Federated learning has recently garnered significant attention, especially within the domain of supervised learning. However, despite the abundance of unlabeled data on end-users, unsupervised learning problems such as clustering in the federated setting remain underexplored. In this paper, we investigate the federated clustering problem, with a focus on federated k-means. We outline the challenge posed by its non-convex objective and data heterogeneity in the federated framework. To tackle these challenges, we adopt a new perspective by studying the structures of local solutions in k-means and propose a one-shot algorithm called FeCA (Federated Centroid Aggregation). FeCA adaptively refines local solutions on clients, then aggregates these refined solutions to recover the global solution of the entire dataset in a single round. We empirically demonstrate the robustness of FeCA under various federated scenarios on both synthetic and real-world data. Additionally, we extend FeCA to representation learning and present DeepFeCA, which combines Deep-Cluster and FeCA for unsupervised feature learning in the federated setting.

As language models become more general purpose, increased attention needs to be paid to detecting out-of-distribution (OOD) instances, i.e., those not belonging to any of the distributions seen during training. Existing methods for detecting OOD data are computationally complex and storage-intensive. We propose a novel soft clustering approach for OOD detection based on non-negative kernel regression. Our approach greatly reduces computational and space complexities (up to 11x improvement in inference time and 87% reduction in storage requirements) and outperforms existing approaches by up to 4 AUROC points on four different benchmarks. We also introduce an entropy-constrained version of our algorithm, which leads to further reductions in storage requirements (up to 97% lower than comparable approaches) while retaining competitive performance. Our soft clustering approach for OOD detection highlights its potential for detecting tail-end phenomena in extreme-scale data settings.

Application-specific quantum computers offer the most efficient means to tackle problems intractable by classical computers. Realizing these architectures necessitates a deep understanding of quantum circuit properties and their relationship to execution outcomes on quantum devices. Our study aims to perform for the first time a rigorous examination of quantum circuits by introducing graph theory-based metrics extracted from their qubit interaction graph and gate dependency graph alongside conventional parameters describing the circuit itself. This methodology facilitates a comprehensive analysis and clustering of quantum circuits. Furthermore, it uncovers a connection between parameters rooted in both qubit interaction and gate dependency graphs, and the performance metrics for quantum circuit mapping, across a range of established quantum device and mapping configurations. Among the various device configurations, we particularly emphasize modular (i.e., multi-core) quantum computing architectures due to their high potential as a viable solution for quantum device scalability. This thorough analysis will help us to: i) identify key attributes of quantum circuits that affect the quantum circuit mapping performance metrics; ii) predict the performance on a specific chip for similar circuit structures; iii) determine preferable combinations of mapping techniques and hardware setups for specific circuits; and iv) define representative benchmark sets by clustering similarly structured circuits.

Stop location detection, within human mobility studies, has an impacts in multiple fields including urban planning, transport network design, epidemiological modeling, and socio-economic segregation analysis. However, it remains a challenging task because classical density clustering algorithms often struggle with noisy or incomplete GPS datasets. This study investigates the application of classification algorithms to enhance density-based methods for stop identification. Our approach incorporates multiple features, including individual routine behavior across various time scales and local characteristics of individual GPS points. The dataset comprises privacy-preserving and anonymized GPS points previously labeled as stops by a sequence-oriented, density-dependent algorithm. We simulated data gaps by removing point density from select stops to assess performance under sparse data conditions. The model classifies individual GPS points within trajectories as potential stops or non-stops. Given the highly imbalanced nature of the dataset, we prioritized recall over precision in performance evaluation. Results indicate that this method detects most stops, even in the presence of spatio-temporal gaps and that points classified as false positives often correspond to recurring locations for devices, typically near previous stops. While this research contributes to mobility analysis techniques, significant challenges persist. The lack of ground truth data limits definitive conclusions about the algorithm's accuracy. Further research is needed to validate the method across diverse datasets and to incorporate collective behavior inputs.

We investigate the use of clustering methods on data produced by a stochastic simulator, with applications in anomaly detection, pre-optimization, and online monitoring. We introduce an agglomerative clustering algorithm that clusters multivariate empirical distributions using the regularized Wasserstein distance and apply the proposed methodology on a call-center model.

