Community detection is the task of clustering objects based on their pairwise relationships. Most of the model-based community detection methods, such as the stochastic block model and its variants, are designed for networks with binary (yes/no) edges. In many practical scenarios, edges often possess continuous weights, spanning positive and negative values, which reflect varying levels of connectivity. To address this challenge, we introduce the heterogeneous block covariance model (HBCM) that defines a community structure within the covariance matrix, where edges have signed and continuous weights. Furthermore, it takes into account the heterogeneity of objects when forming connections with other objects within a community. A novel variational expectation-maximization algorithm is proposed to estimate the group membership. The HBCM provides provable consistent estimates of memberships, and its promising performance is observed in numerical simulations with different setups. The model is applied to a single-cell RNA-seq dataset of a mouse embryo and a stock price dataset. Supplementary materials for this article are available online.

Computational Fluid Dynamics (CFD) is an indispensable method of fluid modelling in engineering applications, reducing the need for physical prototypes and testing for tasks such as design optimisation and performance analysis. Depending on the complexity of the system under consideration, models ranging from low to high fidelity can be used for prediction, allowing significant speed-up. However, the choice of model requires information about the actual dynamics of the flow regime. Correctly identifying the regions/clusters of flow that share the same dynamics has been a challenging research topic to date. In this study, we propose a novel hybrid approach to flow clustering. It consists of characterising each sample point of the system with equation-based features, i.e. features are budgets that represent the contribution of each term from the original governing equation to the local dynamics at each sample point. This was achieved by applying the Sparse Identification of Nonlinear Dynamical systems (SINDy) method pointwise to time evolution data. The method proceeds with equation-based clustering using the Girvan-Newman algorithm. This allows the detection of communities that share the same physical dynamics. The algorithm is implemented in both Eulerian and Lagrangian frameworks. In the Lagrangian, i.e. dynamic approach, the clustering is performed on the trajectory of each point, allowing the change of clusters to be represented also in time. The performance of the algorithm is first tested on a flow around a cylinder. The construction of the dynamic clusters in this test case clearly shows the evolution of the wake from the steady state solution through the transient to the oscillatory solution. Dynamic clustering was then successfully tested on turbulent flow data. Two distinct and well-defined clusters were identified and their temporal evolution was reconstructed.

Advancements in artificial intelligence, machine learning, and deep learning have catalyzed the transformation of big data analytics and management into pivotal domains for research and application. This work explores the theoretical foundations, methodological advancements, and practical implementations of these technologies, emphasizing their role in uncovering actionable insights from massive, high-dimensional datasets. The study presents a systematic overview of data preprocessing techniques, including data cleaning, normalization, integration, and dimensionality reduction, to prepare raw data for analysis. Core analytics methodologies such as classification, clustering, regression, and anomaly detection are examined, with a focus on algorithmic innovation and scalability. Furthermore, the text delves into state-of-the-art frameworks for data mining and predictive modeling, highlighting the role of neural networks, support vector machines, and ensemble methods in tackling complex analytical challenges. Special emphasis is placed on the convergence of big data with distributed computing paradigms, including cloud and edge computing, to address challenges in storage, computation, and real-time analytics. The integration of ethical considerations, including data privacy and compliance with global standards, ensures a holistic perspective on data management. Practical applications across healthcare, finance, marketing, and policy-making illustrate the real-world impact of these technologies. Through comprehensive case studies and Python-based implementations, this work equips researchers, practitioners, and data enthusiasts with the tools to navigate the complexities of modern data analytics. It bridges the gap between theory and practice, fostering the development of innovative solutions for managing and leveraging data in the era of artificial intelligence.

