arXiv subjects

Angelos Markos

Publications and source records attributed to Angelos Markos.

6 recordsLinked to original sources

arXiv2026

Sparse clustering via the Deterministic Information Bottleneck algorithm

Cluster analysis relates to the task of assigning objects into groups which ideally present some desirable characteristics. When a cluster structure is confined to a subset of the feature space, traditional clustering techniques face unprecedented challenges. We present an information theoretic framework that overcomes the problems associated with sparse data, allowing for joint feature weighting and clustering. Our proposal constitutes a competitive alternative to existing clustering algorithms for sparse data, as demonstrated through simulations on synthetic data. The effectiveness of our method is established by an application on a real-world genomics data set.

stat.ML↗

arXiv2024

Unbiased mixed variables distance

Defining a distance in a mixed setting requires the quantification of observed differences of variables of different types and of variables that are measured on different scales. There exist several proposals for mixed variable distances, however, such distances tend to be biased towards specific variable types and measurement units. That is, the variable types and scales influence the contribution of individual variables to the overall distance. In this paper, we define unbiased mixed variable distances for which the contributions of individual variables to the overall distance are not influenced by measurement types or scales. We define the relevant concepts to quantify such biases and we provide a general formulation that can be used to construct unbiased mixed variable distances.

stat.ME↗

arXiv2024

A Deterministic Information Bottleneck Method for Clustering Mixed-Type Data

In this paper, we present an information-theoretic method for clustering mixed-type data, that is, data consisting of both continuous and categorical variables. The proposed approach extends the Information Bottleneck principle to heterogeneous data through generalised product kernels, integrating continuous, nominal, and ordinal variables within a unified optimization framework. We address the following challenges: developing a systematic bandwidth selection strategy that equalises contributions across variable types, and proposing an adaptive hyperparameter updating scheme that ensures a valid solution into a predetermined number of potentially imbalanced clusters. Through simulations on 28,800 synthetic data sets and ten publicly available benchmarks, we demonstrate that the proposed method, named DIBmix, achieves superior performance compared to four established methods (KAMILA, K-Prototypes, FAMD with K-Means, and PAM with Gower's dissimilarity). Results show DIBmix particularly excels when clusters exhibit size imbalances, data contain low or moderate cluster overlap, and categorical and continuous variables are equally represented. The method presents a significant advantage over traditional centroid-based algorithms, establishing DIBmix as a competitive and theoretically grounded alternative for mixed-type data clustering.

stat.ME↗

arXiv2023

A general framework for implementing distances for categorical variables

The degree to which subjects differ from each other with respect to certain properties measured by a set of variables, plays an important role in many statistical methods. For example, classification, clustering, and data visualization methods all require a quantification of differences in the observed values. We can refer to the quantification of such differences, as distance. An appropriate definition of a distance depends on the nature of the data and the problem at hand. For distances between numerical variables, there exist many definitions that depend on the size of the observed differences. For categorical data, the definition of a distance is more complex, as there is no straightforward quantification of the size of the observed differences. Consequently, many proposals exist that can be used to measure differences based on categorical variables. In this paper, we introduce a general framework that allows for an efficient and transparent implementation of distances between observations on categorical variables. We show that several existing distances can be incorporated into the framework. Moreover, our framework quite naturally leads to the introduction of new distance formulations and allows for the implementation of flexible, case and data specific distance definitions. Furthermore, in a supervised classification setting, the framework can be used to construct distances that incorporate the association between the response and predictor variables and hence improve the performance of distance-based classifiers.

stat.ML↗

arXiv2022

Benchmarking distance-based partitioning methods for mixed-type data

Clustering mixed-type data, that is, observation by variable data that consist of both continuous and categorical variables poses novel challenges. Foremost among these challenges is the choice of the most appropriate clustering method for the data. This paper presents a benchmarking study comparing eight distance-based partitioning methods for mixed-type data in terms of cluster recovery performance. A series of simulations carried out by a full factorial design are presented that examined the effect of a variety of factors on cluster recovery. The amount of cluster overlap, the percentage of categorical variables in the data set, the number of clusters and the number of observations had the largest effects on cluster recovery and in most of the tested scenarios. KAMILA, K-Prototypes and sequential Factor Analysis and K-Means clustering typically performed better than other methods. The study can be a useful reference for practitioners in the choice of the most appropriate method.

stat.ME↗

arXiv2022

Hierarchical clustering of mixed-type data based on barycentric coding

Clustering of mixed-type datasets can be a particularly challenging task as it requires taking into account the associations between variables with different level of measurement, i.e., nominal, ordinal and/or interval. In some cases, hierarchical clustering is considered a suitable approach, as it makes few assumptions about the data and its solution can be easily visualized. Since most hierarchical clustering approaches assume variables are measured on the same scale, a simple strategy for clustering mixed-type data is to homogenize the variables before clustering. This would mean either recoding the continuous variables as categorical ones or vice versa. However, typical discretization of continuous variables implies loss of information. In this work, an agglomerative hierarchical clustering approach for mixed-type data is proposed, which relies on a barycentric coding of continuous variables. The proposed approach minimizes information loss and is compatible with the framework of correspondence analysis. The utility of the method is demonstrated on real and simulated data.

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