Semi-supervised Clustering via Adversarially Enhanced Intent Propagation

1 Introduction

Semi-supervised clustering combines the strengths of semisupervised learning and clustering analysis, leveraging limited prior knowledge (e.g., pairwise constraints or groundtruth labels) to guide the formation of cluster structures that better align with user preferences. In practice, determining whether two samples belong to the same class is often easier than obtaining ground-truth labels for individual samples. However, due to the scarcity and high cost of supervision, most existing methods rely on sparse and static user-intent constraints during training, which often leads to significant degradation in clustering performance under weak supervision.

In recent years, several semi-supervised models have attempted to alleviate the sparsity of initial user intents. Methods such as [´Smieja et al., 2020; Wu et al., 2024] propagate pseudo-labels across the dataset via neural networks, while others (e.g., [Sun, 2025]) focus on discovering new constraints from local neighborhood structures. Additionally, [Wang et al., 2023] leverage both class labels and pairwise constraints to propagate user intents. Although these methods partially alleviate the sparsity of user intents, they fail to explicitly handle the propagation of gray samples that markedly deviate from the initial constraints. Ignoring or misappropriating these high-value samples can introduce a substantial number of noisy pseudo-user intents, severely compromising clustering performance.

Specifically, real-world data often includes gray samples that deviate from initial user intents, exhibiting ambiguous semantics and unclear boundaries. In contrast, distinct samples closely align with the initial intent and are easily recognized by clustering models. Although difficult to identify, gray samples often carry rich semantic information that can improve clustering structures. Figure 1 compares the directions of constraint propagation under different methods in the feature space. Traditional constraint propagation (CP) methods often overlook the propagation of supervision among gray samples, which can result in the loss of critical discriminative constraints. In contrast, an ideal propagation strategy should extend constraints to higher-order samples, rather than being limited to those highly similar to the initial constrained pairs. Under limited supervision, accurately identifying high-value gray samples and expanding them into reliable pseudo-user intents remains a core bottleneck in semi-supervised clustering.

To address these challenges, we propose the Adversarially Enhanced Constraint Propagation (AECP) module, which propagates supervision locally and employs an adversarial mechanism between two link types to globally enhance graysample confidence, producing higher-quality pseudo-user intents. Based on AECP, the semi-supervised AEPIC framework jointly optimizes these pseudo-user intents during representation learning and clustering to improve overall performance.

The main contributions of this paper are summarized as follows:

• We propose a novel Adversarially Enhanced Propagation-driven Intent-aware Clustering (AEPIC) framework, in which the Intent-Aware Regularization (IAR) module integrates the expanded pseudo-user intents into both representation learning and clustering. By jointly optimizing these two stages, AEPIC substantially improves clustering performance under sparse supervision.
• We design the Adversarially Enhanced Constraint Propagation (AECP) module to address limitations of existing propagation methods in identifying informationrich gray samples. AECP employs a global adversarial mechanism over supervisory connections to uncover constraint relationships among gray samples that are mispropagated or overlooked, enabling higher-quality expansion of pseudo-user intents.
• We conduct extensive experiments on 5 real-world datasets. Under identical sparse supervision, AEPIC consistently outperforms state-of-the-art semisupervised clustering methods, demonstrating its effectiveness and generality.

2 RelatedWork

2.1 Semi-Supervised Clustering

Semi-supervised clustering leverages limited prior knowledge, such as must-link and cannot-link constraints, to guide clustering toward user-aligned structures. Early works extended classical algorithms with constraints: COP-Kmeans [Wagstaff et al., 2001] incorporated pairwise constraints into K-means, exploiting symmetry and transitivity to improve clustering; MLC-Kmeans [Huang et al., 2008] introduced the Must-Link Set for better centroid estimation; CLWC [Cheng et al., 2008] jointly learned local weighted distance metrics and constraints.