Machine learning systems are increasingly being used in critical decision making such as healthcare, finance, and criminal justice. Concerns around their fairness have resulted in several bias mitigation techniques that emphasize the need for high-quality data to ensure fairer decisions. However, the role of earlier stages of machine learning pipelines in mitigating model bias has not been explored well. In this paper, we focus on the task of acquiring additional labeled data points for training the downstream machine learning model to rapidly improve its fairness. Since not all data points in a data pool are equally beneficial to the task of fairness, we generate an ordering in which data points should be acquired. We present DataSift, a data acquisition framework based on the idea of data valuation that relies on partitioning and multi-armed bandits to determine the most valuable data points to acquire. Over several iterations, DataSift selects a partition and randomly samples a batch of data points from the selected partition, evaluates the benefit of acquiring the batch on model fairness, and updates the utility of partitions depending on the benefit. To further improve the effectiveness and efficiency of evaluating batches, we leverage influence functions that estimate the effect of acquiring a batch without retraining the model. We empirically evaluate DataSift on several real-world and synthetic datasets and show that the fairness of a machine learning model can be significantly improved even while acquiring a few data points.

Local clustering aims to find a compact cluster near the given starting instances. This work focuses on graph local clustering, which has broad applications beyond graphs because of the internal connectivities within various modalities. While most existing studies on local graph clustering adopt the discrete graph setting (i.e., unweighted graphs without self-loops), real-world graphs can be more complex. In this paper, we extend the non-approximating Andersen-Chung-Lang ("ACL") algorithm beyond discrete graphs and generalize its quadratic optimality to a wider range of graphs, including weighted, directed, and self-looped graphs and hypergraphs. Specifically, leveraging PageRank, we propose two algorithms: GeneralACL for graphs and HyperACL for hypergraphs. We theoretically prove that, under two mild conditions, both algorithms can identify a quadratically optimal local cluster in terms of conductance with at least 1/2 probability. On the property of hypergraphs, we address a fundamental gap in the literature by defining conductance for hypergraphs from the perspective of hypergraph random walks. Additionally, we provide experiments to validate our theoretical findings.

The k-means algorithm can simplify large-scale spatial vectors, such as 2D geo-locations and 3D point clouds, to support fast analytics and learning. However, when processing large-scale datasets, existing k-means algorithms have been developed to achieve high performance with significant computational resources, such as memory and CPU usage time. These algorithms, though effective, are not well-suited for resource-constrained devices. In this paper, we propose a fast, memory-efficient, and cost-predictable k-means called Dask-means. We first accelerate k-means by designing a memory-efficient accelerator, which utilizes an optimized nearest neighbor search over a memory-tunable index to assign spatial vectors to clusters in batches. We then design a lightweight cost estimator to predict the memory cost and runtime of the k-means task, allowing it to request appropriate memory from devices or adjust the accelerator's required space to meet memory constraints, and ensure sufficient CPU time for running k-means. Experiments show that when simplifying datasets with scale such as $10^6$, Dask-means uses less than $30$MB of memory, achieves over $168$ times speedup compared to the widely-used Lloyd's algorithm. We also validate Dask-means on mobile devices, where it demonstrates significant speedup and low memory cost compared to other state-of-the-art (SOTA) k-means algorithms. Our cost estimator estimates the memory cost with a difference of less than $3\%$ from the actual ones and predicts runtime with an MSE up to $33.3\%$ lower than SOTA methods.

Recently, deep matrix factorization has been established as a powerful model for unsupervised tasks, achieving promising results, especially for multi-view clustering. However, existing methods often lack effective feature selection mechanisms and rely on empirical hyperparameter selection. To address these issues, we introduce a novel Deep Matrix Factorization with Adaptive Weights for Multi-View Clustering (DMFAW). Our method simultaneously incorporates feature selection and generates local partitions, enhancing clustering results. Notably, the features weights are controlled and adjusted by a parameter that is dynamically updated using Control Theory inspired mechanism, which not only improves the model's stability and adaptability to diverse datasets but also accelerates convergence. A late fusion approach is then proposed to align the weighted local partitions with the consensus partition. Finally, the optimization problem is solved via an alternating optimization algorithm with theoretically guaranteed convergence. Extensive experiments on benchmark datasets highlight that DMFAW outperforms state-of-the-art methods in terms of clustering performance.

