Clustering is an unsupervised learning task that aims to partition data into a set of clusters. In many applications, these clusters correspond to real-world constructs (e.g., electoral districts, playlists, TV channels) whose benefit can only be attained by groups when they reach a minimum level of representation (e.g., 50\% to elect their desired candidate). In this paper, we study the k-means and k-medians clustering problems with the additional constraint that each group (e.g., demographic group) must have a minimum level of representation in at least a given number of clusters. We formulate the problem through a mixed-integer optimization framework and present an alternating minimization algorithm, called MiniReL, that directly incorporates the fairness constraints. While incorporating the fairness criteria leads to an NP-Hard assignment problem within the algorithm, we provide computational approaches that make the algorithm practical even for large datasets. Numerical results show that the approach is able to create fairer clusters with practically no increase in the clustering cost across standard benchmark datasets.

Conditional Tabular Generative Adversarial Networks (CTGAN) and their various derivatives are attractive for their ability to efficiently and flexibly create synthetic tabular data, showcasing strong performance and adaptability. However, there are certain critical limitations to such models. The first is their inability to preserve the semantic integrity of contextually correlated words or phrases. For instance, skillset in freelancer profiles is one such attribute where individual skills are semantically interconnected and indicative of specific domain interests or qualifications. The second challenge of traditional approaches is that, when applied to generate contextually correlated tabular content, besides generating semantically shallow content, they consume huge memory resources and CPU time during the training stage. To address these problems, we introduce a novel framework, CTGKrEW (Conditional Tabular GAN with KMeans Clustering and Word Embedding), which is adept at generating realistic synthetic tabular data where attributes are collections of semantically and contextually coherent words. CTGKrEW is trained and evaluated using a dataset from Upwork, a realworld freelancing platform. Comprehensive experiments were conducted to analyze the variability, contextual similarity, frequency distribution, and associativity of the generated data, along with testing the framework's system feasibility. CTGKrEW also takes around 99\% less CPU time and 33\% less memory footprints than the conventional approach. Furthermore, we developed KrEW, a web application to facilitate the generation of realistic data containing skill-related information. This application, available at https://riyasamanta.github.io/krew.html, is freely accessible to both the general public and the research community.

In the field of eXplainable AI (XAI) in language models, the progression from local explanations of individual decisions to global explanations with high-level concepts has laid the groundwork for mechanistic interpretability, which aims to decode the exact operations. However, this paradigm has not been adequately explored in image models, where existing methods have primarily focused on classspecific interpretations. This paper introduces a novel approach to systematically trace the entire pathway from input through all intermediate layers to the final output within the whole dataset. We utilize Pointwise Feature Vectors (PFVs) and Effective Receptive Fields (ERFs) to decompose model embeddings into interpretable Concept Vectors. Then, we calculate the relevance between concept vectors with our Generalized Integrated Gradients (GIG), enabling a comprehensive, dataset-wide analysis of model behavior. In the field of eXplainable AI (XAI), efforts have historically transitioned from Local explanation to Global explanation to Mechanistic Interpretability. While local explanation methods including Selvaraju et al. (2016); Montavon et al. (2017); Sundararajan et al. (2017); Han et al. (2024) have focused on explaining specific decisions for individual instances, global explanation methods seek to uncover overall patterns and behaviors applicable across the entire dataset (Wu et al., 2022; Xuanyuan et al., 2023; Singh et al., 2024).

Building trees to represent or to fit distances is a critical component of phylogenetic analysis, metric embeddings, approximation algorithms, geometric graph neural nets, and the analysis of hierarchical data. Much of the previous algorithmic work, however, has focused on generic metric spaces (i.e., those with no a priori constraints). Leveraging several ideas from the mathematical analysis of hyperbolic geometry and geometric group theory, we study the tree fitting problem as finding the relation between the hyperbolicity (ultrametricity) vector and the error of tree (ultrametric) embedding. That is, we define a vector of hyperbolicity (ultrametric) values over all triples of points and compare the $\ell_p$ norms of this vector with the $\ell_q$ norm of the distortion of the best tree fit to the distances. This formulation allows us to define the average hyperbolicity (ultrametricity) in terms of a normalized $\ell_1$ norm of the hyperbolicity vector. Furthermore, we can interpret the classical tree fitting result of Gromov as a $p = q = \infty$ result. We present an algorithm HCCRootedTreeFit such that the $\ell_1$ error of the output embedding is analytically bounded in terms of the $\ell_1$ norm of the hyperbolicity vector (i.e., $p = q = 1$) and that this result is tight. Furthermore, this algorithm has significantly different theoretical and empirical performance as compared to Gromov's result and related algorithms. Finally, we show using HCCRootedTreeFit and related tree fitting algorithms, that supposedly standard data sets for hierarchical data analysis and geometric graph neural networks have radically different tree fits than those of synthetic, truly tree-like data sets, suggesting that a much more refined analysis of these standard data sets is called for.

While Agent-Based Models can create detailed artificial societies based on individual differences and local context, they can be computationally intensive. Modelers may offset these costs through a parsimonious use of the model, for example by using smaller population sizes (which limits analyses in sub-populations), running fewer what-if scenarios, or accepting more uncertainty by performing fewer simulations. Alternatively, researchers may accelerate simulations via hardware solutions (e.g., GPU parallelism) or approximation approaches that operate a tradeoff between accuracy and compute time. In this paper, we present an approximation that combines agents who `think alike', thus reducing the population size and the compute time. Our innovation relies on representing agent behaviors as networks of rules (Fuzzy Cognitive Maps) and empirically evaluating different measures of distance between these networks. Then, we form groups of think-alike agents via community detection and simplify them to a representative agent. Case studies show that our simplifications remain accuracy.

