We study the computational problem of computing a fair means clustering of discrete vectors, which admits an equivalent formulation as editing a colored matrix into one with few distinct color-balanced rows by changing at most $k$ values. While NP-hard in both the fairness-oblivious and the fair settings, the problem is well-known to admit a fixed-parameter algorithm in the former ``vanilla'' setting. As our first contribution, we exclude an analogous algorithm even for highly restricted fair means clustering instances. We then proceed to obtain a full complexity landscape of the problem, and establish tractability results which capture three means of circumventing our obtained lower bound: placing additional constraints on the problem instances, fixed-parameter approximation, or using an alternative parameterization targeting tree-like matrices.

This work introduces FiRE/FiRE.1, a novel sketching-based algorithm for anomaly detection to quickly identify rare cell sub-populations in large-scale single-cell RNA sequencing data. This method demonstrated superior performance against state-of-the-art techniques. Furthermore, the thesis proposes Enhash, a fast and resource-efficient ensemble learner that uses projection hashing to detect concept drift in streaming data, proving highly competitive in time and accuracy across various drift types.

This article presents a novel pretopology-based algorithm designed to address the challenges of clustering mixed data without the need for dimensionality reduction. Leveraging Disjunctive Normal Form, our approach formulates customizable logical rules and adjustable hyperparameters that allow for user-defined hierarchical cluster construction and facilitate tailored solutions for heterogeneous datasets. Through hierarchical dendrogram analysis and comparative clustering metrics, our method demonstrates superior performance by accurately and interpretably delineating clusters directly from raw data, thus preserving data integrity. Empirical findings highlight the algorithm's robustness in constructing meaningful clusters and reveal its potential in overcoming issues related to clustered data explainability. The novelty of this work lies in its departure from traditional dimensionality reduction techniques and its innovative use of logical rules that enhance both cluster formation and clarity, thereby contributing a significant advancement to the discourse on clustering mixed data.

This paradigm challenges traditional data management and analysis techniques by demanding innovative solutions capable of processing, analyzing, and deriving insights from vast and diverse datasets. In particular, the inclusion of mixed data types, such as numerical and categorical variables, poses significant challenges to conventional methodologies, necessitating the development of novel approaches to effectively leverage the wealth of information available [2]. Traditionally, data handling methods were designed around homogeneous datasets, typically consisting of numerical values. However, the big data paradigm introduces a multitude of data types, including structured, unstructured, and semi-structured data, which demand a departure from traditional approaches. Moreover, the three primary characteristics of big data--volume, velocity, and variety--amplify the complexity of data analysis, requiring scalable and adaptable solutions capable of processing large volumes of data at high speeds while accommodating diverse data formats and structures. These methods for handling mixed data often involve separate analyses of categorical and numerical variables, treating them as distinct entities rather than integrating their interdependencies.

This article attempts answering the following problematic: How to model and classify energy consumption profiles over a large distributed territory to optimize the management of buildings' consumption? Doing case-by-case in depth auditing of thousands of buildings would require a massive amount of time and money as well as a significant number of qualified people. Thus, an automated method must be developed to establish a relevant and effective recommendations system. To answer this problematic, pretopology is used to model the sites' consumption profiles and a multi-criterion hierarchical classification algorithm, using the properties of pretopological space, has been developed in a Python library. To evaluate the results, three data sets are used: A generated set of dots of various sizes in a 2D space, a generated set of time series and a set of consumption time series of 400 real consumption sites from a French Energy company. On the point data set, the algorithm is able to identify the clusters of points using their position in space and their size as parameter. On the generated time series, the algorithm is able to identify the time series clusters using Pearson's correlation with an Adjusted Rand Index (ARI) of 1. Keywords: Artificial intelligence data analysis clustering algorithms pretopology

Ensuring the resilience of computer-based railways is increasingly crucial to account for uncertainties and changes due to the growing complexity and criticality of these systems. Although their software relies on strict verification and validation processes following well-established best-practices and certification standards, anomalies can still occur at run-time due to residual faults, system and environmental modifications that were unknown at design-time, or other emergent cyber-threat scenarios. This paper explores run-time control-flow anomaly detection using process mining to enhance the resilience of ERTMS/ETCS L2 (European Rail Traffic Management System / European Train Control System Level 2). Process mining allows learning the actual control flow of the system from its execution traces, thus enabling run-time monitoring through online conformance checking. In addition, anomaly localization is performed through unsupervised machine learning to link relevant deviations to critical system components. We test our approach on a reference ERTMS/ETCS L2 scenario, namely the RBC/RBC Handover, to show its capability to detect and localize anomalies with high accuracy, efficiency, and explainability.