With deep learning, constrained clustering has been embedded into neural networks. SDEC [Ren et al., 2019] extends DEC [Xie et al., 2016] by integrating pairwise constraints into deep representations; DCC [Zhang et al., 2019] builds on IDEC [Guo et al., 2017] to leverage pairwise constraints and richer side information, including continuous constraints and domain knowledge. Similarly, [Hsu and Kira, 2015] trained neural networks with prior constraints to learn cluster-friendly representations from raw data.

Despite incorporating user intent, these methods rely on sparse, static supervision. Acquiring high-quality prior knowledge is costly, limiting constraint effectiveness and motivating dynamic, scalable propagation of user intent under limited supervision.

2.2 Constraint Propagation

Constraint propagation extends limited pairwise usersupervised signals to unlabeled sample pairs, enhancing constraint utilization and model learning under sparse supervision. Early work focused on traditional frameworks: [Lu and Carreira-Perpinan, 2008] used Gaussian processes but was limited to binary classification; [Li et al., 2008] formulated propagation as a semidefinite programming (SDP) problem, extendable to multi-class cases but computationally expensive; [Yu and Shi, 2004] supported only must-link constraints, limiting applicability.

To address these issues, [Lu and Peng, 2013a] proposed E 2 CP, an exhaustive and efficient method jointly propagating must-link and cannot-link constraints while reducing computational cost. [Jia et al., 2020] employed an adversarial mechanism to propagate the two links independently. However, both rely on traditional similarity learning and lack dynamic modeling of confidence matrices, limiting constraint exploitation. [Yin et al., 2023] leverages limited supervision to construct richer similarity matrices. For multimodal data, [Lu and Peng, 2013b] proposed a unified intra- and inter-view propagation framework, whereas [Eaton et al., 2010] propagates constraints across views using local similarity metrics, enabling partial cross-view transfer.

Despite these advances, challenges remain. For gray samples whose features deviate from initial supervision, existing methods often propagate constraints only to similar samples, overlooking or mispropagating informative gray samples, which introduces noise and reduces the effectiveness of user-intent propagation.

3 Methods

3.1 Network Architecture

We propose a novel Adversarially Enhanced Intent Propagation Clustering (AEPIC) model to tackle propagate in semisupervised personalized clustering. As shown in Figure 2, AEPIC comprises two main components: the Adversarially Enhanced Constraint Propagation (AECP) module and the Intent-Aware Regularization (IAR) module. The AECP module includes Local Supervised Reconstruction (LSR) and Global Adversarial Propagation (GAP), with Enhanced Constraint Propagation (ECP) further improving propagation. The IAR module incorporates the propagated pseudo-user intents into model learning, enhancing clustering under sparse supervision.

3.2 AECPmodule

Local Supervised Reconstruction (LSR)

In intent propagation, high-similarity sample pairs do not always indicate must-link relations, and vice versa, since traditional similarity matrices are typically unsupervised and may not reflect user supervision accurately. To better leverage supervisory information, we reconstruct local similarities from the initial pairwise constraints, producing a graph that aligns more closely with user clustering preferences locally.

To encode the initial user-provided intentions, we define a pairwise constraint matrix T = {tij}n×n, where each entry indicates the type of relationship between instances xi and xj as follows:

For each sample xi, we learn a neighbor weight vector wi = [wi1,wi2, . . . ,wik]T , where k denotes the number of neighbors. The objective is to learn neighborhood weights that are aligned with user intents. The corresponding optimization function is formulated as:

Each term in the objective function is defined as follows: Ni denotes the k-nearest neighbor set of sample xi. Gi ∈ Rk×k is the local Gram difference matrix, defined as:

where κij = ⟨xi, xj⟩ denotes the similarity between samples xi and xj computed using a kernel function.

Hij is a constraint indicator defined as:

λ controls the influence of the constraint alignment term, and µ is a regularization coefficient to prevent overfitting.

