Can the Virtual Labels Obtained by Traditional LP Approaches Be Well Encoded in WLR?

Interpolation-Based Contrastive Learning for Few-Label Semi-Supervised Learning

Semi-supervised learning (SSL) has long been proved to be an effective technique to construct powerful models with limited labels. In the existing literature, consistency regularization-based methods, which force the perturbed samples to have similar predictions with the original ones have attracted much attention for their promising accuracy. However, we observe that the performance of such methods decreases drastically when the labels get extremely limited, e.g., 2 or 3 labels for each category. Our empirical study finds that the main problem lies with the drift of semantic information in the procedure of data augmentation. The problem can be alleviated when enough supervision is provided. However, when little guidance is available, the incorrect regularization would mislead the network and undermine the performance of the algorithm. To tackle the problem, we: 1) propose an interpolation-based method to construct more reliable positive sample pairs and 2) design a novel contrastive loss to guide the embedding of the learned network to change linearly between samples so as to improve the discriminative capability of the network by enlarging the margin decision boundaries. Since no destructive regularization is introduced, the performance of our proposed algorithm is largely improved. Specifically, the proposed algorithm outperforms the second best algorithm (Comatch) with 5.3% by achieving 88.73% classification accuracy when only two labels are available for each class on the CIFAR-10 dataset. Moreover, we further prove the generality of the proposed method by improving the performance of the existing state-of-the-art algorithms considerably with our proposed strategy. The corresponding code is available at https://github.com/xihongyang1999/ICL_SSL.

Graph-Based Semi-Supervised Learning: A Comprehensive Review

Semi-supervised learning (SSL) has tremendous value in practice due to the utilization of both labeled and unlabelled data. An essential class of SSL methods, referred to as graph-based semi-supervised learning (GSSL) methods in the literature, is to first represent each sample as a node in an affinity graph, and then, the label information of unlabeled samples can be inferred based on the structure of the constructed graph. GSSL methods have demonstrated their advantages in various domains due to their uniqueness of structure, the universality of applications, and their scalability to large-scale data. Focusing on GSSL methods only, this work aims to provide both researchers and practitioners with a solid and systematic understanding of relevant advances as well as the underlying connections among them. The concentration on one class of SSL makes this article distinct from recent surveys that cover a more general and broader picture of SSL methods yet often neglect the fundamental understanding of GSSL methods. In particular, a significant contribution of this article lies in a newly generalized taxonomy for GSSL under the unified framework, with the most up-to-date references and valuable resources such as codes, datasets, and applications. Furthermore, we present several potential research directions as future work with our insights into this rapidly growing field.

GraphHop: An Enhanced Label Propagation Method for Node Classification

A scalable semisupervised node classification method on graph-structured data, called GraphHop, is proposed in this work. The graph contains all nodes' attributes and link connections but labels of only a subset of nodes. Graph convolutional networks (GCNs) have provided superior performance in node label classification over the traditional label propagation (LP) methods for this problem. Nevertheless, current GCN algorithms suffer from a considerable amount of labels for training because of high model complexity or cannot be easily generalized to large-scale graphs due to the expensive cost of loading the entire graph and node embeddings. Besides, nonlinearity makes the optimization process a mystery. To this end, an enhanced LP method, called GraphHop, is proposed to tackle these problems. GraphHop can be viewed as a smoothening LP algorithm, in which each propagation alternates between two steps: label aggregation and label update. In the label aggregation step, multihop neighbor embeddings are aggregated to the center node. In the label update step, new embeddings are learned and predicted for each node based on aggregated results from the previous step. The two-step iteration improves the graph signal smoothening capacity. Furthermore, to encode attributes, links, and labels on graphs effectively under one framework, we adopt a two-stage training process, i.e., the initialization stage and the iteration stage. Thus, the smooth attribute information extracted from the initialization stage is consistently imposed in the propagation process in the iteration stage. Experimental results show that GraphHop outperforms state-of-the-art graph learning methods on a wide range of tasks in graphs of various sizes (e.g., multilabel and multiclass classification on citation networks, social graphs, and commodity consumption graphs).

Graph-Based Class-Imbalance Learning With Label Enhancement

Class imbalance is a common issue in the community of machine learning and data mining. The class-imbalance distribution can make most classical classification algorithms neglect the significance of the minority class and tend toward the majority class. In this article, we propose a label enhancement method to solve the class-imbalance problem in a graph manner, which estimates the numerical label and trains the inductive model simultaneously. It gives a new perspective on the class-imbalance learning based on the numerical label rather than the original logical label. We also present an iterative optimization algorithm and analyze the computation complexity and its convergence. To demonstrate the superiority of the proposed method, several single-label and multilabel datasets are applied in the experiments. The experimental results show that the proposed method achieves a promising performance and outperforms some state-of-the-art single-label and multilabel class-imbalance learning methods.