In this paper, we provide a novel perspective on the underlying structure of real-world data with ground-truth clusters via characterization of an abundantly observed yet often overlooked density-geometry correlation, that manifests itself as a multi-layered manifold structure. We leverage this correlation to design CoreSPECT (Core Space Projection based Enhancement of Clustering Techniques), a general framework that improves the performance of generic clustering algorithms. Our framework boosts the performance of clustering algorithms by applying them to strategically selected regions, then extending the partial partition to a complete partition for the dataset using a novel neighborhood graph based multi-layer propagation procedure. We provide initial theoretical support of the functionality of our framework under the assumption of our model, and then provide large-scale real-world experiments on 19 datasets that include standard image datasets as well as genomics datasets. We observe two notable improvements. First, CoreSPECT improves the NMI of K-Means by 20% on average, making it competitive to (and in some cases surpassing) the state-of-the-art manifold-based clustering algorithms, while being orders of magnitude faster. Secondly, our framework boosts the NMI of HDBSCAN by more than 100% on average, making it competitive to the state-of-the-art in several cases without requiring the true number of clusters and hyper-parameter tuning. The overall ARI improvements are higher.

Cell clustering is crucial for uncovering cellular heterogeneity in single-cell RNA sequencing (scRNA-seq) data by identifying cell types and marker genes. Despite its importance, benchmarks for scRNA-seq clustering methods remain fragmented, often lacking standardized protocols and failing to incorporate recent advances in artificial intelligence. To fill these gaps, we present scCluBench, a comprehensive benchmark of clustering algorithms for scRNA-seq data. First, scCluBench provides 36 scRNA-seq datasets collected from diverse public sources, covering multiple tissues, which are uniformly processed and standardized to ensure consistency for systematic evaluation and downstream analyses. To evaluate performance, we collect and reproduce a range of scRNA-seq clustering methods, including traditional, deep learning-based, graph-based, and biological foundation models. We comprehensively evaluate each method both quantitatively and qualitatively, using core performance metrics as well as visualization analyses. Furthermore, we construct representative downstream biological tasks, such as marker gene identification and cell type annotation, to further assess the practical utility. scCluBench then investigates the performance differences and applicability boundaries of various clustering models across diverse analytical tasks, systematically assessing their robustness and scalability in real-world scenarios. Overall, scCluBench offers a standardized and user-friendly benchmark for scRNA-seq clustering, with curated datasets, unified evaluation protocols, and transparent analyses, facilitating informed method selection and providing valuable insights into model generalizability and application scope.

Recent years have shown that malware attacks still happen with high frequency. Malware experts seek to categorize and classify incoming samples to confirm their trustworthiness or prove their maliciousness. One of the ways in which groups of malware samples can be identified is through malware clustering. Despite the efforts of the community, malware clustering which incorporates benign samples has been under-explored. Moreover, despite the availability of larger public benchmark malware datasets, malware clustering studies have avoided fully utilizing these datasets in their experiments, often resorting to small datasets with only a few families. Additionally, the current state-of-the-art solutions for malware clustering remain unclear. In our study, we evaluate malware clustering quality and establish the state-of-the-art on Bodmas and Ember - two large public benchmark malware datasets. Ours is the first study of malware clustering performed on whole malware benchmark datasets. Additionally, we extend the malware clustering task by incorporating benign samples. Our results indicate that incorporating benign samples does not significantly degrade clustering quality. We find that there are differences in the quality of the created clusters between Ember and Bodmas, as well as a private industry dataset. Contrary to popular opinion, our top clustering performers are K-Means and BIRCH, with DBSCAN and HAC falling behind.

Bipartite networks are widely used to encode the ecological interactions. Being able to compare the organization of bipartite networks is a first step toward a better understanding of how environmental factors shape community structure and resilience. Yet current methods for structure detection in bipartite networks overlook shared patterns across collections of networks. We introduce the \emph{colBiSBM}, a family of probabilistic models for collections of bipartite networks that extends the classical Latent Block Model (LBM). The proposed framework assumes that networks are independent realizations of a shared mesoscale structure, encoded through common inter-block connectivity parameters. We establish identifiability conditions for the different variants of \emph{colBiSBM} and develop a variational EM algorithm for parameter estimation, coupled with an adaptation of the Integrated Classification Likelihood (ICL) criterion for model selection. We demonstrate how our approach can be used to classify networks based on their topology or organization. Simulation studies highlight the ability of \emph{colBiSBM} to recover common structures, improve clustering performance, and enhance link prediction by borrowing strength across networks. An application to plant--pollinator networks highlights how the method uncovers shared ecological roles and partitions networks into sub-collections with similar connectivity patterns. These results illustrate the methodological and practical advantages of joint modeling over separate network analyses in the study of bipartite systems.