We prove that any set of n points in d dimensions (rows in a matrix A \in \RR {n \times d}) can be projected into t \Omega(k / \eps 2) dimensions, for any \eps \in (0,1/3), in O(n d \lceil \eps {-2} k/ \log(d) \rceil) time, such that with constant probability the optimal k -partition of the point set is preserved within a factor of 2 \eps . The projection is done by post-multiplying A with a d \times t random matrix R having entries 1/\sqrt{t} or -1/\sqrt{t} with equal probability. A numerical implementation of our technique and experiments on a large face images dataset verify the speed and the accuracy of our theoretical results.

This paper investigates the potential of Digital Twins (DTs) to enhance network performance in densely populated urban areas, specifically focusing on vehicular networks. The study comprises two phases. In Phase I, we utilize traffic data and AI clustering to identify critical locations, particularly in crowded urban areas with high accident rates. In Phase II, we evaluate the advantages of twinning vehicular networks through three deployment scenarios: edge-based twin, cloud-based twin, and hybrid-based twin. Our analysis demonstrates that twinning significantly reduces network delays, with virtual twins outperforming physical networks. Virtual twins maintain low delays even with increased vehicle density, such as 15.05 seconds for 300 vehicles. Moreover, they exhibit faster computational speeds, with cloud-based twins being 1.7 times faster than edge twins in certain scenarios. These findings provide insights for efficient vehicular communication and underscore the potential of virtual twins in enhancing vehicular networks in crowded areas while emphasizing the importance of considering real-world factors when making deployment decisions.

Conventional fair graph clustering methods face two primary challenges: i) They prioritize balanced clusters at the expense of cluster cohesion by imposing rigid constraints, ii) Existing methods of both individual and group-level fairness in graph partitioning mostly rely on eigen decompositions and thus, generally lack interpretability. To address these issues, we propose iFairNMTF, an individual Fairness Nonnegative Matrix Tri-Factorization model with contrastive fairness regularization that achieves balanced and cohesive clusters. By introducing fairness regularization, our model allows for customizable accuracy-fairness trade-offs, thereby enhancing user autonomy without compromising the interpretability provided by nonnegative matrix tri-factorization. Experimental evaluations on real and synthetic datasets demonstrate the superior flexibility of iFairNMTF in achieving fairness and clustering performance.

We found that a simple property of clusters in a clustered dataset of news correlate strongly with importance and urgency of news (IUN) as assessed by LLM. We verified our finding across different news datasets, dataset sizes, clustering algorithms and embeddings. The found correlation should allow using clustering (as an alternative to LLM) for identifying the most important urgent news, or for filtering out unimportant articles.

Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods. Recently, there has been a surge of interest in explaining the classic k-means algorithm, leading to efficient algorithms that approximate k-means clusters using axis-aligned decision trees. However, interpretable variants of k-means have limited applicability in practice, where more flexible clustering methods are often needed to obtain useful partitions of the data. In this work, we investigate interpretable kernel clustering, and propose algorithms that construct decision trees to approximate the partitions induced by kernel k-means, a nonlinear extension of k-means. We further build on previous work on explainable k-means and demonstrate how a suitable choice of features allows preserving interpretability without sacrificing approximation guarantees on the interpretable model. The increasing predictive power of machine learning has made it a popular tool in many scientific fields. Sensitive applications such as healthcare or autonomous driving however require more than just good accuracy--it is also crucial for a model's decisions to be interpretable (Tjoa & Guan, 2020; Varshney & Alemzadeh, 2017). Unfortunately, popular machine learning models are not transparent and are often referred to as "black box" approaches. The demand for explainable machine learning has led to the development of several tools over the last few years, albeit mostly for supervised learning. Methods such as LIME or Shapley values (Ribeiro et al., 2016; Lundberg & Lee, 2017) are designed to explain the prediction of any given machine learning model.

