZ18]

Xiuyi Jia, Weiwei Li, Junyu Liu, and Yu Zhang. Label distribution learning by exploiting label correlations. In Proceedings of the AAAI Conference on Artificial Intelligence, 3310–3317. 2018. URL: https://doi.org/10.1609/aaai.v32i1.11664.

[LDL-ZZ18]

Peng Zhao and Zhi-Hua Zhou. Label distribution learning by optimal transport. In Proceedings of the AAAI Conference on Artificial Intelligence, 4506–4513. 2018. URL: https://doi.org/10.1609/aaai.v32i1.11609.

[LDL-CWFL18] (1,2)

Mengting Chen, Xinggang Wang, Bin Feng, and Wenyu Liu. Structured random forest for label distribution learning. Neurocomputing, 320:171–182, 2018. URL: https://doi.org/10.1016/j.neucom.2018.09.002.

[LDL-YSS17] (1,2)

Jufeng Yang, Ming Sun, and Xiaoxiao Sun. Learning visual sentiment distributions via augmented conditional probability neural network. In Proceedings of the AAAI Conference on Artificial Intelligence, 224–230. 2017. URL: https://doi.org/10.1609/aaai.v31i1.10485.

[LDL-SZGY17]

Wei Shen, Kai Zhao, Yilu Guo, and Alan Yuille. Label distribution learning forests. In Advances in Neural Information Processing Systems, 834–843. 2017.

[LDL-XGX16]

Chao Xing, Xin Geng, and Hui Xue. Logistic boosting regression for label distribution learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 4489–4497. 2016. URL: https://doi.org/10.1109/CVPR.2016.486.

[LDL-Gen16] (1,2,3,4,5,6)

Xin Geng. Label distribution learning. IEEE Transactions on Knowledge and Data Engineering, 28(7):1734–1748, 2016. URL: https://doi.org/10.1109/TKDE.2016.2545658.

[LDL-GH15]

Xin Geng and Peng Hou. Pre-release prediction of crowd opinion on movies by label distribution learning. In Proceedings of the International Joint Conference on Artificial Intelligence, 3511–3517. 2015.

[LDL-GYZ13]

Xin Geng, Chao Yin, and Zhi-Hua Zhou. Facial age estimation by learning from label distributions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(10):2401–2412, 2013. URL: https://doi.org/10.1109/TPAMI.2013.51.

[LDL-WZYY23] (1,2,3)

Changsong Wen, Xin Zhang, Xingxu Yao, and Jufeng Yang. Ordinal label distribution learning. In Proceedings of the IEEE/CVF International Conference on Computer Vision, 23481–23491. 2023. URL: https://doi.org/10.1109/ICCV51070.2023.02146.

[LDL-LWY+22] (1,2)

Qiang Li, Jingjing Wang, Zhaoliang Yao, Yachun Li, Pengju Yang, Jingwei Yan, Chunmao Wang, and Shiliang Pu. Unimodal-concentrated loss: fully adaptive label distribution learning for ordinal regression. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 20513–20522. 2022. URL: https://doi.org/10.1109/CVPR52688.2022.01986.

Further Reading

[LDL-WLG25]

Jing Wang, Jianhui Lv, and Xin Geng. Label distribution learning by partitioning label distribution manifold. IEEE Transactions on Neural Networks and Learning Systems, 36(2):3786–3796, 2025. URL: https://doi.org/10.1109/TNNLS.2023.3341807.

[LDL-YJ24]

Peiqiu Yu and Xiuyi Jia. Exploiting indirect linear correlation for label distribution learning. Neurocomputing, pages 128022, 2024. URL: https://doi.org/10.1016/j.neucom.2024.128022.

[LDL-TCGJ23]

Chao Tan, Sheng Chen, Xin Geng, and Genlin Ji. A label distribution manifold learning algorithm. Pattern Recognition, 135:109112, 2023. URL: https://doi.org/10.1016/j.patcog.2022.109112.

[LDL-WG23]

Jing Wang and Xin Geng. Label distribution learning by exploiting label distribution manifold. IEEE Transactions on Neural Networks and Learning Systems, 34(2):839–852, 2023. URL: https://doi.org/10.1109/TNNLS.2021.3103178.

