One-Step Abductive Multi-Target Learning with Diverse Noisy Label Samples

学习以清洁：用于噪声标签纠正的强化学习

Learning to Clean: Reinforcement Learning for Noisy Label Correction

本文提出了一种基于强化学习的噪声标签纠正方法，通过深度特征表示策略网络实现标签纠正，实验表明其在多个数据集上优于现有技术。

Semi-Supervised Cascaded Clustering for Classification of Noisy Label Data

The performance of supervised classification techniques often deteriorates when the data has noisy labels. Even the semi-supervised classification approaches have largely focused only on the problem of handling missing labels. Most of the approaches addressing the noisy label data rely on deep neural networks (DNN) that require huge datasets for classification tasks. This poses a serious challenge especially in process and manufacturing industries, where the data is limited and labels are noisy. We propose a semi-supervised cascaded clustering (SSCC) algorithm to extract patterns and generate …

解决长尾噪声标签学习问题：一种考虑标签稀有性的标签翻新两阶段解决方案

Addressing Long-Tail Noisy Label Learning Problems: a Two-Stage Solution with Label Refurbishment Considering Label Rarity

针对真实数据集的长尾噪声标签学习问题，提出结合软标签翻新与多专家集成学习的两阶段LR²方法，通过对比学习获无偏特征、BANC损失训练分类器初步预测，再翻新标签用于集成学习，在多个基准数据集上准确率超越现有最优方法。

Learning with Noisy Labels by Efficient Transition Matrix Estimation to Combat Label Miscorrection

Recent studies on learning with noisy labels have shown remarkable performance by exploiting a small clean dataset. In particular, model agnostic meta-learning-based label correction methods further improve performance by correcting noisy labels on the fly. However, there is no safeguard on the label miscorrection, resulting in unavoidable performance degradation. Moreover, every training step requires at least three back-propagations, significantly slowing down the training speed. To mitigate these issues, we propose a robust and efficient method that learns a label transition matrix on the f…

噪声与变化标签分布下的在线多标签分类

Online Multi-Label Classification under Noisy and Changing Label Distribution

针对多标签数据流中噪声标签与标签分布变化问题，提出NCLD算法，通过局部特征图重建标签评分、无偏排序损失和分布变化检测实现鲁棒的在线多标签分类。

FedNoisy：联邦噪声标签学习基准

FedNoisy: Federated Noisy Label Learning Benchmark

本研究推出首个标准化联邦噪声标签学习基准FedNoisy，涵盖6个数据集的20种基础设置、标准化模拟流程及9种基线实现，通过全面实验为该领域方法开发提供参考与验证支持。

通过最优传输从噪声标签中学习长尾数据

Learning from Noisy Labels for Long-tailed Data via Optimal Transport

本文针对长尾分布与噪声标签并存的数据，提出损失-距离交叉选择模块结合最优传输生成伪标签的半监督方法，有效提升模型鲁棒性并超越现有最优方法。

From Noisy Prediction to True Label: Noisy Prediction Calibration via Generative Model

Noisy labels are inevitable yet problematic in machine learning society. It ruins the generalization of a classifier by making the classifier over-fitted to noisy labels. Existing methods on noisy label have focused on modifying the classifier during the training procedure. It has two potential problems. First, these methods are not applicable to a pre-trained classifier without further access to training. Second, it is not easy to train a classifier and regularize all negative effects from noisy labels, simultaneously. We suggest a new branch of method, Noisy Prediction Calibration (NPC) in l…

鲁棒自训练与闭环标签修正用于噪声标签学习

Robust Self-Training with Closed-loop Label Correction for Learning from Noisy Labels

本文提出一种基于解耦双层优化的自训练标签修正框架，通过分类器和神经修正函数的协同进化，在小规模干净数据基础上利用噪声后验模拟和中间特征转移真实知识，形成闭环反馈系统以防止误差放大，实验表明其在CIFAR和Clothing1M等数据集上具有更优性能。

利用标签相关性的多标签噪声转移矩阵估计：理论与算法

Multi-Label Noise Transition Matrix Estimation with Label Correlations: Theory and Algorithm

本文研究噪声多标签学习中类别相关转移矩阵的估计问题，提出一种利用标签相关性且无需锚点和精确后验拟合的新估计器，通过求解双线性分解问题实现可识别估计，并从理论和实验上验证了其有效性和分类性能。

