This paper presents a novel non-rigid point set registration method that is inspired by unsupervised clustering analysis. Unlike previous approaches that treat the source and target point sets as separate entities, we develop a holistic framework where they are formulated as clustering centroids and clustering members, separately. We then adopt Tikhonov regularization with an $\ell_1$-induced Laplacian kernel instead of the commonly used Gaussian kernel to ensure smooth and more robust displacement fields. Our formulation delivers closed-form solutions, theoretical guarantees, independence from dimensions, and the ability to handle large deformations. Subsequently, we introduce a clustering-improved Nystr\"om method to effectively reduce the computational complexity and storage of the Gram matrix to linear, while providing a rigorous bound for the low-rank approximation. Our method achieves high accuracy results across various scenarios and surpasses competitors by a significant margin, particularly on shapes with substantial deformations. Additionally, we demonstrate the versatility of our method in challenging tasks such as shape transfer and medical registration.

End-to-end neural diarization (EEND) models offer significant improvements over traditional embedding-based Speaker Diarization (SD) approaches but falls short on generalizing to long-form audio with large number of speakers. EEND-vector-clustering method mitigates this by combining local EEND with global clustering of speaker embeddings from local windows, but this requires an additional speaker embedding framework alongside the EEND module. In this paper, we propose a novel framework applying EEND both locally and globally for long-form audio without separate speaker embeddings. This approach achieves significant relative DER reduction of 13% and 10% over the conventional 1-pass EEND on Callhome American English and RT03-CTS datasets respectively and marginal improvements over EEND-vector-clustering without the need for additional speaker embeddings. Furthermore, we discuss the computational complexity of our proposed framework and explore strategies for reducing processing times.

DBSCAN and OPTICS are powerful algorithms for identifying clusters of points in domains where few assumptions can be made about the structure of the data. In this paper, we leverage these strengths and introduce a new algorithm, LINSCAN, designed to seek lineated clusters that are difficult to find and isolate with existing methods. In particular, by embedding points as normal distributions approximating their local neighborhoods and leveraging a distance function derived from the Kullback Leibler Divergence, LINSCAN can detect and distinguish lineated clusters that are spatially close but have orthogonal covariances. We demonstrate how LINSCAN can be applied to seismic data to identify active faults, including intersecting faults, and determine their orientation. Finally, we discuss the properties a generalization of DBSCAN and OPTICS must have in order to retain the stability benefits of these algorithms.

In this paper, we propose a scalable community detection algorithm using hypergraph modularity function, h-Louvain. It is an adaptation of the classical Louvain algorithm in the context of hypergraphs. We observe that a direct application of the Louvain algorithm to optimize the hypergraph modularity function often fails to find meaningful communities. We propose a solution to this issue by adjusting the initial stage of the algorithm via carefully and dynamically tuned linear combination of the graph modularity function of the corresponding two-section graph and the desired hypergraph modularity function. The process is guided by Bayesian optimization of the hyper-parameters of the proposed procedure. Various experiments on synthetic as well as real-world networks are performed showing that this process yields improved results in various regimes.

This review summarizes popular unsupervised learning methods, and gives an overview of their past, current, and future uses in astronomy. Unsupervised learning aims to organise the information content of a dataset, in such a way that knowledge can be extracted. Traditionally this has been achieved through dimensionality reduction techniques that aid the ranking of a dataset, for example through principal component analysis or by using auto-encoders, or simpler visualisation of a high dimensional space, for example through the use of a self organising map. Other desirable properties of unsupervised learning include the identification of clusters, i.e. groups of similar objects, which has traditionally been achieved by the k-means algorithm and more recently through density-based clustering such as HDBSCAN. More recently, complex frameworks have emerged, that chain together dimensionality reduction and clustering methods. However, no dataset is fully unknown. Thus, nowadays a lot of research has been directed towards self-supervised and semi-supervised methods that stand to gain from both supervised and unsupervised learning.

This paper introduces a robust zero-trust architecture (ZTA) tailored for the decentralized system that empowers efficient remote work and collaboration within IoT networks. Using blockchain-based federated learning principles, our proposed framework includes a robust aggregation mechanism designed to counteract malicious updates from compromised clients, enhancing the security of the global learning process. Moreover, secure and reliable trust computation is essential for remote work and collaboration. The robust ZTA framework integrates anomaly detection and trust computation, ensuring secure and reliable device collaboration in a decentralized fashion. We introduce an adaptive algorithm that dynamically adjusts to varying user contexts, using unsupervised clustering to detect novel anomalies, like zero-day attacks. To ensure a reliable and scalable trust computation, we develop an algorithm that dynamically adapts to varying user contexts by employing incremental anomaly detection and clustering techniques to identify and share local and global anomalies between nodes. Future directions include scalability improvements, Dirichlet process for advanced anomaly detection, privacy-preserving techniques, and the integration of post-quantum cryptographic methods to safeguard against emerging quantum threats.