[LDL-ZMSZ22]

Tianyue Zhang, Yingke Mao, Furao Shen, and Jian Zhao. Label distribution learning through exploring nonnegative components. Neurocomputing, 501:212–221, 2022. URL: https://doi.org/10.1016/j.neucom.2022.06.017.

[LDL-JLZ+21]

Xiuyi Jia, Zechao Li, Xiang Zheng, Weiwei Li, and Sheng-Jun Huang. Label distribution learning with label correlations on local samples. IEEE Transactions on Knowledge and Data Engineering, 33(4):1619–1631, 2021. URL: https://doi.org/10.1109/TKDE.2019.2943337.

[LDL-XJS+20]

Suping Xu, Hengrong Ju, Lin Shang, Witold Pedrycz, Xibei Yang, and Chun Li. Label distribution learning: a local collaborative mechanism. International Journal of Approximate Reasoning, 121:59–84, 2020. URL: https://doi.org/10.1016/j.ijar.2020.02.003.

[LDL-JZL+19]

Xiuyi Jia, Xiang Zheng, Weiwei Li, Changqing Zhang, and Zechao Li. Facial emotion distribution learning by exploiting low-rank label correlations locally. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 9841–9850. 2019. URL: https://doi.org/10.1109/CVPR.2019.01007.

[LDL-WG19a]

Jing Wang and Xin Geng. Theoretical analysis of label distribution learning. In Proceedings of the AAAI Conference on Artificial Intelligence, 5256–5263. 2019. URL: https://doi.org/10.1609/aaai.v33i01.33015256.

[LDL-WG19b]

Ke Wang and Xin Geng. Discrete binary coding based label distribution learning. In Proceedings of the International Joint Conference on Artificial Intelligence, 3733–3739. 2019. URL: https://doi.org/10.24963/ijcai.2019/518.

[LDL-XSS19]

Suping Xu, Lin Shang, and Furao Shen. Latent semantics encoding for label distribution learning. In Proceedings of the International Joint Conference on Artificial Intelligence, 3982–3988. 2019. URL: https://doi.org/10.24963/ijcai.2019/553.

[LDL-WG18]

Ke Wang and Xin Geng. Discrete binary coding based label distribution learning. In Proceedings of the International Joint Conference on Artificial Intelligence, 3733–3739. 2018. URL: https://doi.org/10.24963/ijcai.2018/386.

[LDL-GXX+17]

Bin-Bin Gao, Chao Xing, Chen-Wei Xie, Jianxin Wu, and Xin Geng. Deep label distribution learning with label ambiguity. IEEE Transactions on Image Processing, 26(6):2825–2838, 2017. URL: https://doi.org/10.1109/TIP.2017.2689998.

[LDL-HGHL17]

Peng Hou, Xin Geng, Zeng-Wei Huo, and Jia-Qi Lv. Semi-supervised adaptive label distribution learning for facial age estimation. In Proceedings of the AAAI Conference on Artificial Intelligence, 2015–2021. 2017. URL: https://doi.org/10.1609/aaai.v31i1.10822.

[LDL-YGZ16]

Xu Yang, Xin Geng, and Deyu Zhou. Sparsity conditional energy label distribution learning for age estimation. In Proceedings of the International Joint Conference on Artificial Intelligence, 2259–2265. 2016. URL: https://www.ijcai.org/Abstract/16/322.

[LDL-KFCB15]

Peter Kontschieder, Madalina Fiterau, Antonio Criminisi, and Samuel Rota Bulo. Deep neural decision forests. In Proceedings of the IEEE/CVF International Conference on Computer Vision, 1467–1475. 2015. URL: https://doi.org/10.1109/ICCV.2015.172.

[LDL-GSMZ10]

Xin Geng, Kate Smith-Miles, and Zhi-Hua Zhou. Facial age estimation by learning from label distributions. In Proceedings of the AAAI Conference on Artificial Intelligence, 451–456. 2010. URL: https://doi.org/10.1609/aaai.v24i1.7657.