Image-Based Convolutional Clustering

• Image-based convolutional clustering is a method that uses deep convolutional encoders to transform image data into feature spaces optimized for semantic cluster discovery.
• It employs both soft and hard assignment strategies—including Student's t-distribution kernels and k-means—to enhance clustering accuracy and robustness.
• Robust evaluation metrics and multi-view techniques validate performance across diverse applications, from industrial monitoring to large-scale image datasets.

Image-based convolutional clustering encompasses a diverse methodology space interfacing deep convolutional neural architectures with unsupervised clustering, leveraging the high-dimensional structure and spatial localities of image data. This class of approaches substitutes or augments classical distance-based clustering with representations learned from convolutional encoders, producing feature spaces where clusters correspond more closely to semantic or operational patterns. The field has advanced with architectures for both generic natural image clustering as well as for structured signals (e.g., industrial time series engineered into image-like matrices), and incorporates innovations in representation learning, cluster assignment, ensemble and hierarchical methodologies, and robust internal evaluation metrics.

1. Transformation of Input Data and Feature Learning

The cornerstone of image-based convolutional clustering is the transformation of raw data into forms amenable to convolutional processing, followed by representation learning that sculpts the embedding space for downstream clustering. For visual images, this process is usually direct: high-dimensional RGB or grayscale arrays are input to a convolutional backbone, which may be a standard classifier such as ResNet, VGG, or self-supervised variants (e.g., SimCLR, Barlow Twins, CLIP), possibly fine-tuned for unsupervised clustering (Zhu et al., 4 Aug 2024, Song et al., 2023). For structured non-image data such as univariate or multivariate time series, featurization schemes that map sequences to image-like matrices are central. In TS-IDEC (Ma et al., 17 Nov 2025), each univariate time series of length $N$ is converted to a $n_s \times n_s$ grayscale image via overlapping sliding windows, preserving both local and global temporal context. Each row of the matrix encodes a local segment; overlapping ensures smooth transitions and retention of temporal structure.

Post-representation, deep convolutional autoencoders serve as the primary architecture for extracting latent features, typically using sequential convolution and pooling layers yielding a compact latent variable $z$, followed by symmetrically mirrored decoders for reconstruction (Ma et al., 17 Nov 2025, Li et al., 2017). These representations form the substrate upon which clustering penalties, auxiliary losses, or explicit cluster assignment modules act.

2. Cluster Assignment Strategies: Soft, Hard, and Hybrid Modes

Assignment of cluster labels in convolutionally-derived latent spaces is varied. A central scheme is soft assignment via Student's t-distribution-based kernels (Ma et al., 17 Nov 2025, Li et al., 2017), where for centroid $\mu_j$ and embedding $z_i$, the soft probability is

$$q_{ij} = \frac{(1 + \|z_i - \mu_j\|^2/\alpha)^{-(\alpha+1)/2}}{\sum_{j'}(1 + \|z_i - \mu_{j'}\|^2/\alpha)^{-(\alpha+1)/2}}$$

with $\alpha$ typically set to 1. This assignment can be sharpened by constructing a target distribution $p_{ij}$ proportional to $q_{ij}^2$ normalized by population frequency, and the alignment between $Q$ and $P$ is measured by the Kullback-Leibler divergence, driving the encoder to produce maximally cluster-discriminative features.

Hard assignments are also retained, typically via k-means applied post hoc to the learned latent space. Hybrid (dual-mode) selection strategies are increasingly adopted: for example, TS-IDEC performs both soft assignment during training and hard clustering via k-means, then selects between the two based on cluster plausibility and composite internal evaluation metrics (Ma et al., 17 Nov 2025).

Hierarchical and ensemble assignment strategies have emerged for increasing robustness and representational power: agglomerative clustering is integrated directly in the loss function for embedding layers (Ghazanfari et al., 2020), while ensemble frameworks, such as DeepCluE, draw from multiple layers' representations and fuse diverse base clusterings via transfer-cut consensus on a bipartite cluster/sample graph (Huang et al., 2022).

3. Evaluation, Internal Validation, and Robustness

Clustering quality assessment in the absence of ground truth is a recurrent challenge. Classical metrics—Silhouette score ($S$), Calinski–Harabasz index ($CH$), and Davies–Bouldin index ($DB$)—often exhibit conflicting preferences. Composite or harmonized metrics have thus been formulated; for instance, the $S_{eva}$ metric in TS-IDEC combines min-max and rank-normalizations of $S$, $CH$, and inverted $DB$ to yield a robust, scale-invariant single quality measure:

$$S_{eva} = \frac{1}{3}(\tilde S + \widetilde{CH} + \widetilde{DB})$$

where each term is the average of min-max and rank-normalized versions of the corresponding metric (Ma et al., 17 Nov 2025).

