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- Initialization strategies for clustering mixed-type data with the
k-prototypes algorithm-
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Abstract: One of the most popular partitioning cluster algorithms is k-means, which is only applicable to numerical data. An extension to mixed-type data containing numerical and categorical variables is the k-prototypes algorithm. Due to its iterative structure, the algorithm may only converges to a local minimum rather than a global minimum. Therefore, just like the solution of the original k-means, the resulting cluster partition suffers from the initialization. In general, there are two ways of achieving an improvement of the random-based initialization of the algorithm: One possibility is to determine concrete initial cluster centers, and the other strategy is to repeat the algorithm with different randomly chosen initial centers. In this work, algorithm initializations of both options are analyzed and evaluated comparatively in a benchmark study. Therefore, selected initialization strategies of the k-means algorithm are transformed to the application on mixed-type data. For the simulation study, several data sets are artificially generated and cluster partitions are determined by using the competing initialization strategies. It is shown that an improvement of the cluster algorithm’s target criterion can be achieved as well as the ability to identify appropriate groups, even with manageable time expenditure.
PubDate: 2025-06-12
- Modeling time-dependent population proportions in a finite mixture model
setting-
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Abstract: This paper focuses on modeling population proportions with finite mixtures of Dirichlet distributions in a time-sensitive setting. Specifically, we assume that the proportions are observed in blocks or sequenc...
PubDate: 2025-06-06
- Mixed-type kernel-based quantification of similarity for clustering
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Abstract: Similarity-based clustering groups observations based on their degree of proximity, which are often calculated using similarity functions. However, existing similarity functions often have limitations in effectively capturing the relationships within mixed numeric and categorical data, called mixed-type data. These functions may oversimplify the degree of proximity for observations in mixed-type datasets, leading to suboptimal clustering outcomes. We propose a flexible similarity learning approach using kernel functions to quantify proximity for each data type and balance between them. Our approach allows for the induction of distance metrics using a similarity function, either through positive definite kernel functions or by defining equivalence classes. We demonstrate that the proposed kernel summation similarity function improves spectral clustering accuracy over existing similarity functions and distance metrics on simulated and real-world mixed-type datasets. We show that this similarity learning approach benefits multivariate data structures by balancing similarities across variables, and remains invariant to data dimensionality and noise on large, imbalanced datasets.
PubDate: 2025-05-31
- Special issue on “Advances in clustering, classification and related
methods”-
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PubDate: 2025-05-29
- Variational inference for estimating dynamic stochastic block models
through an evolutionary algorithm-
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Abstract: Dynamic temporal networks are important structures to capture node dependencies and their evolution over time. The dynamic stochastic block model, commonly used with longitudinal network data, is estimated maximizing the likelihood function through the variational expectation-maximization (VEM) algorithm. However, maximization is challenging due to the presence of multiple local maxima. In this paper, we first conduct a simulation study to assess the performance of six different parameter initialization strategies. Second, we introduce a novel specification of the VEM through a genetic algorithm, enabling a more comprehensive exploration of the parameter space. Results from both simulations and historical data on infectious disease transmission highlight the advantages of this approach in overcoming convergence to local maxima and improving node clustering in temporal network data.
PubDate: 2025-05-23
- Improving the computational performance of TCLUST through ensemble
initialization-
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Abstract: Outliers are known to be detrimental to widely used clustering techniques. Robust clustering alternatives have been introduced to better resist outlying observations. Among these, robust clustering methods based on trimming have proven effective by allowing the removal of a fraction of observations where outliers are likely to be found, with TCLUST being one of the most popular for handling elliptically contoured clusters. The algorithm for applying TCLUST can be seen as an extension of the concentration steps used in the fast-MCD algorithm for computing the Minimum Covariance Determinant. However, obtaining good initializations for these concentration steps in TCLUST is more complex than in MCD. This initialization task is particularly challenging unless both the number of clusters and the dimensionality are small. To address this, a new ensemble initialization procedure for TCLUST will be presented, which takes advantage of partially correct information from all iterated random initializations rather than focusing solely on the best individual one found. Initial experiments suggest that this methodology could improve the computational performance of the standard TCLUST algorithm.
PubDate: 2025-05-22
- Without pain – clustering categorical data using a Bayesian mixture of
finite mixtures of latent class analysis models-
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Abstract: We propose a Bayesian approach for model-based clustering of multivariate categorical data where variables are allowed to be associated within clusters and the number of clusters is unknown. The approach uses a two-layer mixture of finite mixtures model where the component distributions are approximated using latent class analysis models. A careful specification of priors with suitable hyperparameter values is crucial to identify the two-layer structure and obtain a parsimonious cluster solution. We outline the Bayesian estimation based on Markov chain Monte Carlo sampling with the telescoping sampler and describe how to obtain an identified clustering model by resolving the label switching issue. Empirical demonstrations in a simulation study using artificial data as well as a data set on low back pain indicate the good clustering performance of the proposed approach provided the selected hyperparameters induce sufficient shrinkage.
