Mixed Data Clustering Survey and Challenges

📝 Abstract

The advent of the big data paradigm has transformed how industries manage and analyze information, ushering in an era of unprecedented data volume, velocity, and variety. Within this landscape, mixed-data clustering has become a critical challenge, requiring innovative methods that can effectively exploit heterogeneous data types, including numerical and categorical variables. Traditional clustering techniques, typically designed for homogeneous datasets, often struggle to capture the additional complexity introduced by mixed data, underscoring the need for approaches specifically tailored to this setting. Hierarchical and explainable algorithms are particularly valuable in this context, as they provide structured, interpretable clustering results that support informed decision-making. This paper introduces a clustering method grounded in pretopological spaces. In addition, benchmarking against classical numerical clustering algorithms and existing pretopological approaches yields insights into the performance and effectiveness of the proposed method within the big data paradigm.

💡 Analysis

The advent of the big data paradigm has transformed how industries manage and analyze information, ushering in an era of unprecedented data volume, velocity, and variety. Within this landscape, mixed-data clustering has become a critical challenge, requiring innovative methods that can effectively exploit heterogeneous data types, including numerical and categorical variables. Traditional clustering techniques, typically designed for homogeneous datasets, often struggle to capture the additional complexity introduced by mixed data, underscoring the need for approaches specifically tailored to this setting. Hierarchical and explainable algorithms are particularly valuable in this context, as they provide structured, interpretable clustering results that support informed decision-making. This paper introduces a clustering method grounded in pretopological spaces. In addition, benchmarking against classical numerical clustering algorithms and existing pretopological approaches yields insights into the performance and effectiveness of the proposed method within the big data paradigm.

📄 Content

Mixed Data Clustering Survey and Challenges Guillaume Guerard1,2* and Sonia Djebali1† 1L´eonard de Vinci Pˆole Universitaire, Research Center, 12 Avenue L´eonard de Vinci, Paris La D´efense, 92916, France. 2LI-PARAD Laboratory EA 7432, Versailles University, 55 Avenue de Paris, Versailles, 78035, France. *Corresponding author(s). E-mail(s): guillaume.guerard@devinci.fr; Contributing authors: sonia.djebali@devinci.fr; †These authors contributed equally to this work. Abstract The advent of the big data paradigm has revolutionized the way industries han- dle and analyze information, ushering in an era characterized by unprecedented volumes, velocities, and varieties of data. In this context, mixed data clustering emerges as a critical challenge, necessitating innovative approaches to effectively harness the wealth of heterogeneous data types, including numerical and categor- ical variables. Traditional methods, designed for homogeneous datasets, often fall short in accommodating the complexities introduced by mixed data, highlight- ing the need for novel clustering techniques tailored to this context. Hierarchical and explainable algorithms play a pivotal role in addressing these challenges, offering structured frameworks that enable interpretable clustering results, which are essential for informed decision-making. This paper presents a method based on pretopological spaces. Moreover, benchmarking against traditional numerical clustering methods and pretopological approaches provides valuable insights into the performance and efficacy of our novel clustering algorithm within the big data paradigm. Keywords: Big Data, Pretopology, Mixed Data, Clustering 1 Introduction The big data paradigm represents a seismic shift in the way industries approach and harness data, characterized by unprecedented volumes, velocities, and varieties of 1 arXiv:2512.03070v1 [cs.LG] 27 Nov 2025 information [1]. 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 categor- ical and numerical variables, treating them as distinct entities rather than integrating their interdependencies. While this approach may provide insights into individual data types, it fails to capture the inherent relationships and interactions between different variables, limiting the holistic understanding of the dataset. As such, there is a press- ing need to bridge the gap between traditional methodologies and the complexities introduced by mixed data in the context of machine learning, especially clustering methods. Understanding the limitations of clustering methods and identifying the gaps in current approaches is essential for advancing mixed data analysis. By critically assess- ing existing methodologies and their applicability to diverse datasets, we can pinpoint areas for improvement and develop innovative solutions tailored to the complexities of mixed data. Moreover, establishing a comprehensive understanding of traditional methods enables researchers to build upon existing knowledge and leverage insights from diverse disciplines to address emerging challenges effectively. Considering the big data paradigm, there is a growing need for hierarchical and explainable algorithms for mixed data clustering in all sectors [3–7]. Hierarchical clus- tering offers a structured approach that aligns well with the complexities of mixed data, allowing for the identification of nested patterns and relationships within the dataset. Moreover, hierarchical clustering facilitates interpretability by organizing data into a hierarchical, tree-like structure, enabling stakeholders to understand the underlying logic behind clustering decisions. In an era where transparency and accountability are paramount, explainable algorithms play a crucial role in fostering trust and confi- dence in the clustering process, especially in sensitive domains such as healthcare and finance. Therefore, the development of hierarch

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