We present a novel representation learning method for downstream tasks such as anomaly detection and unsupervised transient classification in high-energy datasets. This approach enabled the discovery of a new fast X-ray transient (FXT) in the Chandra archive, XRT 200515, a needle-in-the-haystack event and the first Chandra FXT of its kind. Recent serendipitous breakthroughs in X-ray astronomy, including FXTs from binary neutron star mergers and an extragalactic planetary transit candidate, highlight the need for systematic transient searches in X-ray archives. We introduce new event file representations, E-t Maps and E-t-dt Cubes, designed to capture both temporal and spectral information, effectively addressing the challenges posed by variable-length event file time series in machine learning applications. Our pipeline extracts low-dimensional, informative features from these representations using principal component analysis or sparse autoencoders, followed by clustering in the embedding space with DBSCAN. New transients are identified within transient-dominant clusters or through nearest-neighbor searches around known transients, producing a catalog of 3,539 candidates (3,427 flares and 112 dips). XRT 200515 exhibits unique temporal and spectral variability, including an intense, hard <10 s initial burst followed by spectral softening in an ~800 s oscillating tail. We interpret XRT 200515 as either the first giant magnetar flare observed at low X-ray energies or the first extragalactic Type I X-ray burst from a faint LMXB in the LMC. Our method extends to datasets from other observatories such as XMM-Newton, Swift-XRT, eROSITA, Einstein Probe, and upcoming missions like AXIS.

Self-supervised heterogeneous graph learning (SHGL) has shown promising potential in diverse scenarios. However, while existing SHGL methods share a similar essential with clustering approaches, they encounter two significant limitations: (i) noise in graph structures is often introduced during the message-passing process to weaken node representations, and (ii) cluster-level information may be inadequately captured and leveraged, diminishing the performance in downstream tasks. In this paper, we address these limitations by theoretically revisiting SHGL from the spectral clustering perspective and introducing a novel framework enhanced by rank and dual consistency constraints. Specifically, our framework incorporates a rank-constrained spectral clustering method that refines the affinity matrix to exclude noise effectively. Additionally, we integrate node-level and cluster-level consistency constraints that concurrently capture invariant and clustering information to facilitate learning in downstream tasks. We theoretically demonstrate that the learned representations are divided into distinct partitions based on the number of classes and exhibit enhanced generalization ability across tasks. Experimental results affirm the superiority of our method, showcasing remarkable improvements in several downstream tasks compared to existing methods.

Intelligent streetlight systems divide the streetlight network into multiple sectors, activating only the streetlights in the corresponding sectors when traffic elements pass by, rather than all streetlights, effectively reducing energy waste. This strategy requires streetlights to understand their neighbor relationships to illuminate only the streetlights in their respective sectors. However, manually configuring the neighbor relationships for a large number of streetlights in complex large-scale road streetlight networks is cumbersome and prone to errors. Due to the crisscrossing nature of roads, it is also difficult to determine the neighbor relationships using GPS or communication positioning. In response to these issues, this article proposes a systematic approach to model the streetlight network as a social network and construct a neighbor relationship probabilistic graph using IoT event records of streetlights detecting traffic elements. Based on this, a multi-objective genetic algorithm based probabilistic graph clustering method is designed to discover the neighbor relationships of streetlights. Considering the characteristic that pedestrians and vehicles usually move at a constant speed on a section of a road, speed consistency is introduced as an optimization objective, which, together with traditional similarity measures, forms a multi-objective function, enhancing the accuracy of neighbor relationship discovery. Extensive experiments on simulation datasets were conducted, comparing the proposed algorithm with other probabilistic graph clustering algorithms. The results demonstrate that the proposed algorithm can more accurately identify the neighbor relationships of streetlights compared to other algorithms, effectively achieving adaptive streetlight control for traffic elements.