As a compromise between supervised and unsupervised learning, semi-supervised learning (SSL) harnesses both labeled and unlabeled data to enhance learning performance. Graph-based semi-supervised learning (GSSL) has emerged as a prominent approach owing to its versatility in representing sample interdependencies via graph structures. However, traditional GSSL methods face high time cost when computing matrix inverses, making them inefficient for large datasets. To address this, some researchers have introduced anchors as a bridge to accelerate the process. Nevertheless, most anchor-based models suffer from one or more of the following issues: (1) The anchor graph-based construction of the adjacency matrix has limitations; (2) The objective functions are typically non-convex, leading to local optima and requiring multiple runs to achieve good performance. To tackle these challenges, we develop a probability-driven approach to build the adjacency matrix, defining sample similarity as the probability of sharing the same anchor. Based on this strategy, we design a model (CFSL) with a strictly convex objective function, guaranteeing a globally optimal solution without iterative optimization. Experiments on multiple datasets indicate that our algorithm yields strong performance.

This paper proposes a deep pseudo-label method for unsupervised feature selection, which learns non-linear representations to generate pseudo-labels and trains a Neural Network (NN) to select informative features via self-Knowledge Distillation (KD). Specifically, the proposed method divides a standard NN into two sub-components: an encoder and a predictor, and introduces a dependency subnet. It works by self-supervised pretraining the encoder to produce informative representations and then alternating between two steps: (1) learning pseudo-labels by combining the clustering results of the encoder's outputs with the NN's prediction outputs, and (2) updating the NN's parameters by globally selecting a subset of features to predict the pseudo-labels while updating the subnet's parameters through self-KD. Self-KD is achieved by encouraging the subnet to locally capture a subset of the NN features to produce class probabilities that match those produced by the NN. This allows the model to self-absorb the learned inter-class knowledge and evaluate feature diversity, removing redundant features without sacrificing performance. Meanwhile, the potential discriminative capability of a NN can also be self-excavated without the assistance of other NNs. The two alternate steps reinforce each other: in step (2), by predicting the learned pseudo-labels and conducting selfKD, the discrimination of the outputs of both the NN and the encoder is gradually enhanced, while the self-labeling method in step (1) leverages these two improvements to further refine the pseudo-labels for step (2), resulting in the superior performance. Extensive experiments show the proposed method significantly outperforms state-of-the-art methods across various datasets.

Anchor-based clustering methods have attracted increasing attention due to their ability to provide efficient and scalable solutions in clustering tasks, such as subspace, multi-view and ensemble clustering. Nevertheless, the majority of anchor-based methods view anchors merely as tools, concentrating on diminishing computational complexity within original data space. However, in fact, clustering can be directly performed on anchors and then the anchor clustering results could be propagated to original data. Due to the much smaller volume of anchors, this could significantly reduce the computational complexity of clustering algorithms. Building upon this idea, in this paper, we propose a fast anchor graph clustering method (FAGC) via maximizing within-cluster similarity. Inspired by the relaxation and discretization model in spectral clustering, we also propose two corresponding models, namely FAGC-R and FAGC-D. FAGC-R first obtains spectral embedding of anchors and then discretizes the embedding to obtain anchor indicator matrix. While FAGC-D directly solves the discrete anchor membership matrix. Once anchor clustering results are obtained, original data labels can be obtained through anchor label transmission. Extensive experiments conducted on synthetic and real datasets illustrate the effectiveness and efficiency of the proposed methods.

In practical applications, multi-view subspace clustering is hindered by data noise that disrupts the ideal block-diagonal structure of self-representation matrices, thereby degrading performance. Moreover, many existing methods rely solely on sample features, overlooking the valuable structural information in affinity matrices (e.g., pairwise relationships). While conventional contrastive learning strategies often introduce false negative pairs due to noise and unreliable sample selection. To address these challenges, we propose a pseudo-label guided bidirectional discriminative deep multi-view subspace clustering method (PBDMSC). Our approach first employs pseudo-label guided contrastive learning, using previous cluster assignments to select reliable positive and negative samples, which mitigates incorrect pairings and enhances low-dimensional representations. Then, a discriminative self-representation learning method is introduced that leverages pseudo-labels to enforce homogeneous expression constraints and incorporates a bidirectional attention mechanism to preserve the structured information from affinity matrices, thereby enhancing robustness. Experimental results on six real-world datasets demonstrate that our proposed method achieves state-of-the-art clustering performance.

In this paper, we propose a novel algorithm to solve the row-sparse principal component analysis problem without relying on any data structure assumption. Sparse principal component analysis was proposed to improve the interpretability of principal component analysis by restricting the number of non-zero elements in each loading vector, but the varying sparsity patterns among different leading vectors may result in trouble on some occasions, such as feature selection. Then row-sparse principal component analysis was proposed, which demands the same sparse pattern among different loading vectors. However, the optimization of row-sparse principal component analysis problems is NP-hard. Although some algorithms were proposed to solve this problem, but they are only applicable to the specific data structure. In this paper, we transform the original row-sparse principal component analysis problem into a new equivalent problem that can be solved by coordinate descent method without relying on any data structure assumption. Then by carefully eliminating redundant structures to avoid repeating computation, we propose a more efficient coordinate descent method to solve this problem. Furthermore, no parameter needs to be tuned in our algorithm. Finally, extensive experiments are conducted on the real world data sets to demonstrate the superiority of our algorithm.

Linear discriminant analysis (LDA) is one of commonly used supervised subspace learning methods. However, LDA will be powerless faced with the no-label situation. In this paper, the unsupervised LDA (Un-LDA) is proposed and first formulated as a seamlessly unified objective optimization which guarantees convergence during the iteratively alternative solving process. The objective optimization is in both the ratio trace and the trace ratio forms, forming a complete framework of a new approach to jointly clustering and unsupervised subspace learning. The extension of LDA into Un-LDA enables to not only complete unsupervised subspace learning via the explicitly presented subspace projection matrix but also simultaneously finish clustering and even clustering out-of-sample data via the explicitly presented transformation matrix. To overcome the difficulty in solving the non-convex objective optimization, we mathematically prove that the Un-LDA optimization in both forms can be transformed into the simple K-means clustering optimization when the subspace is determined. The Un-LDA optimization is eventually completed by alternatively optimizing the clusters using K-means and the subspace using the supervised LDA methods and iterating this whole process until convergence or stopping criterion. The experiments demonstrate that our proposed Un-LDA algorithms are comparable or even much superior to the counterparts.