释放正则化策略在噪声标签学习中的潜力

Unleashing the Potential of Regularization Strategies in Learning with Noisy Labels

本文证明交叉熵损失结合学习率衰减、权重平均和数据增强等常规正则化策略，可超越复杂的噪声标签学习算法，呼吁重新评估该领域的基准与专用算法的作用。

NCSAM: 噪声补偿的锐度感知最小化用于噪声标签学习

NCSAM Noise-Compensated Sharpness-Aware Minimization for Noisy Label Learning

提出NCSAM方法，通过噪声补偿扰动修正噪声标签引起的优化偏差，缓解对噪声标签的记忆，在合成和真实噪声标签基准上优于SAM基线。

Towards Federated Learning against Noisy Labels via Local Self-Regularization

Federated learning (FL) aims to learn joint knowledge from a large scale of decentralized devices with labeled data in a privacy-preserving manner. However, since high-quality labeled data require expensive human intelligence and efforts, data with incorrect labels (called noisy labels) are ubiquitous in reality, which inevitably cause performance degradation. Although a lot of methods are proposed to directly deal with noisy labels, these methods either require excessive computation overhead or violate the privacy protection principle of FL. To this end, we focus on this issue in FL with the …

Context-based Virtual Adversarial Training for Text Classification with Noisy Labels

Deep neural networks (DNNs) have a high capacity to completely memorize noisy labels given sufficient training time, and its memorization, unfortunately, leads to performance degradation. Recently, virtual adversarial training (VAT) attracts attention as it could further improve the generalization of DNNs in semi-supervised learning. The driving force behind VAT is to prevent the models from overfitting data points by enforcing consistency between the inputs and the perturbed inputs. This strategy could be helpful in learning from noisy labels if it prevents neural models from learning noisy s…

Selective-Supervised Contrastive Learning with Noisy Labels

Deep networks have strong capacities of embedding data into latent representations and finishing following tasks. However, the capacities largely come from high-quality annotated labels, which are expensive to collect. Noisy labels are more affordable, but result in corrupted representations, leading to poor generalization performance. To learn robust representations and handle noisy labels, we propose selective-supervised contrastive learning (Sel-CL) in this paper. Specifically, Sel-CL extend supervised contrastive learning (Sup-CL), which is powerful in representation learning, but is degra…

Clusterability as an Alternative to Anchor Points When Learning with Noisy Labels

The label noise transition matrix, characterizing the probabilities of a training instance being wrongly annotated, is crucial to designing popular solutions to learning with noisy labels. Existing works heavily rely on finding "anchor points" or their approximates, defined as instances belonging to a particular class almost surely. Nonetheless, finding anchor points remains a non-trivial task, and the estimation accuracy is also often throttled by the number of available anchor points. In this paper, we propose an alternative option to the above task. Our main contribution is the discovery of…

Mitigating Memorization in Sample Selection for Learning with Noisy Labels

Because deep learning is vulnerable to noisy labels, sample selection techniques, which train networks with only clean labeled data, have attracted a great attention. However, if the labels are dominantly corrupted by few classes, these noisy samples are called dominant-noisy-labeled samples, the network also learns dominant-noisy-labeled samples rapidly via content-aware optimization. In this study, we propose a compelling criteria to penalize dominant-noisy-labeled samples intensively through class-wise penalty labels. By averaging prediction confidences for the each observed label, we obtai…

Rethinking Noisy Label Models: Labeler-Dependent Noise with Adversarial Awareness

Most studies on learning from noisy labels rely on unrealistic models of i.i.d. label noise, such as class-conditional transition matrices. More recent work on instance-dependent noise models are more realistic, but assume a single generative process for label noise across the entire dataset. We propose a more principled model of label noise that generalizes instance-dependent noise to multiple labelers, based on the observation that modern datasets are typically annotated using distributed crowdsourcing methods. Under our labeler-dependent model, label noise manifests itself under two modalit…

Learning from Noisy Label Distributions

In this paper, we consider a novel machine learning problem, that is, learning a classifier from noisy label distributions. In this problem, each instance with a feature vector belongs to at least one group. Then, instead of the true label of each instance, we observe the label distribution of the instances associated with a group, where the label distribution is distorted by an unknown noise. Our goals are to (1) estimate the true label of each instance, and (2) learn a classifier that predicts the true label of a new instance. We propose a probabilistic model that considers true label distri…