Once the neighbor weight vector wi is learned for each sample xi, we construct a new similarity matrix W, where each entry reflects the learned edge weight in the similarity graph:

Although supervision is used to reconstruct the local graph, propagated signals remain mostly confined to samples similar to the initial supervised ones. Many gray samples, whose features differ substantially, receive lower confidence and are often ignored or mispropagated, degrading clustering performance. To address this, we propose an adversarial enhancement strategy to globally increase sample confidence.

Global Adversarial Propagation (GAP)

To address omissions or errors in propagating constraints among gray samples, we introduce a global dual-channel adversarial enhancement module. The main purpose of this module is to simultaneously propagate two semantically distinct types of constraints (Must-link and Cannot-link) while enforcing mutual exclusivity, so that each sample pair attains high confidence in at most one link. This effectively strengthens the propagation of constraints for gray samples.

To achieve this, we formulate the propagation as a dualchannel adversarial optimization problem:

Here, S and D ∈ Rn×n are the learned propagation graphs for must-link and cannot-link constraints, respectively. M and C ∈ Rn×n denote the corresponding initial user intent matrices, defined similarly to Equation (1), and Hij indicates whether a sample pair corresponds to the initial supervisory information.

The graph Laplacian L is constructed as L = A -W, where A is the degree matrix and W is the k-nearest neighbor adjacency matrix. Hyperparameters α, β, and γ control the relative influence of the regularization, supervision, and adversarial terms.

Finally, the learned propagation confidence matrices S and D are optimized with an adversarial loss that ensures each sample pair exhibits high confidence in at most one matrix, while remaining consistent with the original graph structure. These matrices can be interpreted as global confidence estimators for the corresponding relational links, where higher values indicate a greater likelihood that the links should exist.

Enhanced Constraint Propagation (ECP)

To further refine the intent-aware similarity graph, we design an enhancement fusion mechanism. This module dynamically adjusts the edge weights of W based on the confidence comparison between S and D, enabling selective enhancement or suppression of graph edges. Specifically, the edge update is computed as

We then adopt the Efficient Exhaustive Constraint Propagation (E2CP) method, which models constraint propagation as a graph-based binary label propagation problem. This allows the enhanced propagation graph to extend user intents to unlabeled sample pairs, thereby globally propagating supervisory signals and improving constraint utilization. The propagation results are then discretized to generate pseudosupervision information for semi-supervised clustering.

To ensure consistency in the graph structure, we first symmetrize the enhanced similarity matrix as ˜ W = 1 2 (˜ W +˜ W ⊤). The normalized graph Laplacian is then defined as

where ˜D = diag(dii) and dii = ∑nj=1 ˜ Wij .

Let t ∈ Rn×n denote the initial user intent matrix. The vertical propagation result Fv is computed to propagate user intents along columns by minimizing

which admits the closed-form solution

Similarly, the horizontal propagation result Fh propagates intents along rows:

By combining both vertical and horizontal directions, we obtain the final propagation result:

We treat F as a pseudo-constraint intent matrix, where Fij indicates the propagated confidence for sample pair (xi, xj), normalized to [-1, 1]. The final pseudo-constraint matrix ˆR is obtained by thresholding F with τ and a dynamically adjusted secondary threshold ˆ τ to control propagation quality:

3.3 IARModule

To integrate the learned pseudo-user intents into clustering, we employ an intent regularization strategy that incorporates them into both representation learning (IRRL) and clustering (IRC), guiding the overall learning process.

Intent-Regularized Representation Learning (IRRL)

We build our model upon a deep auto-encoder (AE) architecture [Michelucci, 2022]. Through encoder-decoder pretraining, the AE learns a low-dimensional latent representation Z while reconstructing the input features ˆX. The reconstruction loss is defined as

where n denotes the number of samples, xi is the input document representation, and ˆxi is its reconstruction.

This module aims to incorporate propagated user intents into representation learning, encouraging the latent space to be consistent with user-specified clustering preferences. To this end, we construct an affinity matrix based on the learned latent representations Z as follows:

where nor(Z) denotes the normalization operation applied to Z to reduce scale differences among features, and ai,j represents the (i, j)-th element of the affinity matrix A.