PubDate: 2025-05-18
- Unsupervised learning from attributed networks
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Abstract: Unlike the plain network where only the topological structure is available, nodes of attributed networks possess rich attributed information. Thereby, the attributed networks ubiquitous in the real world have attracted much attention in recent years. In our paper, to simultaneously address both attributed network embedding and clustering, we propose a new model. It exploits both content and structure/topological information, capitalizing on their simultaneous use. The proposed model relies on the approximation of the relaxed continuous embedding solution by the true discrete clustering. Thus, we show that incorporating an embedding representation provides simpler and more interpretable solutions. Moreover, we show how our proposed approach is related to some other clustering and data embedding methods. To clearly establish various connections, we propose to distinguish two variants. Experimental results demonstrate that the proposed algorithm performs better, in terms of clustering and embedding, than the state-of-the-art algorithms, including deep learning methods dedicated to similar tasks for attributed network datasets.
PubDate: 2025-05-14
- Comparing flexible modelling approaches: the varying-thresholds model
versus quantile regression-
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Abstract: The varying-thresholds model (VTM) is a novel methodology proposed by Tutz ( Flexible predictive distributions from varying-thresholds modelling. https://doi.org/10.48550/arXiv.2103.13324, arXiv:2103.13324 2021) capable of estimating the whole conditional distribution of a response variable in a regression setting. It can be used for continuous, ordinal and count responses. In this study, conditional quantiles and prediction intervals estimated through VTM are compared with those of quantile regression. The comparison is based on a set of data-generating models to assess the performance of the two methodologies regarding the coverage and width of prediction intervals. The simulation study encompasses settings with several functional forms and types of errors. In addition, a discrete version of the continuous ranked probability score is proposed as a tool to choose the best link function for the binary models used in the fitting of VTM. In summary, the varying-thresholds model is a flexible methodology that can be broadly applied with light assumptions; it is advantageous over quantile regression when the conditional quantile function is misspecified.
PubDate: 2025-05-14
- Censored trajectory data clustering using mixture of semi-Markov models
with application to targeted marketing-
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Abstract: A trajectory is a spatio-temporal data instance in which a customer or user moves between a set of discrete states while spending a certain amount of time in each state. Using trajectory data as a proxy for customers’ behavior and performing clustering can help to devise targeted marketing strategies. However, the censoring is often encountered due to the inability to observe the complete trajectories. In addition, the exact number of clusters is often unknown. In this work, we propose a novel mixture model-based clustering methodology to analyze the trajectory data and decipher different user segments based on their behavior. Each cluster is profiled using a semi-Markov model while considering the effect of censoring. Each entity is assigned to a cluster based on its similarity to the cluster’s profile. Entity assignments and cluster profiles are simultaneously inferred using a robust expectation maximization algorithm. In the simulation study, our methodology demonstrates better performance than existing methods. The effectiveness of our methodology is further corroborated using a real data set obtained from an internet music provider, where the obtained clustering results are found to be helpful in devising better marketing strategies to target users in different segments.
PubDate: 2025-05-05
- Correction to: Statistical jump model for mixed-type data with missing
data imputation-
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PubDate: 2025-05-02
- Modelling time-inhomogeneous incomplete records of point processes using
variants of hidden Markov models-
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Abstract: Many point processes such as earthquakes or volcanic eruptions have incomplete records with the degree of incompleteness varying over time. For these point processes, the number of missing events between each pair of consecutively observed events can be a random variable that may depend on time, effecting the estimation of parameters or hazard. Such incomplete point processes can be modelled by compound renewal processes where the sum of renewal processes is a random variable because of random variable number of missing events. We propose shifted compound Poisson-Gamma and time-dependent shifted compound Poisson-Gamma renewal processes. Since the number of missing events can be regarded as an unobserved process, the proposed renewal processes are introduced to use in the framework of different types of homogeneous and inhomogeneous hidden Markov models to model the time-dependent variable number of missing events between each pair of consecutively observed events of incomplete point processes. Simulation experiments are employed to check the performance of proposed renewal processes with hidden Markov models. We apply the proposed models to the large magnitude explosive volcanic eruptions database to analyze the time-dependent incompleteness and demonstrate how we estimate the completeness of the record and the future hazard rate.
PubDate: 2025-04-23
- When non-response makes estimates from a census a small area estimation
problem: the case of the survey on graduates’ employment status in Italy
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Abstract: Since 1998, AlmaLaurea—a consortium of 80 Italian universities and a member of the Italian National Statistical System—has conducted an annual census on graduates’ employment status. The survey provides estimates of descriptive indicators at both the population level and for specific subpopulations (domains) of interest, such as degree programmes. Some domains have very few observations due to a small population size and non-response. In this paper, we address this estimation problem within a Small Area Estimation framework. Specifically, we propose using generalized linear mixed models that incorporate two variables as proxies for graduates’ response propensity, making the assumption of non-informative non-response more plausible. Degree programme estimates of employment rates are derived as (semi-parametric) empirical best predictions using a finite mixture of logistic regression models, with their mean squared error estimated via a second-order, bias-corrected, analytical estimator. Sensitivity analysis is conducted to assess the explanatory power of variables modelling response propensity and to evaluate potential correlations between area-specific random effects and observed heterogeneity.
