We study k-median clustering under the sequential no-substitution setting. In this setting, a data stream is sequentially observed, and some of the points are selected by the algorithm as cluster centers. However, a point can be selected as a center only immediately after it is observed, before observing the next point. In addition, a selected center cannot be substituted later. We give the first algorithm for this setting that obtains a constant approximation factor on the optimal cost under a random arrival order, an exponential improvement over previous work. This is also the first constant approximation guarantee that holds without any structural assumptions on the input data. Moreover, the number of selected centers is only quasi-linear in k. Our algorithm and analysis are based on a careful cost estimation that avoids outliers, a new concept of a linear bin division, and a multiscale approach to center selection.

This paper studies the k-means++ algorithm for clustering as well as the class of D` sampling algorithms to which k-means++ belongs. It is shown that for any constant factor β > 1, selecting βk cluster centers by D` sampling yields a constant-factor approximation to the optimal clustering with k centers, in expectation and without conditions on the dataset. This result extends the previously known O(log k) guarantee for the case β = 1 to the constant-factor bi-criteria regime. It also improves upon an existing constant-factor bi-criteria result that holds only with constant probability.

The local search methods have been widely used to solve the clustering problems. In practice, local search algorithms for clustering problems mainly adapt the single-swap strategy, which enables them to handle large-scale datasets and achieve linear running time in the data size.

This result extends the previously known O(log k) guarantee for the case β = 1 to the constant-factor bi-criteria regime. It also improves upon an existing constant-factor bi-criteria result that holds only with constant probability.

Federated learning (FL) offers a decentralized training approach for machine learning models, prioritizing data privacy. However, the inherent heterogeneity in FL networks, arising from variations in data distribution, size, and device capabilities, poses challenges in user federation. Recognizing this, Personalized Federated Learning (PFL) emphasizes tailoring learning processes to individual data profiles. In this paper, we address the complexity of clustering users in PFL, especially in dynamic networks, by introducing a dynamic Upper Confidence Bound (dUCB) algorithm inspired by the multi-armed bandit (MAB) approach. The dUCB algorithm ensures that new users can effectively find the best cluster for their data distribution by balancing exploration and exploitation. The performance of our algorithm is evaluated in various cases, showing its effectiveness in handling dynamic federated learning scenarios.

Personas are models of users that incorporate motivations, wishes, and objectives; These models are employed in user-centred design to help design better user experiences and have recently been employed in adaptive systems to help tailor the personalized user experience. Designing with personas involves the production of descriptions of fictitious users, which are often based on data from real users. The majority of data-driven persona development performed today is based on qualitative data from a limited set of interviewees and transformed into personas using labour-intensive manual techniques. In this study, we propose a method that employs the modelling of user stereotypes to automate part of the persona creation process and addresses the drawbacks of the existing semi-automated methods for persona development. The description of the method is accompanied by an empirical comparison with a manual technique and a semi-automated alternative (multiple correspondence analysis). The results of the comparison show that manual techniques differ between human persona designers leading to different results. The proposed algorithm provides similar results based on parameter input, but was more rigorous and will find optimal clusters, while lowering the labour associated with finding the clusters in the dataset. The output of the method also represents the largest variances in the dataset identified by the multiple correspondence analysis.