Furthermore, [30, 31] pointed out to conduct CL with reconstruction regularization to achieve robust representations for downstream tasks. RINCE [15] (a short name of Robust InfoNCE) is a variant of InfoNCE contrastive loss that considers noise in false positive sample pairs.

The stochastic block model (SBM) is a fundamental model for studying graph clustering or community detection in networks. It has received great attention in the last decade and the balanced case, i.e., assuming all clusters have large size, has been well studied. However, our understanding of SBM with unbalanced communities (arguably, more relevant in practice) is still limited. In this paper, we provide a simple SVD-based algorithm for recovering the communities in the SBM with communities of varying sizes.We improve upon a result of Ailon, Chen and Xu [ICML 2013; JMLR 2015] by removing the assumption that there is a large interval such that the sizes of clusters do not fall in, and also remove the dependency of the size of the recoverable clusters on the number of underlying clusters. We further complement our theoretical improvements with experimental comparisons.Under the planted clique conjecture, the size of the clusters that can be recovered by our algorithm is nearly optimal (up to poly-logarithmic factors) when the probability parameters are constant. As a byproduct, we obtain an efficient clustering algorithm with sublinear query complexity in a faulty oracle model, which is capable of detecting all clusters larger than $\tilde{\Omega}({\sqrt{n}})$, even in the presence of $\Omega(n)$ small clusters in the graph. In contrast, previous efficient algorithms that use a sublinear number of queries are incapable of recovering any large clusters if there are more than $\tilde{\Omega}(n^{2/5})$ small clusters.

We propose a framework for the joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems from multi-trajectory data. This learning task is a challenging non-convex mixed-integer optimization problem, which we address through a novel three-stage approach. First, we leverage shared structure across agent interactions to recover a low-rank embedding of the system parameters via matrix sensing. Second, we identify discrete interaction types by clustering within the learned embedding. Third, we recover the network weight matrix and kernel coefficients through matrix factorization and a post-processing refinement. We provide theoretical guarantees with estimation error bounds under a Restricted Isometry Property (RIP) assumption and establish conditions for the exact recovery of interaction types based on cluster separability. Numerical experiments on synthetic datasets, including heterogeneous predator-prey systems, demonstrate that our method yields an accurate reconstruction of the underlying dynamics and is robust to noise.

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.

Task-oriented semantic communication (SemCom) prioritizes task execution over accurate symbol reconstruction and is well-suited to emerging intelligent applications. Cooperative multi-task SemCom (CMT-SemCom) further improves task execution performance. However, [1] demonstrates that cooperative multi-tasking can be either constructive or destructive. Moreover, the existing CMT-SemCom framework is not directly applicable to distributed multi-user scenarios, such as non-terrestrial satellite networks, where each satellite employs an individual semantic encoder. In this paper, we extend our earlier CMT-SemCom framework to distributed settings by proposing a federated learning (FL) based CMT-SemCom that enables cooperative multi-tasking across distributed users. Moreover, to address performance degradation caused by negative information transfer among heterogeneous tasks, we propose a semantic-aware task clustering method integrated in the FL process to ensure constructive cooperation based on an information-theoretic approach. Unlike common clustering methods that rely on high-dimensional data or feature space similarity, our proposed approach operates in the low-dimensional semantic domain to identify meaningful task relationships. Simulation results based on a LEO satellite network setup demonstrate the effectiveness of our approach and performance gain over unclustered FL and individual single-task SemCom.

This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the introduction of statistics. We show that density distribution has its fundamental limitation -- high-density bias, irrespective of the algorithms used to perform clustering. Existing density-based clustering algorithms have employed different algorithmic means to counter the effect of the high-density bias with some success, but the fundamental limitation of using density distribution remains an obstacle to discovering clusters of arbitrary shapes, sizes and densities. Using the mass distribution as a better foundation, we propose a new algorithm which maximizes the total mass of all clusters, called mass-maximization clustering (MMC). The algorithm can be easily changed to maximize the total density of all clusters in order to examine the fundamental limitation of using density distribution versus mass distribution. The key advantage of the MMC over the density-maximization clustering is that the maximization is conducted without a bias towards dense clusters.

Bayesian optimisation is a sample efficient method for finding a global optimum of expensive black-box objective functions. Historic datasets from related problems can be exploited to help improve performance of Bayesian optimisation by adapting transfer learning methods to various components of the Bayesian optimisation pipeline. In this study we perform an empirical analysis of various ensemble-based transfer learning Bayesian optimisation methods and pipeline components. We expand on previous work in the literature by contributing some specific pipeline components, and three new real-time transfer learning Bayesian optimisation benchmarks. In particular we propose to use a weighting strategy for ensemble surrogate model predictions based on regularised regression with weights constrained to be positive, and a related component for handling the case when transfer learning is not improving Bayesian optimisation performance. We find that in general, two components that help improve transfer learning Bayesian optimisation performance are warm start initialisation and constraining weights used with ensemble surrogate model to be positive.

Self-Organizing Maps provide topology-preserving projections of high-dimensional data and have been widely used for visualization, clustering, and vector quantization. In this work, we show that the activation pattern of a SOM - the squared distances to its prototypes - can be inverted to recover the exact input under mild geometric conditions. This follows from a classical fact in Euclidean distance geometry: a point in $D$ dimensions is uniquely determined by its distances to $D{+}1$ affinely independent references. We derive the corresponding linear system and characterize the conditions under which the inversion is well-posed. Building upon this mechanism, we introduce the Manifold-Aware Unified SOM Inversion and Control (MUSIC) update rule, which enables controlled, semantically meaningful trajectories in latent space. MUSIC modifies squared distances to selected prototypes while preserving others, resulting in a deterministic geometric flow aligned with the SOM's piecewise-linear structure. Tikhonov regularization stabilizes the update rule and ensures smooth motion on high-dimensional datasets. Unlike variational or probabilistic generative models, MUSIC does not rely on sampling, latent priors, or encoder-decoder architectures. If no perturbation is applied, inversion recovers the exact input; when a target cluster or prototype is specified, MUSIC produces coherent semantic variations while remaining on the data manifold. This leads to a new perspective on data augmentation and controllable latent exploration based solely on prototype geometry. We validate the approach using synthetic Gaussian mixtures, the MNIST and the Faces in the Wild dataset. Across all settings, MUSIC produces smooth, interpretable trajectories that reveal the underlying geometry of the learned manifold, illustrating the advantages of SOM-based inversion over unsupervised clustering.