Learning Robust Discriminant Subspace Based on Joint L₂,ₚ- and L₂,ₛ-Norm Distance Metrics

Recently, there are many works on discriminant analysis, which promote the robustness of models against outliers by using L₁- or L_2,1-norm as the distance metric. However, both of their robustness and discriminant power are limited. In this article, we present a new robust discriminant subspace (RDS) learning method for feature extraction, with an objective function formulated in a different form. To guarantee the subspace to be robust and discriminative, we measure the within-class distances based on [Formula: see text]-norm and use [Formula: see text]-norm to measure the between-class distances. This also makes our method include rotational invariance. Since the proposed model involves both [Formula: see text]-norm maximization and [Formula: see text]-norm minimization, it is very challenging to solve. To address this problem, we present an efficient nongreedy iterative algorithm. Besides, motivated by trace ratio criterion, a mechanism of automatically balancing the contributions of different terms in our objective is found. RDS is very flexible, as it can be extended to other existing feature extraction techniques. An in-depth theoretical analysis of the algorithm's convergence is presented in this article. Experiments are conducted on several typical databases for image classification, and the promising results indicate the effectiveness of RDS.

Robust Triple-Matrix-Recovery-Based Auto-Weighted Label Propagation for Classification

The graph-based semisupervised label propagation (LP) algorithm has delivered impressive classification results. However, the estimated soft labels typically contain mixed signs and noise, which cause inaccurate predictions due to the lack of suitable constraints. Moreover, the available methods typically calculate the weights and estimate the labels in the original input space, which typically contains noise and corruption. Thus, the encoded similarities and manifold smoothness may be inaccurate for label estimation. In this article, we present effective schemes for resolving these issues and propose a novel and robust semisupervised classification algorithm, namely the triple matrix recovery-based robust auto-weighted label propagation framework (ALP-TMR). Our ALP-TMR introduces a TMR mechanism to remove noise or mixed signs from the estimated soft labels and improve the robustness to noise and outliers in the steps of assigning weights and predicting the labels simultaneously. Our method can jointly recover the underlying clean data, clean labels, and clean weighting spaces by decomposing the original data, predicted soft labels, or weights into a clean part plus an error part by fitting noise. In addition, ALP-TMR integrates the auto-weighting process by minimizing the reconstruction errors over the recovered clean data and clean soft labels, which can encode the weights more accurately to improve both data representation and classification. By classifying samples in the recovered clean label and weight spaces, one can potentially improve the label prediction results. Extensive simulations verified the effectivenss of our ALP-TMR.

Nonpeaked Discriminant Analysis for Data Representation

Of late, there are many studies on the robust discriminant analysis, which adopt L₁-norm as the distance metric, but their results are not robust enough to gain universal acceptance. To overcome this problem, the authors of this article present a nonpeaked discriminant analysis (NPDA) technique, in which cutting L₁-norm is adopted as the distance metric. As this kind of norm can better eliminate heavy outliers in learning models, the proposed algorithm is expected to be stronger in performing feature extraction tasks for data representation than the existing robust discriminant analysis techniques, which are based on the L₁-norm distance metric. The authors also present a comprehensive analysis to show that cutting L₁-norm distance can be computed equally well, using the difference between two special convex functions. Against this background, an efficient iterative algorithm is designed for the optimization of the proposed objective. Theoretical proofs on the convergence of the algorithm are also presented. Theoretical insights and effectiveness of the proposed method are validated by experimental tests on several real data sets.

Robust Adaptive Embedded Label Propagation With Weight Learning for Inductive Classification

We propose a robust inductive semi-supervised label prediction model over the embedded representation, termed adaptive embedded label propagation with weight learning (AELP-WL), for classification. AELP-WL offers several properties. First, our method seamlessly integrates the robust adaptive embedded label propagation with adaptive weight learning into a unified framework. By minimizing the reconstruction errors over embedded features and embedded soft labels jointly, our AELP-WL can explicitly ensure the learned weights to be joint optimal for representation and classification, which differs from most existing LP models that perform weight learning separately by an independent step before label prediction. Second, existing models usually precalculate the weights over the original samples that may contain unfavorable features and noise decreasing performance. To this end, our model adds a constraint that decomposes original data into a sparse component encoding embedded noise-removed sparse representations of samples and a sparse error part fitting noise, and then performs the adaptive weight learning over the embedded sparse representations. Third, our AELP-WL computes the projected soft labels by trading-off the manifold smoothness and label fitness errors over the adaptive weights and the embedded representations for enhancing the label estimation power. By including a regressive label approximation error for simultaneous minimization to correlate sample features with the embedded soft labels, the out-of-sample issue is naturally solved. By minimizing the reconstruction errors over features and embedded soft labels, classification error and label approximation error jointly, state-of-the-art results are delivered.