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.

Psychological attributes rarely operate in isolation: coaches reason about networks of related traits. We analyze a new dataset of 164 female volleyball players from Italy's C and D leagues that combines standardized psychological profiling with background information. To learn directed relationships among mixed-type variables (ordinal questionnaire scores, categorical demographics, continuous indicators), we introduce latent MMHC, a hybrid structure learner that couples a latent Gaussian copula and a constraint-based skeleton with a constrained score-based refinement to return a single DAG. We also study a bootstrap-aggregated variant for stability. In simulations spanning sample size, sparsity, and dimension, latent Max-Min Hill-Climbing (MMHC) attains lower structural Hamming distance and higher edge recall than recent copula-based learners while maintaining high specificity. Applied to volleyball, the learned network organizes mental skills around goal setting and self-confidence, with emotional arousal linking motivation and anxiety, and locates Big-Five traits (notably neuroticism and extraversion) upstream of skill clusters. Scenario analyses quantify how improvements in specific skills propagate through the network to shift preparation, confidence, and self-esteem. The approach provides an interpretable, data-driven framework for profiling psychological traits in sport and for decision support in athlete development.

This paper proposes a causal discovery method for mixed bivariate data consisting of one continuous and one discrete variable. Existing constraint-based approaches are ineffective in the bivariate setting, as they rely on conditional independence tests that are not suited to bivariate data. Score-based methods either impose strong distributional assumptions or face challenges in fairly comparing causal directions between variables of different types, due to differences in their information content. We introduce a novel approach that determines causal direction by analyzing the monotonicity of the conditional density ratio of the continuous variable, conditioned on different values of the discrete variable. Our theoretical analysis shows that the conditional density ratio exhibits monotonicity when the continuous variable causes the discrete variable, but not in the reverse direction. This property provides a principled basis for comparing causal directions between variables of different types, free from strong distributional assumptions and bias arising from differences in their information content. We demonstrate its effectiveness through experiments on both synthetic and real-world datasets, showing superior accuracy compared to existing methods.

Clustering data objects into homogeneous groups is one of the most important tasks in data mining. Spectral clustering is arguably one of the most important algorithms for clustering, as it is appealing for its theoretical soundness and is adaptable to many real-world data settings. For example, mixed data, where the data is composed of numerical and categorical features, is typically handled via numerical discretization, dummy coding, or similarity computation that takes into account both data types. This paper explores a more natural way to incorporate both numerical and categorical information into the spectral clustering algorithm, avoiding the need for data preprocessing or the use of sophisticated similarity functions. We propose adding extra nodes corresponding to the different categories the data may belong to and show that it leads to an interpretable clustering objective function. Furthermore, we demonstrate that this simple framework leads to a linear-time spectral clustering algorithm for categorical-only data. Finally, we compare the performance of our algorithms against other related methods and show that it provides a competitive alternative to them in terms of performance and runtime.

Building accurate and interpretable Machine Learning (ML) models for heterogeneous/mixed data is a long-standing challenge for algorithms designed for numeric data. This work focuses on developing numeric coding schemes for non-numeric attributes for ML algorithms to support accurate and explainable ML models, methods for lossless visualization of n-D non-numeric categorical data with visual rule discovery in these visualizations, and accurate and explainable ML models for categorical data. This study proposes a classification of mixed data types and analyzes their important role in Machine Learning. It presents a toolkit for enforcing interpretability of all internal operations of ML algorithms on mixed data with a visual data exploration on mixed data. A new Sequential Rule Generation (SRG) algorithm for explainable rule generation with categorical data is proposed and successfully evaluated in multiple computational experiments. This work is one of the steps to the full scope ML algorithms for mixed data supported by lossless visualization of n-D data in General Line Coordinates beyond Parallel Coordinates.

Despite the popularity of feature importance (FI) measures in interpretable machine learning, the statistical adequacy of these methods is rarely discussed. From a statistical perspective, a major distinction is between analyzing a variable's importance before and after adjusting for covariates - i.e., between $\textit{marginal}$ and $\textit{conditional}$ measures. Our work draws attention to this rarely acknowledged, yet crucial distinction and showcases its implications. Further, we reveal that for testing conditional FI, only few methods are available and practitioners have hitherto been severely restricted in method application due to mismatching data requirements. Most real-world data exhibits complex feature dependencies and incorporates both continuous and categorical data (mixed data). Both properties are oftentimes neglected by conditional FI measures. To fill this gap, we propose to combine the conditional predictive impact (CPI) framework with sequential knockoff sampling. The CPI enables conditional FI measurement that controls for any feature dependencies by sampling valid knockoffs - hence, generating synthetic data with similar statistical properties - for the data to be analyzed. Sequential knockoffs were deliberately designed to handle mixed data and thus allow us to extend the CPI approach to such datasets. We demonstrate through numerous simulations and a real-world example that our proposed workflow controls type I error, achieves high power and is in line with results given by other conditional FI measures, whereas marginal FI metrics result in misleading interpretations. Our findings highlight the necessity of developing statistically adequate, specialized methods for mixed data.

The goal of co-clustering is to jointly perform a clustering of rows and a clustering of columns of a data table. Proposed by [Good, 1965] then by [Hartigan, 1975], co-clustering is an extension of the standard clustering that extracts the underlying structure in the data in the form of clusters of row and clusters of columns. The advantage of this technique, over the standard clustering, lies in the joint (simultaneous) analysis of the rows and columns which enables extracting the maximum of information about the interdependence between the two entities. The utility of co-clustering lies in its capacity to create easily interpretable clusters and its capability to reduce a large data table into a significantly smaller matrix having the same structure as the orig-Aichetou Bouchareb, Marc Boullé and Fabrice Clérot: Orange Labs, 2 Avenue Pierre Marzin 22300 Lannion - France, e-mail: firstname.

Artificial intelligence offers a lot of advantages for organisations by creating better and more efficient organisations, improving customer services with conversational AI and reducing a wide variety of risks in different industries. Although we are only at the start of the AI revolution, we can already see that artificial intelligence will have a profound effect on our lives, both positively and negatively. The financial impact of AI on the global economy is estimated to reach US$15.7 trillion by 2030, with 40% of jobs expected to be lost due to artificial intelligence, and global venture capital investment in AI is growing to greater than US$27 billion in 2018. Such estimates of AI potential relate to a broad understanding of its nature and applicability. AI will eventually consist of entirely novel and unrecognisable forms of intelligence, and we can see the first signals of this in the rapid developments of AI. In 2017, Google's Deepmind developed AlphaGo Zero, an AI agent that learned the abstract strategy board game Go with a far more expansive range of moves than chess.