Next, we process the learned pseudo-intent matrix ˆR to obtain a weighted affinity matrix R ∈ Rn×n , enabling better weighting of features across different dimensions:

Subsequently, based on the pseudo-intent matrix learned through intent propagation, we dynamically expand the initial user intents to guide the representation learning process. The corresponding intent-regularized representation learning loss function is defined as:

where ∥·∥F denotes the Frobenius norm, measuring the consistency between the learned representation features and the user-expanded intents.

In summary, the overall objective function of the IRRL module is defined as:

Where, λ1 is a weighting parameter, set to 1.0 in our experiments, and LRE denotes the AE reconstruction loss. This module helps the model align learned feature representations with the expanded user intents.

Intent-Regularized Clustering (IRC)

This module builds upon representation learning by incorporating the propagated pseudo-user intents to guide cluster assignments, enabling the clustering structure to capture unique supervisory constraints among gray samples.

We first perform K-means clustering on the feature representations Z to obtain initial cluster centers {µk}Kk=1 , where K is the number of clusters. In each iteration, the predicted assignment matrix Q is computed as:

where qik is the probability of assigning zi to cluster µk, with α = 1.0 in our experiments.

Clustering is achieved by minimizing the KL divergence between Q and an auxiliary target distribution P:

where the target probabilities are

where fk = ∑ni=1 qik, and the final cluster assignment is ci = argmax k qik. To guide the generation of clustering structures using pseudo-user intents, we construct a cluster consistency matrix B from the assignment matrix Q as:

To incorporate the propagated pseudo-user intents into the clustering process, we adopt the same intent regularization strategy used in the representation learning stage, and transform the pseudo-intent matrix R as follows:

We then define the intent-regularized clustering loss LIC as:

This loss measures the consistency between the propagated pseudo-intents and the clustering assignments, enabling the model to accurately capture the supervisory constraints and achieve more precise clustering results. The overall loss of the IRC module is then defined as:

where λ2 is set to 1.0 in our experiments. When λ2 = 0, the model degenerates to standard clustering without pseudo-user intent guidance.

4 Experiments

4.1 Experiments Settings

Datasets. We evaluate our model on five datasets. Reuters10k contains 10,000 news articles across multiple topics. ACM consists of academic papers from various journals, and Abstract includes paper abstracts from the AMiner platform. USPS has 9,298 handwritten digit images, and Citeseer comprises scientific publications from six categories, represented by word vectors and annotated with citation links.

Baselines.We compare our method with several state-ofthe-art baselines, including classical clustering, deep unsupervised clustering, and deep semi-supervised clustering methods. The classical clustering methods are K-means [McQueen, 1967] and COP-Kmeans [Wagstaff et al., 2001]. Deep unsupervised clustering methods include IDEC [Guo et al., 2017], GAE [Kipf and Welling, 2016], and SDCN [Bo et al., 2020]. Deep semi-supervised clustering methods consist of SDEC [Ren et al., 2019], CPAC [Fogel et al., 2019], DCC [Zhang et al., 2019], ADC [Sun et al., 2022], TBDSC [Duan et al., 2024], and IPDC [Xu et al., 2025].

evaluation metrics.We evaluate clustering performance using standard metrics: clustering accuracy (ACC) [Xu et al.,

2003], normalized mutual information (NMI) [Strehl et al., 2000], and adjusted Rand index (ARI), where higher values indicate better results.

4.2 Comparison with State-of-the-Art

To evaluate AEPIC's clustering performance, we compare it with representative baselines using 500 initial pairwise constraints, evenly split between must-link and cannot-link pairs.

Table 2 presents results on 5 benchmark datasets. With the same constraints, AEPIC consistently outperforms classical deep clustering and recent semi-supervised methods, demonstrating the effectiveness and robustness of our constraint propagation strategy.