Anti-Money Laundering (AML) is a crucial task in ensuring the integrity of financial systems. One keychallenge in AML is identifying high-risk groups based on their behavior. Unsupervised learning, particularly clustering, is a promising solution for this task. However, the use of hundreds of features todescribe behavior results in a highdimensional dataset that negatively impacts clustering performance.In this paper, we investigate the effectiveness of combining clustering method agglomerative hierarchicalclustering with four dimensionality reduction techniques -Independent Component Analysis (ICA), andKernel Principal Component Analysis (KPCA), Singular Value Decomposition (SVD), Locality Preserving Projections (LPP)- to overcome the issue of high-dimensionality in AML data and improve clusteringresults. This study aims to provide insights into the most effective way of reducing the dimensionality ofAML data and enhance the accuracy of clustering-based AML systems. The experimental results demonstrate that KPCA outperforms other dimension reduction techniques when combined with agglomerativehierarchical clustering. This superiority is observed in the majority of situations, as confirmed by threedistinct validation indices.

In recent years, federated learning (FL) has emerged as a promising technique for training machine learning models in a decentralized manner while also preserving data privacy. The non-independent and identically distributed (non-i.i.d.) nature of client data, coupled with constraints on client or edge devices, presents significant challenges in FL. Furthermore, learning across a high number of communication rounds can be risky and potentially unsafe for model exploitation. Traditional FL approaches may suffer from these challenges. Therefore, we introduce FedSiKD, which incorporates knowledge distillation (KD) within a similarity-based federated learning framework. As clients join the system, they securely share relevant statistics about their data distribution, promoting intra-cluster homogeneity. This enhances optimization efficiency and accelerates the learning process, effectively transferring knowledge between teacher and student models and addressing device constraints. FedSiKD outperforms state-of-the-art algorithms by achieving higher accuracy, exceeding by 25\% and 18\% for highly skewed data at $\alpha = {0.1,0.5}$ on the HAR and MNIST datasets, respectively. Its faster convergence is illustrated by a 17\% and 20\% increase in accuracy within the first five rounds on the HAR and MNIST datasets, respectively, highlighting its early-stage learning proficiency. Code is publicly available and hosted on GitHub (https://github.com/SimuEnv/FedSiKD)

The paper introduces a Signed Generalized Random Dot Product Graph (SGRDPG) model, which is a variant of the Generalized Random Dot Product Graph (GRDPG), where, in addition, edges can be positive or negative. The setting is extended to a multiplex version, where all layers have the same collection of nodes and follow the SGRDPG. The only common feature of the layers of the network is that they can be partitioned into groups with common subspace structures, while otherwise all matrices of connection probabilities can be all different. The setting above is extremely flexible and includes a variety of existing multiplex network models as its particular cases. The paper fulfills two objectives. First, it shows that keeping signs of the edges in the process of network construction leads to a better precision of estimation and clustering and, hence, is beneficial for tackling real world problems such as analysis of brain networks. Second, by employing novel algorithms, our paper ensures equivalent or superior accuracy than has been achieved in simpler multiplex network models. In addition to theoretical guarantees, both of those features are demonstrated using numerical simulations and a real data example.

One of the main challenges of decentralized machine learning paradigms such as Federated Learning (FL) is the presence of local non-i.i.d. datasets. Device-to-device transfers (D2D) between distributed devices has been shown to be an effective tool for dealing with this problem and robust to stragglers. In an unsupervised case, however, it is not obvious how data exchanges should take place due to the absence of labels. In this paper, we propose an approach to create an optimal graph for data transfer using Reinforcement Learning. The goal is to form links that will provide the most benefit considering the environment's constraints and improve convergence speed in an unsupervised FL environment. Numerical analysis shows the advantages in terms of convergence speed and straggler resilience of the proposed method to different available FL schemes and benchmark datasets.

Offline policy learning aims to discover decision-making policies from previously-collected datasets without additional online interactions with the environment. As the training dataset is fixed, its quality becomes a crucial determining factor in the performance of the learned policy. This paper studies a dataset characteristic that we refer to as multi-behavior, indicating that the dataset is collected using multiple policies that exhibit distinct behaviors. In contrast, a uni-behavior dataset would be collected solely using one policy. We observed that policies learned from a uni-behavior dataset typically outperform those learned from multi-behavior datasets, despite the uni-behavior dataset having fewer examples and less diversity. Therefore, we propose a behavior-aware deep clustering approach that partitions multi-behavior datasets into several uni-behavior subsets, thereby benefiting downstream policy learning. Our approach is flexible and effective; it can adaptively estimate the number of clusters while demonstrating high clustering accuracy, achieving an average Adjusted Rand Index of 0.987 across various continuous control task datasets. Finally, we present improved policy learning examples using dataset clustering and discuss several potential scenarios where our approach might benefit the offline policy learning community.