A Novel Perspective for Positive-Unlabeled Learning via Noisy Labels

Positive-unlabeled learning refers to the process of training a binary classifier using only positive and unlabeled data. Although unlabeled data can contain positive data, all unlabeled data are regarded as negative data in existing positive-unlabeled learning methods, which resulting in diminishing performance. We provide a new perspective on this problem -- considering unlabeled data as noisy-labeled data, and introducing a new formulation of PU learning as a problem of joint optimization of noisy-labeled data. This research presents a methodology that assigns initial pseudo-labels to unlab…

面向噪声标签的噪声早停（Noisy Early Stopping）方法

Noisy Early Stopping for Noisy Labels

针对噪声标签场景下无噪声验证集获取难、早停实施成本高的问题，提出噪声早停（NES）方法，利用同分布噪声验证集实现接近最优的早停效果，给出理论依据并验证其在标准基准上的稳健性能。

面向噪声标签学习中的可辨识性：一种多项式混合建模方法

Towards the Identifiability in Noisy Label Learning: A Multinomial Mixture Modelling Approach

本文提出一种数据驱动方法，通过为每个实例生成多个独立同分布噪声标签并利用多项式混合建模，使噪声标签学习问题可辨识，从而无需启发式方法即可准确估计干净标签，并在多种基准上表现优异。

To Aggregate or Not? Learning with Separate Noisy Labels

The rawly collected training data often comes with separate noisy labels collected from multiple imperfect annotators (e.g., via crowdsourcing). A typical way of using these separate labels is to first aggregate them into one and apply standard training methods. The literature has also studied extensively on effective aggregation approaches. This paper revisits this choice and aims to provide an answer to the question of whether one should aggregate separate noisy labels into single ones or use them separately as given. We theoretically analyze the performance of both approaches under the empi…

Towards Robust Graph Neural Networks for Noisy Graphs with Sparse Labels

Graph Neural Networks (GNNs) have shown their great ability in modeling graph structured data. However, real-world graphs usually contain structure noises and have limited labeled nodes. The performance of GNNs would drop significantly when trained on such graphs, which hinders the adoption of GNNs on many applications. Thus, it is important to develop noise-resistant GNNs with limited labeled nodes. However, the work on this is rather limited. Therefore, we study a novel problem of developing robust GNNs on noisy graphs with limited labeled nodes. Our analysis shows that both the noisy edges …

Learning from Multiple Annotator Noisy Labels via Sample-wise Label Fusion

Data lies at the core of modern deep learning. The impressive performance of supervised learning is built upon a base of massive accurately labeled data. However, in some real-world applications, accurate labeling might not be viable; instead, multiple noisy labels (instead of one accurate label) are provided by several annotators for each data sample. Learning a classifier on such a noisy training dataset is a challenging task. Previous approaches usually assume that all data samples share the same set of parameters related to annotator errors, while we demonstrate that label error learning s…

Learning from Noisy Crowd Labels with Logics

This paper explores the integration of symbolic logic knowledge into deep neural networks for learning from noisy crowd labels. We introduce Logic-guided Learning from Noisy Crowd Labels (Logic-LNCL), an EM-alike iterative logic knowledge distillation framework that learns from both noisy labeled data and logic rules of interest. Unlike traditional EM methods, our framework contains a ``pseudo-E-step'' that distills from the logic rules a new type of learning target, which is then used in the ``pseudo-M-step'' for training the classifier. Extensive evaluations on two real-world datasets for te…

To Smooth or Not? When Label Smoothing Meets Noisy Labels

Label smoothing (LS) is an arising learning paradigm that uses the positively weighted average of both the hard training labels and uniformly distributed soft labels. It was shown that LS serves as a regularizer for training data with hard labels and therefore improves the generalization of the model. Later it was reported LS even helps with improving robustness when learning with noisy labels. However, we observed that the advantage of LS vanishes when we operate in a high label noise regime. Intuitively speaking, this is due to the increased entropy of $\mathbb{P}(\text{noisy label}|X)$ when…

