The core concept of GC is to create a smaller, more manageable graph that retains the characteristics of the original graph.

The metric backbone of a weighted graph is the union of all-pairs shortest paths.

We propose In-Context Clustering (ICC), a flexible LLM-based procedure for clustering data from diverse distributions. Unlike traditional clustering algorithms constrained by predefined similarity measures, ICC flexibly captures complex relationships among inputs through an attention mechanism. We show that pretrained LLMs exhibit impressive zero-shot clustering capabilities on text-encoded numeric data, with attention matrices showing salient cluster patterns. Spectral clustering using attention matrices offers surprisingly competitive performance. We further enhance the clustering capabilities of LLMs on numeric and image data through fine-tuning using the Next Token Prediction (NTP) loss. Moreover, the flexibility of LLM prompting enables text-conditioned image clustering, a capability that classical clustering methods lack. Our work extends in-context learning to an unsupervised setting, showcasing the effectiveness and flexibility of LLMs for clustering. Our code is available at https://agenticlearning.ai/icc.

University of Leeds GISRUK 2024 Summary This abstract advocates for employing clustering techniques to classify vacation rental properties active during the Covid pandemic to identify inherent patterns and behaviours . The dataset, a collaboration betwee n the ESRC funded Consumer Data Research Centre (CDRC) and AirDNA, encompasses data for over a million properties and hosts. Utili s ing K - means and K - medoids clustering techniques, we identify homogenous groups and their common characteristics. Our findings enhance comprehension of the intricacies of vacation rental evaluations and could potentially be utilised in the creation of targeted, cluster - specific policies. KEYWORDS: Covid - 19, Hospitality, Clustering, Unsupervised Machine Learnin g 1. Introduction Travel and tourism ha ve been embedded into our human experience for centuries.

This study applies BERTopic, a transformer-based topic modeling technique, to the lmsys-chat-1m dataset, a multilingual conversational corpus built from head-to-head evaluations of large language models (LLMs). Each user prompt is paired with two anonymized LLM responses and a human preference label, used to assess user evaluation of competing model outputs. The main objective is uncovering thematic patterns in these conversations and examining their relation to user preferences, particularly if certain LLMs are consistently preferred within specific topics. A robust preprocessing pipeline was designed for multilingual variation, balancing dialogue turns, and cleaning noisy or redacted data. BERTopic extracted over 29 coherent topics including artificial intelligence, programming, ethics, and cloud infrastructure. We analysed relationships between topics and model preferences to identify trends in model-topic alignment. Visualization techniques included inter-topic distance maps, topic probability distributions, and model-versus-topic matrices. Our findings inform domain-specific fine-tuning and optimization strategies for improving real-world LLM performance and user satisfaction.

We show that the problem of identifying different signal components from a time-frequency representation can be equivalently phrased as a graph clustering problem: given a graph $G=(V,E)$ one aims to identify `clusters', subgraphs that are strongly connected and have relatively few connections between them. The graph clustering problem is well studied, we show how these ideas can suggest (many) new ways to identify signal components. Numerical experiments illustrate the ideas.

We introduce Bridged Clustering, a semi-supervised framework to learn predictors from any unpaired input $X$ and output $Y$ dataset. Our method first clusters $X$ and $Y$ independently, then learns a sparse, interpretable bridge between clusters using only a few paired examples. At inference, a new input $x$ is assigned to its nearest input cluster, and the centroid of the linked output cluster is returned as the prediction $\hat{y}$. Unlike traditional SSL, Bridged Clustering explicitly leverages output-only data, and unlike dense transport-based methods, it maintains a sparse and interpretable alignment. Through theoretical analysis, we show that with bounded mis-clustering and mis-bridging rates, our algorithm becomes an effective and efficient predictor. Empirically, our method is competitive with SOTA methods while remaining simple, model-agnostic, and highly label-efficient in low-supervision settings.

We introduce FAEclust, a novel functional autoencoder framework for cluster analysis of multi-dimensional functional data, data that are random realizations of vector-valued random functions. Our framework features a universal-approximator encoder that captures complex nonlinear interdependencies among component functions, and a universal-approximator decoder capable of accurately reconstructing both Euclidean and manifold-valued functional data. Stability and robustness are enhanced through innovative regularization strategies applied to functional weights and biases. Additionally, we incorporate a clustering loss into the network's training objective, promoting the learning of latent representations that are conducive to effective clustering. A key innovation is our shape-informed clustering objective, ensuring that the clustering results are resistant to phase variations in the functions. We establish the universal approximation property of our non-linear decoder and validate the effectiveness of our model through extensive experiments.

Understanding treatment effect heterogeneity is vital for scientific and policy research.