Duy-Tai Dinh

Tai Dinh, Wong Hauchi, Philippe Fournier-Viger et al.

The clustering of categorical data is a common and important task in computer science, offering profound implications across a spectrum of applications. Unlike purely numerical data, categorical data often lack inherent ordering as in nominal data, or have varying levels of order as in ordinal data, thus requiring specialized methodologies for efficient organization and analysis. This review provides a comprehensive synthesis of categorical data clustering in the past twenty-five years, starting from the introduction of K-modes. It elucidates the pivotal role of categorical data clustering in diverse fields such as health sciences, natural sciences, social sciences, education, engineering and economics. Practical comparisons are conducted for algorithms having public implementations, highlighting distinguishing clustering methodologies and revealing the performance of recent algorithms on several benchmark categorical datasets. Finally, challenges and opportunities in the field are discussed.

Duy-Tai Dinh, Tsutomu Fujinami, Van-Nam Huynh

The problem of estimating the number of clusters (say k) is one of the major challenges for the partitional clustering. This paper proposes an algorithm named k-SCC to estimate the optimal k in categorical data clustering. For the clustering step, the algorithm uses the kernel density estimation approach to define cluster centers. In addition, it uses an information-theoretic based dissimilarity to measure the distance between centers and objects in each cluster. The silhouette analysis based approach is then used to evaluate the quality of different clustering obtained in the former step to choose the best k. Comparative experiments were conducted on both synthetic and real datasets to compare the performance of k-SCC with three other algorithms. Experimental results show that k-SCC outperforms the compared algorithms in determining the number of clusters for each dataset.

Tai Dinh, Wong Hauchi, Daniil Lisik et al.

This paper explores the critical role of data clustering in data science, emphasizing its methodologies, tools, and diverse applications. Traditional techniques, such as partitional and hierarchical clustering, are analyzed alongside advanced approaches such as data stream, density-based, graph-based, and model-based clustering for handling complex structured datasets. The paper highlights key principles underpinning clustering, outlines widely used tools and frameworks, introduces the workflow of clustering in data science, discusses challenges in practical implementation, and examines various applications of clustering. By focusing on these foundations and applications, the discussion underscores clustering's transformative potential. The paper concludes with insights into future research directions, emphasizing clustering's role in driving innovation and enabling data-driven decision-making.

Michal Koren, Or Peretz, Tai Dinh et al.

Sequential decisions in volatile, high-stakes settings require more than maximizing expected return; they require principled uncertainty management. This paper presents the Uncertainty-Aware Markov Decision Process (UAMDP), a unified framework that couples Bayesian forecasting, posterior-sampling reinforcement learning, and planning under a conditional value-at-risk (CVaR) constraint. In a closed loop, the agent updates its beliefs over latent dynamics, samples plausible futures via Thompson sampling, and optimizes policies subject to preset risk tolerances. We establish regret bounds that converge to the Bayes-optimal benchmark under standard regularity conditions. We evaluate UAMDP in two domains-high-frequency equity trading and retail inventory control-both marked by structural uncertainty and economic volatility. Relative to strong deep learning baselines, UAMDP improves long-horizon forecasting accuracy (RMSE decreases by up to 25\% and sMAPE by 32\%), and these gains translate into economic performance: the trading Sharpe ratio rises from 1.54 to 1.74 while maximum drawdown is roughly halved. These results show that integrating calibrated probabilistic modeling, exploration aligned with posterior uncertainty, and risk-aware control yields a robust, generalizable approach to safer and more profitable sequential decision-making.

Hugo Sträng, Tai Dinh

The silhouette coefficient quantifies, for each observation, the balance between within-cluster cohesion and between-cluster separation, taking values in [-1, 1]. The average silhouette width (ASW) is a widely used internal measure of clustering quality, with higher values indicating more cohesive and well-separated clusters. However, the dataset-specific maximum of ASW is typically unknown, and the standard upper limit of 1 is rarely attainable. In this work, we derive for each data point a sharp upper bound on its silhouette width and aggregate these to obtain a canonical upper bound on the ASW. This bound-often substantially below 1-enhances the interpretability of empirical ASW values by indicating how close a given clustering result is to the best possible outcome on that dataset. It can be used to confirm global optimality, guide the evaluation of clustering solutions, and be refined to incorporate minimum cluster-size constraints for greater practical relevance. Finally, we extend the framework to establish a corresponding bound for the macro-averaged silhouette.