FINE Samples for Learning with Noisy Labels

Modern deep neural networks (DNNs) become frail when the datasets contain noisy (incorrect) class labels. Robust techniques in the presence of noisy labels can be categorized into two folds: developing noise-robust functions or using noise-cleansing methods by detecting the noisy data. Recently, noise-cleansing methods have been considered as the most competitive noisy-label learning algorithms. Despite their success, their noisy label detectors are often based on heuristics more than a theory, requiring a robust classifier to predict the noisy data with loss values. In this paper, we propose …

BoMD：用于噪声胸部X光片分类的多标签描述符包

BoMD: Bag of Multi-label Descriptors for Noisy Chest X-ray Classification

本文提出BoMD方法，通过优化多标签描述符包并与BERT语义描述符对齐，检测并平滑重标注噪声样本，从而提升噪声多标签胸部X光片分类的准确率与鲁棒性。

Extended T: Learning with Mixed Closed-set and Open-set Noisy Labels

The label noise transition matrix $T$, reflecting the probabilities that true labels flip into noisy ones, is of vital importance to model label noise and design statistically consistent classifiers. The traditional transition matrix is limited to model closed-set label noise, where noisy training data has true class labels within the noisy label set. It is unfitted to employ such a transition matrix to model open-set label noise, where some true class labels are outside the noisy label set. Thus when considering a more realistic situation, i.e., both closed-set and open-set label noise occurs…

SplitNet: Learnable Clean-Noisy Label Splitting for Learning with Noisy Labels

Annotating the dataset with high-quality labels is crucial for performance of deep network, but in real world scenarios, the labels are often contaminated by noise. To address this, some methods were proposed to automatically split clean and noisy labels, and learn a semi-supervised learner in a Learning with Noisy Labels (LNL) framework. However, they leverage a handcrafted module for clean-noisy label splitting, which induces a confirmation bias in the semi-supervised learning phase and limits the performance. In this paper, we for the first time present a learnable module for clean-noisy la…

GMM Discriminant Analysis with Noisy Label for Each Class

Real world datasets often contain noisy labels, and learning from such datasets using standard classification approaches may not produce the desired performance. In this paper, we propose a Gaussian Mixture Discriminant Analysis (GMDA) with noisy label for each class. We introduce flipping probability and class probability and use EM algorithms to solve the discriminant problem with label noise. We also provide the detail proofs of convergence. Experimental results on synthetic and real-world datasets show that the proposed approach notably outperforms other four state-of-art methods.

NLNL: Negative Learning for Noisy Labels

Convolutional Neural Networks (CNNs) provide excellent performance when used for image classification. The classical method of training CNNs is by labeling images in a supervised manner as in "input image belongs to this label" (Positive Learning; PL), which is a fast and accurate method if the labels are assigned correctly to all images. However, if inaccurate labels, or noisy labels, exist, training with PL will provide wrong information, thus severely degrading performance. To address this issue, we start with an indirect learning method called Negative Learning (NL), in which the CNNs are …

Robustness of Accuracy Metric and its Inspirations in Learning with Noisy Labels

For multi-class classification under class-conditional label noise, we prove that the accuracy metric itself can be robust. We concretize this finding's inspiration in two essential aspects: training and validation, with which we address critical issues in learning with noisy labels. For training, we show that maximizing training accuracy on sufficiently many noisy samples yields an approximately optimal classifier. For validation, we prove that a noisy validation set is reliable, addressing the critical demand of model selection in scenarios like hyperparameter-tuning and early stopping. Prev…

Evaluating Multi-label Classifiers with Noisy Labels

Multi-label classification (MLC) is a generalization of standard classification where multiple labels may be assigned to a given sample. In the real world, it is more common to deal with noisy datasets than clean datasets, given how modern datasets are labeled by a large group of annotators on crowdsourcing platforms, but little attention has been given to evaluating multi-label classifiers with noisy labels. Exploiting label correlations now becomes a standard component of a multi-label classifier to achieve competitive performance. However, this component makes the classifier more prone to p…

SELC: Self-Ensemble Label Correction Improves Learning with Noisy Labels

Deep neural networks are prone to overfitting noisy labels, resulting in poor generalization performance. To overcome this problem, we present a simple and effective method self-ensemble label correction (SELC) to progressively correct noisy labels and refine the model. We look deeper into the memorization behavior in training with noisy labels and observe that the network outputs are reliable in the early stage. To retain this reliable knowledge, SELC uses ensemble predictions formed by an exponential moving average of network outputs to update the original noisy labels. We show that training…