For example, on Reuters-10k, with only 500 constraints, AEPIC surpasses the best semi-supervised baseline by 2.75%, 11.35%, and 4.24% in ACC, NMI, and ARI, respectively, highlighting the efficacy of user intent expansion under limited supervision.

Table 2 (AEPIC variants) further compares the performance of different model variants. Here, AEPIC w/o ISR and AEPIC w/o GAP denote the removal of the reconstruction and adversarial modules, respectively. The results demonstrate that both modules are essential for achieving improved clustering performance.

4.3 Ablation Studies

We conducted ablation experiments on the AEPIC framework and its AECP module. In these experiments, the AECP constraint propagation was disabled in each of the two intent regularization stages, as shown in Table 3 ("CP" indicates the module is enabled). The results demonstrate that AECP plays a critical role in both intent regularization stages, and propagating user supervision significantly improves clustering performance.

4.4 Parameter Study Analysis

Sensitivity analyses on the ACM dataset evaluate AEPIC's stability across dual thresholds (τ, ˆ τ), adversarial weights (α, β), and the consistency coefficient γ.As shown in Fig. 3(a), curriculum-based τ [Wang et al., 2022] balances convergence speed and pseudo-constraint quality, while ˆ τ further refines selection. Optimal NMI occurs at τ = 1 × 10-4 (avoiding noise and sparsity), with smaller ˆ τ consistently enhancing performance. Figs. 3(b) and 3(c) demonstrate the robustness of AEPIC's, showing minimal variation across wide ranges of α, β ∈ [10-3 , 101 ] and γ ∈ [10, 50].

4.5 Analysis of Initial Constraints Experiments

To assess the impact of initial pairwise constraints on AEPIC, we conducted clustering experiments under varying settings. Notably, without initial constraints, the model receives no supervision.

As shown in Figure 4, even a small number of constraints (e.g., 100 pairs) substantially improves clustering, as propagation amplifies their value. Performance continues to rise with more constraints, but the improvement rate slows. This indicates that, as the number of constraints grows, the highvalue information available for further optimization gradually decreases, and the model's reliance on additional constraints diminishes, leading to slower performance gains.

4.6 Convergence Analysis

Figure 5 illustrates the convergence curves of the two intent regularization modules in our model, namely the IRRL and IRC modules, visualized on the USPS dataset. In the IRRL module (Figure5 a), the clustering metrics exhibit noticeable fluctuations in the later training stages, likely due to the unstable quality of propagated pseudo-user constraints and their ineffective incorporation into the clustering structure. In contrast, the IRC module (Figure5 b) shows significantly improved convergence after approximately 30 training epochs, resulting in more stable clustering performance.

4.7 Visualization Results

Figure 6 illustrates the evolution of AEPIC's feature space on the ACM dataset: (a) the original features are sparse with unclear cluster boundaries; (b) pretraining enhances intercluster separability and feature structure; (c) intent-aware regularization during representation learning pulls similar samples together and separates dissimilar ones, producing clusters aligned with the underlying manifold; (d) further regularization during clustering yields more compact, well-separated clusters, guided by additional propagated constraints. These results show that the learned pseudo-intents effectively capture true semantics, improving the discrimination of ambiguous and boundary samples and enhancing overall clustering performance.

5 Conclusion

This paper proposes AEPIC, a semi-supervised clustering framework that incorporates user intents into both representation learning and clustering. To better capture ambiguous samples that deviate from supervision, we introduce the Adversarially Enhanced Constraint Propagation (AECP) module, which combines local structure reconstruction with global adversarial enhancement to improve constraint propagation and generate higher-quality pseudo-user intents. Experiments on multiple datasets show that AEPIC achieves superior clustering performance, with future work extending it to multimodal and large-scale scenarios.

Acknowledgments

This research was supported by the National Key R&D Program of China (No.2023YFC3304500), and the Guizhou Provincial Science and Technology Department Project (No. Qiankehe MS[2026] 077).