We consider the problem of clustering a sample of probability distributions from a random distribution on $\mathbb R^p$. Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing kernel Hilbert space (RKHS) $\mathcal H$. By mapping each distribution to its corresponding kernel mean embedding in $\mathcal H$, we obtain a sample in this RKHS where we carry out the $K$-means clustering procedure, which provides an unsupervised classification of the original sample. The procedure is simple and computationally feasible even for dimension $p>1$. The simulation studies provide insight into the choice of the kernel and its tuning parameter. The performance of the proposed clustering procedure is illustrated on a collection of Synthetic Aperture Radar (SAR) images.

Brain atlases are essential for reducing the dimensionality of neuroimaging data and enabling interpretable analysis. However, most existing atlases are predefined, group-level templates with limited flexibility and resolution. We present Deep Cluster Atlas (DCA), a graph-guided deep embedding clustering framework for generating individualized, voxel-wise brain parcellations. DCA combines a pretrained autoencoder with spatially regularized deep clustering to produce functionally coherent and spatially contiguous regions. Our method supports flexible control over resolution and anatomical scope, and generalizes to arbitrary brain structures. We further introduce a standardized benchmarking platform for atlas evaluation, using multiple large-scale fMRI datasets. Across multiple datasets and scales, DCA outperforms state-of-the-art atlases, improving functional homogeneity by 98.8% and silhouette coefficient by 29%, and achieves superior performance in downstream tasks such as autism diagnosis and cognitive decoding. We also observe that a fine-tuned pretrained model achieves superior results on the corresponding task. Codes and models are available at https://github.com/ncclab-sustech/DCA .

The growing demand for reliable electricity in universities necessitates intelligent energy management. This study proposes a machine learning-based load shedding framework for the University of Lagos, designed to optimize distribution and reduce waste. The methodology followed three main stages. First, a dataset of 3,648 hourly records from 55 buildings was compiled to develop building-level consumption models. Second, Principal Component Analysis was applied for dimensionality reduction, and clustering validation techniques were used to determine the optimal number of demand groups. Mini-Batch K-Means was then employed to classify buildings into high-, medium-, and low-demand clusters. Finally, short-term load forecasting was performed at the cluster level using multiple statistical and deep learning models, including ARIMA, SARIMA, Prophet, LSTM, and GRU. Results showed Prophet offered the most reliable forecasts, while Mini-Batch K-Means achieved stable clustering performance. By integrating clustering with forecasting, the framework enabled a fairer, data-driven load shedding strategy that reduces inefficiencies and supports climate change mitigation through sustainable energy management.

Virtual brainstorming sessions have become a central component of collaborative problem solving, yet the large volume and uneven distribution of ideas often make it difficult to extract valuable insights efficiently. Manual coding of ideas is time-consuming and subjective, underscoring the need for automated approaches to support the evaluation of group creativity. In this study, we propose a semantic-driven topic modeling framework that integrates four modular components: transformer-based embeddings (Sentence-BERT), dimensionality reduction (UMAP), clustering (HDBSCAN), and topic extraction with refinement. We evaluate our approach on structured Zoom brainstorming sessions involving student groups tasked with improving their university. Results demonstrate that our model achieves higher topic coherence compared to established methods such as LDA, ETM, and BERTopic, with an average coherence score of 0.687 (CV), outperforming baselines by a significant margin. Beyond improved performance, the model provides interpretable insights into the depth and diversity of topics explored, supporting both convergent and divergent dimensions of group creativity. This work highlights the potential of embedding-based topic modeling for analyzing collaborative ideation and contributes an efficient and scalable framework for studying creativity in synchronous virtual meetings. Introduction Digital communication has become central to modern collaboration, with virtual meetings and conversational agents such as chatbots increasingly shaping how teams interact across geographical and cultural boundaries [1].

We study the problem of releasing a differentially private (DP) synthetic graph $G'$ that well approximates the triangle-motif sizes of all cuts of any given graph $G$, where a motif in general refers to a frequently occurring subgraph within complex networks. Non-private versions of such graphs have found applications in diverse fields such as graph clustering, graph sparsification, and social network analysis. Specifically, we present the first $(\varepsilon,δ)$-DP mechanism that, given an input graph $G$ with $n$ vertices, $m$ edges and local sensitivity of triangles $\ell_{3}(G)$, generates a synthetic graph $G'$ in polynomial time, approximating the triangle-motif sizes of all cuts $(S,V\setminus S)$ of the input graph $G$ up to an additive error of $\tilde{O}(\sqrt{m\ell_{3}(G)}n/\varepsilon^{3/2})$. Additionally, we provide a lower bound of $Ω(\sqrt{mn}\ell_{3}(G)/\varepsilon)$ on the additive error for any DP algorithm that answers the triangle-motif size queries of all $(S,T)$-cut of $G$. Finally, our algorithm generalizes to weighted graphs, and our lower bound extends to any $K_h$-motif cut for any constant $h\geq 2$.