基于设计的带有噪声人类标签的监督学习

Design-Based Supervised Learning with Noisy Human Labels

研究针对自动分类器标记非结构化数据时人类审核标签有噪声的问题，提出PA-DSL方法，利用裁决案例纠正标签并校正分析偏差，在合成和维基百科解毒半合成实验中取得降低均方根误差10%-17%的效果。

利用部件级标签估计噪声类别后验以进行噪声标签学习

Estimating Noisy Class Posterior with Part-level Labels for Noisy Label Learning

本文针对噪声标签导致类别后验估计偏差的问题，引入部件级标签和单对多转移矩阵，构建分类器一致框架以更准确估计噪声类别后验并提升分类性能。

FedNoiL: A Simple Two-Level Sampling Method for Federated Learning with Noisy Labels

Federated learning (FL) aims at training a global model on the server side while the training data are collected and located at the local devices. Hence, the labels in practice are usually annotated by clients of varying expertise or criteria and thus contain different amounts of noises. Local training on noisy labels can easily result in overfitting to noisy labels, which is devastating to the global model through aggregation. Although recent robust FL methods take malicious clients into account, they have not addressed local noisy labels on each device and the impact to the global model. In …

LaplaceConfidence：一种基于图的噪声标签学习方法

LaplaceConfidence: a Graph-based Approach for Learning with Noisy Labels

提出基于图的LaplaceConfidence方法，利用拉普拉斯能量构建低能图以评估标签置信度，结合协同训练与标签修复技术实现鲁棒训练，在合成与真实噪声数据集上优于现有方法。

不完整多视图弱标签学习：含噪声特征与不平衡标签

Incomplete Multi-View Weak-Label Learning with Noisy Features and Imbalanced Labels

针对不完整多视图弱标签学习中噪声特征与不平衡标签问题，提出联合嵌入与自适应加权HSIC降冗余、检测噪声视图，并用焦点损失缓解不平衡，实验验证有效。

针对噪声标签鲁棒性的预训练模型微调

Fine tuning Pre trained Models for Robustness Under Noisy Labels

本文针对带噪声标签数据集的预训练模型微调问题，提出TURN算法，通过先独立调整线性分类器保护特征提取器，再基于降噪数据集微调整个模型，实现鲁棒且高效的去噪性能。

A Simple yet Effective Baseline for Robust Deep Learning with Noisy Labels

Recently deep neural networks have shown their capacity to memorize training data, even with noisy labels, which hurts generalization performance. To mitigate this issue, we provide a simple but effective baseline method that is robust to noisy labels, even with severe noise. Our objective involves a variance regularization term that implicitly penalizes the Jacobian norm of the neural network on the whole training set (including the noisy-labeled data), which encourages generalization and prevents overfitting to the corrupted labels. Experiments on both synthetically generated incorrect label…

Co-learning: Learning from Noisy Labels with Self-supervision

Noisy labels, resulting from mistakes in manual labeling or webly data collecting for supervised learning, can cause neural networks to overfit the misleading information and degrade the generalization performance. Self-supervised learning works in the absence of labels and thus eliminates the negative impact of noisy labels. Motivated by co-training with both supervised learning view and self-supervised learning view, we propose a simple yet effective method called Co-learning for learning with noisy labels. Co-learning performs supervised learning and self-supervised learning in a cooperativ…

On the Robustness of Monte Carlo Dropout Trained with Noisy Labels

The memorization effect of deep learning hinders its performance to effectively generalize on test set when learning with noisy labels. Prior study has discovered that epistemic uncertainty techniques are robust when trained with noisy labels compared with neural networks without uncertainty estimation. They obtain prolonged memorization effect and better generalization performance under the adversarial setting of noisy labels. Due to its superior performance amongst other selected epistemic uncertainty methods under noisy labels, we focus on Monte Carlo Dropout (MCDropout) and investigate why…

基于随机规划的多核学习算法

Multiple Kernel Learning from Noisy Labels by Stochastic Programming

我们研究了从噪声标签中学习多核的问题。这与以前大多数关于多核学习的研究相反，这些研究主要集中在开发有效的算法并假设完美标记的训练样本。直接将现有的多核学习算法应用于噪声标记的示例通常会由于不正确的类分配而导致次优性能。我们解决这个挑战，铸造多内核学习从嘈杂的标签到一个随机规划问题，并提出了一个极大极小公式。我们开发了一个有效的算法来解决相关的凸-凹优化问题的快速收敛速度$O(1/T)$，其中$T$是迭代次数。UCI数据集上的实证研究验证了所提出的框架的有效性和所提出的优化算法的效率。