In recent years, much of the research on clustering algorithms has primarily focused on enhancing their accuracy and efficiency, frequently at the expense of interpretability. However, as these methods are increasingly being applied in high-stakes domains such as healthcare, finance, and autonomous systems, the need for transparent and interpretable clustering outcomes has become a critical concern. This is not only necessary for gaining user trust but also for satisfying the growing ethical and regulatory demands in these fields. Ensuring that decisions derived from clustering algorithms can be clearly understood and justified is now a fundamental requirement. To address this need, this paper provides a comprehensive and structured review of the current state of explainable clustering algorithms, identifying key criteria to distinguish between various methods. These insights can effectively assist researchers in making informed decisions about the most suitable explainable clustering methods for specific application contexts, while also promoting the development and adoption of clustering algorithms that are both efficient and transparent.

Deep supervised learning models require high volume of labeled data to attain sufficiently good results. Although, the practice of gathering and annotating such big data is costly and laborious. Recently, the application of self supervised learning (SSL) in vision tasks has gained significant attention. The intuition behind SSL is to exploit the synchronous relationships within the data as a form of self-supervision, which can be versatile. In the current big data era, most of the data is unlabeled, and the success of SSL thus relies in finding ways to improve this vast amount of unlabeled data available. Thus its better for deep learning algorithms to reduce reliance on human supervision and instead focus on self-supervision based on the inherent relationships within the data. With the advent of ViTs, which have achieved remarkable results in computer vision, it is crucial to explore and understand the various SSL mechanisms employed for training these models specifically in scenarios where there is less label data available. In this survey we thus develop a comprehensive taxonomy of systematically classifying the SSL techniques based upon their representations and pre-training tasks being applied. Additionally, we discuss the motivations behind SSL, review popular pre-training tasks, and highlight the challenges and advancements in this field. Furthermore, we present a comparative analysis of different SSL methods, evaluate their strengths and limitations, and identify potential avenues for future research.

This article proposes a novel fuzzy clustering based anomaly detection method for pump current time series of EDFA systems. The proposed change detection framework (CDF) strategically combines the advantages of entropy analysis (EA) and principle component analysis (PCA) with fuzzy clustering procedures. In the framework, EA is applied for dynamic selection of features for reduction of the feature space and increase of computational performance. Furthermore, PCA is utilized to extract features from the raw feature space to enable generalization capability of the subsequent fuzzy clustering procedures. Three different fuzzy clustering methods, more precisely the fuzzy clustering algorithm, a probabilistic clustering algorithm and a possibilistic clustering algorithm are evaluated for performance and generalization. Hence, the proposed framework has the innovative feature to detect changes in pump current time series at an early stage for arbitrary points of operation, compared to state-of-the-art predefined alarms in commercially used EDFAs. Moreover, the approach is implemented and tested using experimental data. In addition, the proposed framework enables further approaches of applying decentralized predictive maintenance for optical fiber networks.

Unsupervised clustering has emerged as a critical tool for uncovering hidden patterns and insights from vast, unlabeled datasets. However, traditional methods like Partitioning Around Medoids (PAM) struggle with scalability due to their quadratic computational complexity. To address this limitation, we introduce WOA-kMedoids, a novel unsupervised clustering method that incorporates the Whale Optimization Algorithm (WOA), a nature-inspired metaheuristic inspired by the hunting strategies of humpback whales. By optimizing centroid selection, WOA-kMedoids reduces computational complexity of the k-medoids algorithm from quadratic to near-linear with respect to the number of observations. This improvement in efficiency enables WOA-kMedoids to be scalable to large datasets while maintaining high clustering accuracy. We evaluated the performance of WOA-kMedoids on 25 diverse time series datasets from the UCR archive. Our empirical results demonstrate that WOA-kMedoids maintains clustering accuracy similar to PAM. While WOA-kMedoids exhibited slightly higher runtime than PAM on small datasets (less than 300 observations), it outperformed PAM in computational efficiency on larger datasets. The scalability of WOA-kMedoids, combined with its consistently high accuracy, positions it as a promising and practical choice for unsupervised clustering in big data applications. WOA-kMedoids has implications for efficient knowledge discovery in massive, unlabeled datasets across various domains.

In this paper, we investigate the use of probabilistic graphical models, specifically stochastic blockmodels, for the purpose of hierarchical entity clustering on knowledge graphs. These models, seldom used in the Semantic Web community, decompose a graph into a set of probability distributions. The parameters of these distributions are then inferred allowing for their subsequent sampling to generate a random graph. In a non-parametric setting, this allows for the induction of hierarchical clusterings without prior constraints on the hierarchy's structure. Specifically, this is achieved by the integration of the Nested Chinese Restaurant Process and the Stick Breaking Process into the generative model. In this regard, we propose a model leveraging such integration and derive a collapsed Gibbs sampling scheme for its inference. To aid in understanding, we describe the steps in this derivation and provide an implementation for the sampler. We evaluate our model on synthetic and real-world datasets and quantitatively compare against benchmark models. We further evaluate our results qualitatively and find that our model is capable of inducing coherent cluster hierarchies in small scale settings. The work presented in this paper provides the first step for the further application of stochastic blockmodels for knowledge graphs on a larger scale. We conclude the paper with potential avenues for future work on more scalable inference schemes.