The advent of online social networks has led to the development of an abundant literature on the study of online social groups and their relationship to individuals' personalities as revealed by their textual productions. Social structures are inferred from a wide range of social interactions. Those interactions form complex -- sometimes multi-layered -- networks, on which community detection algorithms are applied to extract higher order structures. The choice of the community detection algorithm is however hardily questioned in relation with the cultural production of the individual they classify. In this work, we assume the entangled nature of social networks and their cultural production to propose a definition of cultural based online social groups as sets of individuals whose online production can be categorized as social group-related. We take advantage of this apparently self-referential description of online social groups with a hybrid methodology that combines a community detection algorithm and a natural language processing classification algorithm. A key result of this analysis is the possibility to score community detection algorithms using their agreement with the natural language processing classification. A second result is that we can assign the opinion of a random user at >85% accuracy.

In location-based resource allocation scenarios, the distances between each individual and the facility are desired to be approximately equal, thereby ensuring fairness. Individually fair clustering is often employed to achieve the principle of treating all points equally, which can be applied in these scenarios. This paper proposes a novel algorithm, tilted k-means (TKM), aiming to achieve individual fairness in clustering. We integrate the exponential tilting into the sum of squared errors (SSE) to formulate a novel objective function called tilted SSE. We demonstrate that the tilted SSE can generalize to SSE and employ the coordinate descent and first-order gradient method for optimization. We propose a novel fairness metric, the variance of the distances within each cluster, which can alleviate the Matthew Effect typically caused by existing fairness metrics. Our theoretical analysis demonstrates that the well-known k-means++ incurs a multiplicative error of O(k log k), and we establish the convergence of TKM under mild conditions. In terms of fairness, we prove that the variance generated by TKM decreases with a scaled hyperparameter. In terms of efficiency, we demonstrate the time complexity is linear with the dataset size. Our experiments demonstrate that TKM outperforms state-of-the-art methods in effectiveness, fairness, and efficiency.

The Economic and Product Complexity Indices, introduced as an attempt to measure these capabilities from a country's basket of exported products, have become popular to study economic development, the geography of innovation, and industrial policies. Despite this reception, the interpretation of these indicators proved difficult. Although the original Method of Reflections suggested a direct interconnection between country and product metrics, it has been proved that the Economic and Product Complexity Indices result from a spectral clustering algorithm that separately groups similar countries or similar products, respectively. This recent approach to economic and product complexity conflicts with the original one and treats separately countries and products. However, building on previous interpretations of the indices and the recent evolution in spectral clustering, we show that these indices simultaneously identify two co-clusters of similar countries and products. This viewpoint reconciles the spectral clustering interpretation of the indices with the original Method of Reflections interpretation. By proving the often neglected intimate relationship between country and product complexity, this approach emphasizes the role of a selected set of products in determining economic development while extending the range of applications of these indicators in economics.

Effective clustering of biomedical data is crucial in precision medicine, enabling accurate stratifiction of patients or samples. However, the growth in availability of high-dimensional categorical data, including `omics data, necessitates computationally efficient clustering algorithms. We present VICatMix, a variational Bayesian finite mixture model designed for the clustering of categorical data. The use of variational inference (VI) in its training allows the model to outperform competitors in term of efficiency, while maintaining high accuracy. VICatMix furthermore performs variable selection, enhancing its performance on high-dimensional, noisy data. The proposed model incorporates summarisation and model averaging to mitigate poor local optima in VI, allowing for improved estimation of the true number of clusters simultaneously with feature saliency. We demonstrate the performance of VICatMix with both simulated and real-world data, including applications to datasets from The Cancer Genome Atlas (TCGA), showing its use in cancer subtyping and driver gene discovery. We demonstrate VICatMix's utility in integrative cluster analysis with different `omics datasets, enabling the discovery of novel subtypes. \textbf{Availability:} VICatMix is freely available as an R package, incorporating C++ for faster computation, at \url{https://github.com/j-ackierao/VICatMix}.