Learning From Noisy Singly-labeled Data

Supervised learning depends on annotated examples, which are taken to be the \emph{ground truth}. But these labels often come from noisy crowdsourcing platforms, like Amazon Mechanical Turk. Practitioners typically collect multiple labels per example and aggregate the results to mitigate noise (the classic crowdsourcing problem). Given a fixed annotation budget and unlimited unlabeled data, redundant annotation comes at the expense of fewer labeled examples. This raises two fundamental questions: (1) How can we best learn from noisy workers? (2) How should we allocate our labeling budget to ma…

Instance Correction for Learning with Open-set Noisy Labels

The problem of open-set noisy labels denotes that part of training data have a different label space that does not contain the true class. Lots of approaches, e.g., loss correction and label correction, cannot handle such open-set noisy labels well, since they need training data and test data to share the same label space, which does not hold for learning with open-set noisy labels. The state-of-the-art methods thus employ the sample selection approach to handle open-set noisy labels, which tries to select clean data from noisy data for network parameters updates. The discarded data are seen t…

Learning to Detect Noisy Labels Using Model-Based Features

Label noise is ubiquitous in various machine learning scenarios such as self-labeling with model predictions and erroneous data annotation. Many existing approaches are based on heuristics such as sample losses, which might not be flexible enough to achieve optimal solutions. Meta learning based methods address this issue by learning a data selection function, but can be hard to optimize. In light of these pros and cons, we propose Selection-Enhanced Noisy label Training (SENT) that does not rely on meta learning while having the flexibility of being data-driven. SENT transfers the noise distr…

Meta Label Correction for Noisy Label Learning

Leveraging weak or noisy supervision for building effective machine learning models has long been an important research problem. Its importance has further increased recently due to the growing need for large-scale datasets to train deep learning models. Weak or noisy supervision could originate from multiple sources including non-expert annotators or automatic labeling based on heuristics or user interaction signals. There is an extensive amount of previous work focusing on leveraging noisy labels. Most notably, recent work has shown impressive gains by using a meta-learned instance re-weight…

检测与校正：一种面向噪声标签学习的选择性噪声校正方法

Detect and Correct: A Selective Noise Correction Method for Learning with Noisy Labels

针对噪声标签损害深度学习性能的问题，提出一种基于损失分布识别含噪样本、用选择流程分离样本并学习噪声转移矩阵选择性校正的方法，在多个数据集上实现了准确率和鲁棒性的显著提升。

ExpertNet: Adversarial Learning and Recovery Against Noisy Labels

Today's available datasets in the wild, e.g., from social media and open platforms, present tremendous opportunities and challenges for deep learning, as there is a significant portion of tagged images, but often with noisy, i.e. erroneous, labels. Recent studies improve the robustness of deep models against noisy labels without the knowledge of true labels. In this paper, we advocate to derive a stronger classifier which proactively makes use of the noisy labels in addition to the original images - turning noisy labels into learning features. To such an end, we propose a novel framework, Expe…

Multi-Class Classification from Noisy-Similarity-Labeled Data

A similarity label indicates whether two instances belong to the same class while a class label shows the class of the instance. Without class labels, a multi-class classifier could be learned from similarity-labeled pairwise data by meta classification learning. However, since the similarity label is less informative than the class label, it is more likely to be noisy. Deep neural networks can easily remember noisy data, leading to overfitting in classification. In this paper, we propose a method for learning from only noisy-similarity-labeled data. Specifically, to model the noise, we employ…

Noisy multi-label semi-supervised dimensionality reduction

Noisy labeled data represent a rich source of information that often are easily accessible and cheap to obtain, but label noise might also have many negative consequences if not accounted for. How to fully utilize noisy labels has been studied extensively within the framework of standard supervised machine learning over a period of several decades. However, very little research has been conducted on solving the challenge posed by noisy labels in non-standard settings. This includes situations where only a fraction of the samples are labeled (semi-supervised) and each high-dimensional sample is…