Robustness analyses typically involve sensitivity to hyperparameters (window size, grid partitioning), ablations on clustering mode (soft-only/hard-only), ensemble diversity, and the impact of removing attention mechanisms, grid-jigsaw modules, or contrastive losses (Ma et al., 17 Nov 2025, Song et al., 2023, Huang et al., 2022).

4. Specialized Techniques: Attention Modules, Multi-View, and Jigsaw Representations

Recent methods expand the expressivity of clustering representations via architectural augmentations. Attention-based approaches, such as GATCluster, incorporate a Gaussian attention module to focus representation on object- or context-relevant image regions during unsupervised clustering. The “Label Feature Theorem” in GATCluster formalizes conditions under which cluster membership converges to a one-hot code, yielding provably non-trivial solutions (Niu et al., 2020).

Multi-view and ensemble clustering interpret different feature extraction architectures (e.g., ResNet, VGG, Inception, Xception) as complementary “views” of the same data, with consensus built via neural network fusion layers or consensus functions (Guérin et al., 2018, Huang et al., 2022). The pGJR framework introduces the Grid Jigsaw Representation, partitioning feature maps into local grids and evolving each by a local reconstruction operation, explicitly modeling fine-grained spatial context and leveraging pre-trained CLIP for semantic prior injection (Song et al., 2023).

5. Applications and Case Studies

Image-based convolutional clustering approaches are deployed over a wide application space:

• Industrial process monitoring: TS-IDEC demonstrates unsupervised discovery of operational modes for 3,927 melting cycles of a Nordic foundry, detecting energy-optimal and suboptimal patterns in energy use, thermal dynamics, and process durations (Ma et al., 17 Nov 2025).
• Generic vision benchmarks: Methods are routinely evaluated on CIFAR-10, CIFAR-100, STL-10, ImageNet-10, and ImageNet-Dog; quantitative improvements are measured by ACC, NMI, and ARI. Notably, pGJR delivers converged clustering (ACC 87.5% on CIFAR-10; 97.9% on STL-10) with orders-of-magnitude faster convergence when initializing from CLIP (Song et al., 2023).
• Large-scale image repositories: CNN-based iterative clustering (with feature drift compensation) scales to multi-million image datasets (ILSVRC-val, Places2-train), leveraging mini-batch k-means and cluster-specialist networks for enhanced accuracy and tractable resource usage (Hsu et al., 2017).
• Multi-modal and non-visual domains: Sliding-window embedding schemes for time series yield image-transformed matrices that can be processed analogously to standard images for clustering; this approach generalizes to chemical, smart grid, or machining process data types (Ma et al., 17 Nov 2025).

6. Comparative Analysis and Methodological Advances

A wide spectrum of architectures has been benchmarked against one another:

Methodology	Core Innovations	Notable Results/Findings
TS-IDEC (Ma et al., 17 Nov 2025)	Sliding-window to image, DCAE + dual clustering, S_eva	Best S_eva, superior robustness
pGJR (Song et al., 2023)	CLIP-based features, grid-jigsaw, local refinement	SOTA ACC/NMI/ARI, fast convergence
ICBPL (Zhu et al., 4 Aug 2024)	Self-supervised pretraining, kNN+PEDCC losses	SOTA on CIFAR-10, STL-10, etc.
GATCluster (Niu et al., 2020)	Self-supervised Gaussian attention, label theorem	ACC improvement (STL-10, ImageNet-10)
DeepCluE (Huang et al., 2022)	Multi-layer ensemble, entropy weighting, transfer-cut	Highest NMI/ARI on many datasets

These advances highlight major trends: (1) the increasing integration of feature extraction and clustering in end-to-end differentiable pipelines; (2) explicit modeling of spatial, temporal, or multi-view context; (3) robust quality evaluation and automated model selection; and (4) generalizability across visual and non-visual domains.

7. Challenges, Limitations, and Future Directions

Despite robust progress, several challenges persist. Many clustering pipelines require knowledge of the number of clusters $k$ or suffer from mode collapse without external validation or careful hyperparameterization. Scaling to ultra-large datasets remains non-trivial for algorithms requiring pairwise affinity computation (e.g., t-SNE-based density methods (Ren et al., 2018)); the development of scalable approximate techniques is ongoing. For highly entangled or fine-grained categories, annotation-free clustering can fall short of supervised or semi-supervised alternatives (Zhu et al., 4 Aug 2024). Promising directions include the extension of internal context modeling (e.g., jigsaw, attention, multi-view) to non-visual domains, automated cluster count estimation without ground truth, and integration with weak or self-supervised signals to further close the performance gap to fully supervised classification.

In summary, image-based convolutional clustering represents an overview of deep representation learning and clustering, attaining high performance and interpretability in diverse domains by exploiting the spatial and structural priors inherent to convolutional architectures and with innovations in cluster assignment, ensemble consensus, and robust evaluation (Ma et al., 17 Nov 2025, Song et al., 2023, Zhu et al., 4 Aug 2024, Huang et al., 2022).