PubDate: 2025-04-10
- Statistical jump model for mixed-type data with missing data imputation
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Abstract: In this paper, we address the challenge of clustering mixed-type data with temporal evolution by introducing the statistical jump model for mixed-type data. This novel framework incorporates regime persistence, enhancing interpretability and reducing the frequency of state switches, and efficiently handles missing data. The model is easily interpretable through its state-conditional medians and modes, making it accessible to practitioners and policymakers. We validate our approach through extensive simulation studies and an empirical application to air quality data, demonstrating its superiority in inferring persistent air quality regimes compared to the traditional air quality index. Our contributions include a robust method for mixed-type temporal clustering, effective missing data management, and practical insights for environmental monitoring.
PubDate: 2025-03-25
- Parametric models for distributional data
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Abstract: We present parametric probabilistic models for numerical distributional variables. The proposed models are based on the representation of each distribution by a location measure and inter-quantile ranges, for given quantiles, thereby characterizing the underlying empirical distributions in a flexible way. Multivariate Normal distributions are assumed for the whole set of indicators, considering alternative structures of the variance–covariance matrix. For all cases, maximum likelihood estimators of the corresponding parameters are derived. This modelling allows for hypothesis testing and multivariate parametric analysis. The proposed framework is applied to Analysis of Variance and parametric Discriminant Analysis of distributional data. A simulation study examines the performance of the proposed models in classification problems under different data conditions. Applications to Internet traffic data and Portuguese official data illustrate the relevance of the proposed approach.
PubDate: 2025-03-10
- A low-rank non-convex norm method for multiview graph clustering
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Abstract: This study addresses the challenge of multiview clustering by integrating information from multiple data sources to improve clustering accuracy. We propose CGMVC-NC, a novel Consensus Graph-Based Multi-View Clustering method Using Low-Rank Non-Convex Norm, which effectively captures correlations across views. Unlike traditional methods, CGMVC-NC introduces a non-convex low-rank tensor norm to enhance the representation of shared structures while reducing noise and redundancy. By constructing a consensus graph that preserves essential multiview relationships, our approach ensures more reliable clustering results. Extensive experiments on benchmark datasets confirm its superiority over existing techniques, demonstrating improved clustering performance and robustness in handling complex multiview data.
PubDate: 2025-03-03
- Editorial for ADAC issue 1 of volume 19 (2025)
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PubDate: 2025-02-28
- Weighted embedding and outlier detection of metric space data
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Abstract: This work discusses weighted kernel point projection (WKPP), a new method for embedding metric space or kernel data. WKPP is based on an iteratively weighted generalization of multidimensional scaling and kernel principal component analysis, and one of its main uses is outlier detection. After a detailed derivation of the method and its algorithm, we give theoretical guarantees regarding its convergence and outlier detection capabilities. Additionally, as one of our mathematical contributions, we give a novel characterization of kernelizability, connecting it also to the classical kernel literature. In our empirical examples, WKPP is benchmarked with respect to several competing outlier detection methods, using various different datasets. The obtained results show that WKPP is computationally fast, while simultaneously achieving performance comparable to state-of-the-art methods.
PubDate: 2025-02-27
- Particle swarm optimization for preference rankings
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Abstract: Preference learning, or the analysis of preference rankings, is gaining more and more importance in various scientific disciplines. Preference learning methods allow predicting preferences on a set of alternatives. The ingredients are a pool of evaluators and a set of objects or items to be ranked in order of preference. The rank aggregation problem must be solved in order to aggregate preferences or rankings with the aim to find a consensus or collective decision. Branch-and-bound-like procedures are usable up to problems involving a relatively small number of objects, say less than 200. When the number of items becomes very large, the rank aggregation problem becomes increasingly difficult to approach so that it is universally recognized as an NP-hard problem. Several heuristic methods have been proposed to provide increasingly accurate solutions. These assume the Kemeny axiomatic approach that better deals with tied rankings. In this paper, we adopt a strategy based on Particle Swarm Optimization by adapting procedures born to solve optimization problems in continuous spaces to discrete combinatorial optimization problems. A simulation study shows the performance of the proposed algorithm in a controlled environment. A benchmarking complex data set and two real world data sets with large number of items are considered. As a result, the proposed algorithm provides significant savings in computational time and comparable accuracy with respect to other recent algorithms.
PubDate: 2025-02-17
- Random models for adjusting fuzzy rand index extensions
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Abstract: The adjusted Rand index (ARI) is a widely used method for comparing hard clusterings, but requires a choice of random model that is often left implicit. Several recent works have extended the Rand index to fuzzy clusterings and adjusted for chance agreement with the permutation model, but the assumptions of this random model are difficult to justify for fuzzy clusterings. Previous work on random models for hard clusterings has shown that different random models can impact similarity rankings, so matching the assumptions of the random model to the algorithm is essential. We propose a single framework computing the ARI with three new random models that are intuitive and explainable for both hard and fuzzy clusterings. The theory and assumptions of the proposed models are contrasted with the existing permutation model, and computations on synthetic and benchmark data show that each model has distinct behaviour, meaning accurate model selection is important for the reliability of results.
PubDate: 2025-02-13
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