Clustering complex-shaped clusters is still chal lenging for most existing clustering algorithms. Herein, the peak-padding clustering algorithm (PeakPad)-clustering by padding density peaks with the minimum padding cost-is proposed. PeakPad executes clustering on the density surface and views complex-shaped clusters as combinations of highly associated single-peak clusters. The minimum padding cost that fully considers the surrounding context of a density peak is proposed to reflect a density peak's center potential, enabling PeakPad to have robust center detection performance. Unlike mean-shift (MSC), which detects centers based on their attributes in a complex-shaped density surface embedded in the high-dimensional space of density and features, PeakPad detects centers in a standard-shaped surface embedded in the 2-D density-change (DC) density space (composed of density and DC feature). Such standardization allows PeakPad to have fast and robust cluster center detection performance on complex-shaped clusters based on the minimum padding cost. Besides, PeakPad can provide a reasonable evaluation of the association between single-peak clusters by using the minimum padding cost. As a result, PeakPad can fast capture complex-shaped clusters, achieve robust center detection performance, and be suitable for large datasets. Benchmark test results on both synthetic and real datasets demonstrate the effectiveness of PeakPad.

As partial samples are often absent in certain views, incomplete multi-view clustering has become a challenging task. To tackle data with missing views, current methods either utilize the data similarity relations to recover missing samples or primarily consider the available information of existing samples, typically facing some inherent limitations. Firstly, traditional solutions cannot fully explore the potential information contained in missing samples due to their omission strategy, leading to sub-optimal graphs. Moreover, most methods mainly focus on data recovery from the view level, ignoring the differences among available/missing samples in various views. To this end, we propose a collaborative Similarity Fusion and Consistency Recovery (SFCR) method, which resolves the incomplete multi-view clustering problem by learning a unified similarity graph and recovering missing samples with consistent structures. Specifically, to learn a reliable graph compatible across views, a novel view-to-sample fusion model is designed to adaptively coalesce the view-wise similarities among available samples, not only preserving the complementarity and consistency among views but also properly balancing different samples. Furthermore, the missing samples are effectively recovered under the guidance of the fused similarity graph, so as to maintain the consistent structure of recovered data across views. In this way, the similarity learning and the missing data recovery benefit from each other in a collaborative reinforcement manner. Meanwhile, SFCR can directly obtain the final clustering labels without additional post-processing. Extensive experiments demonstrate the effectiveness and superiority of SFCR.

As a foundational clustering paradigm, Density Peak Clustering (DPC) partitions samples into clusters based on their density peaks, garnering widespread attention. However, traditional DPC methods usually focus on high-density regions, neglecting representative peaks in relatively low-density areas, particularly in datasets with varying densities and multiple peaks. Moreover, existing DPC variants struggle to identify clusters correctly in high-dimensional spaces due to the indistinct distance differences among samples and sparse data distributions. Additionally, existing methods typically adopt a one-step label assignment strategy, making them prone to cascading errors when initial misassignments occur. To address these challenges, we propose an Enhanced Density Peak Clustering (EDPC) method, which creatively incorporates multilayer perceptron (MLP)-based dimensionality reduction and a hierarchical label assignment strategy to significantly improve clustering performance in high-dimensional scenarios. Specifically, we introduce an effective selection condition that combines average densities and density-related distances to generate potential cluster centers, ensuring that peaks across different density regions are considered simultaneously. Furthermore, an MLP, guided by pseudo-labels from sub-clusters, is designed to learn low-dimensional embeddings for high-dimensional data, preserving data locality while enhancing clusterability. Extensive experiments demonstrate the effectiveness and superiority of EDPC against state-of-the-art DPC methods.

Spiking Neural Networks (SNNs) are increasingly explored for their energy efficiency and robustness in real-world applications, yet their privacy risks remain largely unexamined. In this work, we investigate the susceptibility of SNNs to Membership Inference Attacks (MIAs)-a major privacy threat where an adversary attempts to determine whether a given sample was part of the training dataset. While prior work suggests that SNNs may offer inherent robustness due to their discrete, event-driven nature, we find that its resilience diminishes as latency (T) increases. Furthermore, we introduce an input dropout strategy under black box setting, that significantly enhances membership inference in SNNs. Our findings challenge the assumption that SNNs are inherently more secure, and even though they are expected to be better, our results reveal that SNNs exhibit privacy vulnerabilities that are equally comparable to Artificial Neural Networks (ANNs).