We present a unified theory for Mahalanobis-type anomaly detection on Banach spaces, using ideas from Cameron-Martin theory applied to non-Gaussian measures. This approach leads to a basis-free, data-driven notion of anomaly distance through the so-called variance norm of a probability measure, which can be consistently estimated using empirical measures. Our framework generalizes the classical $\mathbb{R}^d$, functional $(L^2[0,1])^d$, and kernelized settings, including the general case of non-injective covariance operator. We prove that the variance norm depends solely on the inner product in a given Hilbert space, and hence that the kernelized Mahalanobis distance can naturally be recovered by working on reproducing kernel Hilbert spaces. Using the variance norm, we introduce the notion of a kernelized nearest-neighbour Mahalanobis distance for semi-supervised anomaly detection. In an empirical study on 12 real-world datasets, we demonstrate that the kernelized nearest-neighbour Mahalanobis distance outperforms the traditional kernelized Mahalanobis distance for multivariate time series anomaly detection, using state-of-the-art time series kernels such as the signature, global alignment, and Volterra reservoir kernels. Moreover, we provide an initial theoretical justification of nearest-neighbour Mahalanobis distances by developing concentration inequalities in the finite-dimensional Gaussian case.

We propose an AutoML system that enables model selection on clustering problems by leveraging optimal transport-based dataset similarity. Our objective is to establish a comprehensive AutoML pipeline for clustering problems and provide recommendations for selecting the most suitable algorithms, thus opening up a new area of AutoML beyond the traditional supervised learning settings. We compare our results against multiple clustering baselines and find that it outperforms all of them, hence demonstrating the utility of similarity-based automated model selection for solving clustering applications.

Active clustering aims to boost the clustering performance by integrating human-annotated pairwise constraints through strategic querying. Conventional approaches with semi-supervised clustering schemes encounter high query costs when applied to large datasets with numerous classes. To address these limitations, we propose a novel Adaptive Active Aggregation and Splitting (A3S) framework, falling within the cluster-adjustment scheme in active clustering. A3S features strategic active clustering adjustment on the initial cluster result, which is obtained by an adaptive clustering algorithm. In particular, our cluster adjustment is inspired by the quantitative analysis of Normalized mutual information gain under the information theory framework and can provably improve the clustering quality. The proposed A3S framework significantly elevates the performance and scalability of active clustering. In extensive experiments across diverse real-world datasets, A3S achieves desired results with significantly fewer human queries compared with existing methods.

Combining machine clustering with deep models has shown remarkable superiority in deep clustering. It modifies the data processing pipeline into two alternating phases: feature clustering and model training. However, such alternating schedule may lead to instability and computational burden issues. We propose a centerless clustering algorithm called Probability Aggregation Clustering (PAC) to proactively adapt deep learning technologies, enabling easy deployment in online deep clustering. PAC circumvents the cluster center and aligns the probability space and distribution space by formulating clustering as an optimization problem with a novel objective function. Based on the computation mechanism of the PAC, we propose a general online probability aggregation module to perform stable and flexible feature clustering over mini-batch data and further construct a deep visual clustering framework deep PAC (DPAC). Extensive experiments demonstrate that PAC has superior clustering robustness and performance and DPAC remarkably outperforms the state-of-the-art deep clustering methods.

Incomplete multi-view clustering (IMVC) aims to cluster multi-view data that are only partially available. This poses two main challenges: effectively leveraging multi-view information and mitigating the impact of missing views. Prevailing solutions employ cross-view contrastive learning and missing view recovery techniques. However, they either neglect valuable complementary information by focusing only on consensus between views or provide unreliable recovered views due to the absence of supervision. To address these limitations, we propose a novel Unified and Robust Representation Learning for Incomplete Multi-View Clustering (URRL-IMVC). URRL-IMVC directly learns a unified embedding that is robust to view missing conditions by integrating information from multiple views and neighboring samples. Firstly, to overcome the limitations of cross-view contrastive learning, URRL-IMVC incorporates an attention-based auto-encoder framework to fuse multi-view information and generate unified embeddings. Secondly, URRL-IMVC directly enhances the robustness of the unified embedding against view-missing conditions through KNN imputation and data augmentation techniques, eliminating the need for explicit missing view recovery. Finally, incremental improvements are introduced to further enhance the overall performance, such as the Clustering Module and the customization of the Encoder. We extensively evaluate the proposed URRL-IMVC framework on various benchmark datasets, demonstrating its state-of-the-art performance. Furthermore, comprehensive ablation studies are performed to validate the effectiveness of our design.