Abstract-- Understanding open-world semantics is critical for robotic planning and control, particularly in unstructured outdoor environments. Existing vision-language mapping approaches typically rely on object-centric segmentation priors, which often fail outdoors due to semantic ambiguities and indistinct class boundaries. We propose OT AS--an Open-vocabulary T oken Alignment method for outdoor Segmentation. OT AS addresses the limitations of open-vocabulary segmentation models by extracting semantic structure directly from the output tokens of pre-trained vision models. By clustering semantically similar structures across single and multiple views and grounding them in language, OT AS reconstructs a geometrically consistent feature field that supports open-vocabulary segmentation queries. Our method operates in a zero-shot manner, without scene-specific fine-tuning, and achieves real-time performance of up to 17 fps. On the Off-Road Freespace Detection dataset, OT AS yields a modest IoU improvement over fine-tuned and open-vocabulary 2D segmentation baselines. In 3D segmentation on T artanAir, it achieves up to a 151% relative IoU improvement compared to existing open-vocabulary mapping methods. Real-world reconstructions further demonstrate OT AS' applicability to robotic deployment. Understanding the open world through semantics is a key challenge for robotics. Vision-Language Models (VLMs), that ground vision in language, have recently been shown to effectively provide semantics for mapping to facilitate task planning and navigation [1], [2]. However, open-vocabulary semantic mapping methods [3], [4], [5] rely on segmentation priors from general-purpose models to reason about the environment.

Graphs have become extremely useful for representing a wide variety of systems in different contexts: biological, social, information... A basic attempt to study them may consist in partitioning the vertices of a graph into clusters that are more densely connected; that is commonly called community detection or graph clustering; see for instance [20, 1]. Community detection and clustering are central problems in machine learning and data science. In particular, the stochastic block model (SBM) [34, 25] has been widely used as a canonical model for community detection and as a building block for clustering with more structural assumptions. In its most general form, the SBM corresponds to a randomly weighted graph model where each node has an unobserved label and the probability of observing a given edge between two nodes depends only on the labels of the nodes under consideration.

Predictions from statistical physics postulate that recovery of the communities in Stochastic Block Model (SBM) is possible in polynomial time above, and only above, the Kesten-Stigum (KS) threshold. This conjecture has given rise to a rich literature, proving that non-trivial community recovery is indeed possible in SBM above the KS threshold, as long as the number $K$ of communities remains smaller than $\sqrt{n}$, where $n$ is the number of nodes in the observed graph. Failure of low-degree polynomials below the KS threshold was also proven when $K=o(\sqrt{n})$. When $K\geq \sqrt{n}$, Chin et al.(2025) recently prove that, in a sparse regime, community recovery in polynomial time is possible below the KS threshold by counting non-backtracking paths. This breakthrough result lead them to postulate a new threshold for the many communities regime $K\geq \sqrt{n}$. In this work, we provide evidences that confirm their conjecture for $K\geq \sqrt{n}$: 1- We prove that, for any density of the graph, low-degree polynomials fail to recover communities below the threshold postulated by Chin et al.(2025); 2- We prove that community recovery is possible in polynomial time above the postulated threshold, not only in the sparse regime of~Chin et al., but also in some (but not all) moderately sparse regimes by essentially counting clique occurence in the observed graph.

Online controlled experiments, also known as A/B testing, are the digital equivalent of randomized controlled trials for estimating the impact of marketing campaigns on website visitors. Stratified sampling is a traditional technique for variance reduction to improve the sensitivity (or statistical power) of controlled experiments; this technique first divides the population into strata (homogeneous subgroups) based on stratification variables and then draws samples from each stratum to avoid sampling bias. To enhance the estimation accuracy of stratified sampling, we focus on the problem of selecting a subset of stratification variables that are effective in variance reduction. We design an efficient algorithm that selects stratification variables one by one by simulating a series of stratified sampling processes. We also estimate the computational complexity of our subset selection algorithm. Computational experiments using synthetic and real-world datasets demonstrate that our method can outperform other variance reduction techniques especially when multiple variables have a certain correlation with the outcome variable. Our subset selection method for stratified sampling can improve the sensitivity of online controlled experiments, thus enabling more reliable marketing decisions.

A Large Language Model (LLM) offers versatility across domains and tasks, purportedly benefiting users with a wide variety of behaviors and preferences. We question this perception about an LLM when users have inherently subjective behaviors and preferences, as seen in their ubiquitous and idiosyncratic browsing of websites or apps. The sequential behavior logs of pages, thus generated, form something akin to each user's self-constructed "language", albeit without the structure and grammar imbued in natural languages. We ask: (i) Can a small LM represent the "language of browsing" better than a large LM? (ii) Can an LM with a single set of parameters (or, single LM) adequately capture myriad users' heterogeneous, subjective behaviors and preferences? (iii) Can a single LM with high average performance, yield low variance in performance to make alignment good at user level? We introduce clusterwise LM training, HeTLM (Heterogeneity aware Training of Language Model), appropriate for subjective behaviors. We find that (i) a small LM trained using a page-level tokenizer outperforms large pretrained or finetuned LMs; (ii) HeTLM with heterogeneous cluster specific set of parameters outperforms a single LM of the same family, controlling for the number of parameters; and (iii) a higher mean and a lower variance in generation ensues, implying improved alignment.