Graph clustering technique is highly effective in detecting complex-shaped clusters, in which graph building is a crucial step. Nevertheless, building a reasonable graph that can exhibit high connectivity within clusters and low connectivity across clusters is challenging. Herein, we design a max-ascent-angle graph called the “Y-graph”, a high-sparse graph that automatically allocates dense edges within clusters and sparse edges across clusters, regardless of their shapes or dimensionality. In the graph, every point$x$is allowed to connect its nearest higher-density neighbor$\delta$, and another higher-density neighbor$\gamma$, satisfying that the angle$\angle \delta x\gamma$is the largest, called “max-ascent-angle”. By seeking the max-ascent-angle, points are automatically connected as the Y-graph, which is a reasonable graph that can effectively balance inter-cluster connectivity and intra-cluster non-connectivity. Besides, an edge weight function is designed to capture the similarity of the neighbor probability distribution, which effectively represents the density connectivity between points. By employing the Normalized-Cut (Ncut) technique, a Ncut-Y algorithm is proposed. Benefiting from the excellent performance of Y-graph, Ncut-Y can fast seek and cut the edges located in the low-density boundaries between clusters, thereby, capturing clusters effectively. Experimental results on both synthetic and real datasets demonstrate the effectiveness of Y-graph and Ncut-Y.

Since most existing single-prototype clustering algorithms are unsuitable for complex-shaped clusters, many multi-prototype clustering algorithms have been proposed. Nevertheless, the automatic estimation of the number of clusters and the detection of complex shapes are still challenging, and to solve such problems usually relies on user-specified parameters and may be prohibitively time-consuming. Herein, a stable-membership-based auto-tuning multi-peak clustering algorithm (SMMP) is proposed, which can achieve fast, automatic, and effective multi-prototype clustering without iteration. A dynamic association-transfer method is designed to learn the representativeness of points to sub-cluster centers during the generation of sub-clusters by applying the density peak clustering technique. According to the learned representativeness, a border-link-based connectivity measure is used to achieve high-fidelity similarity evaluation of sub-clusters. Meanwhile, based on the assumption that a reasonable clustering should have a relatively stable membership state upon the change of clustering thresholds, SMMP can automatically identify the number of sub-clusters and clusters, respectively. Also, SMMP is designed for large datasets. Experimental results on both synthetic and real datasets demonstrated the effectiveness of SMMP.

Most existing clustering algorithms require presetting cluster number and often fail to capture complex shapes. Herein, we propose a clustering algorithm by pruning a density-boosting cluster tree of density mounts—DEnsity MOuntains Separation clustering algorithm (DEMOS). A cluster is assumed to be a density-connected area with multiple (or a single) density mounts (i.e., single-peak clusters) and a relatively large dis-connectivity from density-connected areas of higher densities. Based on this assumption, DEMOS can easily detect the number of clusters and robustly reconstruct their complex shapes. It first builds the dataset into a peak graph, where each density peak represents a density mount. A multi-valley-link-based connectivity estimation method is embedded to efficiently estimate the connectivity between density peaks during peak graph building. Then, by applying a new linkage metric designed based on our assumption, DEMOS builds density mounts into a reasonably density-boosting cluster tree. After obtaining a robust center detection in a clarity-enhancing decision graph (i.e., a two-dimensional plot for detecting centers), DEMOS prunes the cluster tree into final clusters to finish clustering. Experimental results on both synthetic and real datasets demonstrated the effectiveness of DEMOS and its applicability to large-scale data clustering.

Fuzzy c-means (FCM) algorithm as a traditional clustering algorithm for image segmentation cannot effectively preserve local spatial information of pixels, which leads to poor segmentation results with inconsistent regions. For the remedy, superpixel technologies are applied, but spatial information preservation highly relies on the quality of superpixels. Density peak clustering algorithm (DPC) can reconstruct spatial information of arbitrary-shaped clusters, but its high time complexity$O(n^2)$and unrobust allocation strategy decrease its applicability for image segmentation. Herein, a fast density peak clustering method (PGDPC) based on the kNN distance matrix of data with time complexity$O(nlog(n))$is proposed. By using the peak-graph-based allocation strategy, PGDPC is more robust in the reconstruction of spatial information of various complex-shaped clusters, so it can rapidly and accurately segment images into high-consistent segmentation regions. Experiments on synthetic datasets, real and Wireless Capsule Endoscopy (WCE) images demonstrate that PGDPC as a fast and robust clustering algorithm is applicable to image segmentation.