Multimodal graphs, which integrate unstructured heterogeneous data with structured interconnections, offer substantial real-world utility but remain insufficiently explored in unsupervised learning. In this work, we initiate the study of multimodal graph clustering, aiming to bridge this critical gap. Through empirical analysis, we observe that real-world multimodal graphs often exhibit hybrid neighborhood patterns, combining both homophilic and heterophilic relationships. To address this challenge, we propose a novel framework -- \textsc{Disentangled Multimodal Graph Clustering (DMGC)} -- which decomposes the original hybrid graph into two complementary views: (1) a homophily-enhanced graph that captures cross-modal class consistency, and (2) heterophily-aware graphs that preserve modality-specific inter-class distinctions. We introduce a \emph{Multimodal Dual-frequency Fusion} mechanism that jointly filters these disentangled graphs through a dual-pass strategy, enabling effective multimodal integration while mitigating category confusion. Our self-supervised alignment objectives further guide the learning process without requiring labels. Extensive experiments on both multimodal and multi-relational graph datasets demonstrate that DMGC achieves state-of-the-art performance, highlighting its effectiveness and generalizability across diverse settings. Our code is available at https://github.com/Uncnbb/DMGC.

This paper explores the applications of quantum annealing (QA) and classical simulated annealing (SA) to a suite of combinatorial optimization problems in machine learning, namely feature selection, instance selection, and clustering. We formulate each task as a Quadratic Unconstrained Binary Optimization (QUBO) problem and implement both quantum and classical solvers to compare their effectiveness. For feature selection, we propose several QUBO configurations that balance feature importance and redundancy, showing that quantum annealing (QA) produces solutions that are computationally more efficient. In instance selection, we propose a few novel heuristics for instance-level importance measures that extend existing methods. For clustering, we embed a classical-to-quantum pipeline, using classical clustering followed by QUBO-based medoid refinement, and demonstrate consistent improvements in cluster compactness and retrieval metrics. Our results suggest that QA can be a competitive and efficient tool for discrete machine learning optimization, even within the constraints of current quantum hardware.

Despite the outstanding performance of large language models (LLMs) across various NLP tasks, hallucinations in LLMs--where LLMs generate inaccurate responses--remains as a critical problem as it can be directly connected to a crisis of building safe and reliable LLMs. Uncertainty estimation is primarily used to measure hallucination levels in LLM responses so that correct and incorrect answers can be distinguished clearly. This study proposes an effective uncertainty estimation approach, \textbf{Cl}ust\textbf{e}ring-based sem\textbf{an}tic con\textbf{s}ist\textbf{e}ncy (\textbf{Cleanse}). Cleanse quantifies the uncertainty with the proportion of the intra-cluster consistency in the total consistency between LLM hidden embeddings which contain adequate semantic information of generations, by employing clustering. The effectiveness of Cleanse for detecting hallucination is validated using four off-the-shelf models, LLaMA-7B, LLaMA-13B, LLaMA2-7B and Mistral-7B and two question-answering benchmarks, SQuAD and CoQA.

This paper introduces a robust framework for motion segmentation and egomotion estimation using event-based normal flow, tailored specifically for neuromorphic vision sensors. In contrast to traditional methods that rely heavily on optical flow or explicit depth estimation, our approach exploits the sparse, high-temporal-resolution event data and incorporates geometric constraints between normal flow, scene structure, and inertial measurements. The proposed optimization-based pipeline iteratively performs event over-segmentation, isolates independently moving objects via residual analysis, and refines segmentations using hierarchical clustering informed by motion similarity and temporal consistency. Experimental results on the EVIMO2v2 dataset validate that our method achieves accurate segmentation and translational motion estimation without requiring full optical flow computation. This approach demonstrates significant advantages at object boundaries and offers considerable potential for scalable, real-time robotic and navigation applications.

Large Language Models (LLMs) exhibit significant activation sparsity, where only a subset of neurons are active for a given input. Although this sparsity presents opportunities to reduce computational cost, efficiently utilizing it requires predicting activation patterns in a scalable manner. However, direct prediction at the neuron level is computationally expensive due to the vast number of neurons in modern LLMs. To enable efficient prediction and utilization of activation sparsity, we propose a clustering-based activation pattern compression framework. Instead of treating each neuron independently, we group similar activation patterns into a small set of representative clusters. Our method achieves up to 79.34% clustering precision, outperforming standard binary clustering approaches while maintaining minimal degradation in perplexity (PPL) scores. With a sufficiently large number of clusters, our approach attains a PPL score as low as 12.49, demonstrating its effectiveness in preserving model quality while reducing computational overhead. By predicting cluster assignments rather than individual neuron states, future models can efficiently infer activation patterns from pre-computed centroids. We detail the clustering algorithm, analyze its effectiveness in capturing meaningful activation structures, and demonstrate its potential to improve sparse computation efficiency. This clustering-based formulation serves as a foundation for future work on activation pattern prediction, paving the way for efficient inference in large-scale language models.

In network analysis, various matrix representations have been developed to investigate the structural properties of the corresponding network, among which the non-backtracking (NBT) matrix is one such representation. The NBT matrix is well-known for its relationship with the Ihara zeta function [15] defined as an infinite product over equivalence classes of primitive cycles. It was shown in [15, 36] that, for regular graphs, the reciprocal of the Ihara zeta function can be expressed as a polynomial related to the adjacency matrix. The relation between the zeta function and the determinant of the NBT matrix was elucidated in [12], extended to irregular graphs in [3], and an elementary proof was provided in [35]. The connection between the polynomial and the determinant of the NBT matrix, via the Ihara zeta function, is known as the Ihara's formula.

Graph clustering is crucial for unraveling intricate data structures, yet it presents significant challenges due to its unsupervised nature. Recently, goal-directed clustering techniques have yielded impressive results, with contrastive learning methods leveraging pseudo-label garnering considerable attention. Nonetheless, pseudo-label as a supervision signal is unreliable and existing goal-directed approaches utilize only features to construct a single-target distribution for single-center optimization, which lead to incomplete and less dependable guidance. In our work, we propose a novel Dual-Center Graph Clustering (DCGC) approach based on neighbor distribution properties, which includes representation learning with neighbor distribution and dual-center optimization. Specifically, we utilize neighbor distribution as a supervision signal to mine hard negative samples in contrastive learning, which is reliable and enhances the effectiveness of representation learning. Furthermore, neighbor distribution center is introduced alongside feature center to jointly construct a dual-target distribution for dual-center optimization. Extensive experiments and analysis demonstrate superior performance and effectiveness of our proposed method.

--Short text clustering has become increasingly important with the popularity of social media like Twitter, Google+, and Facebook. Existing methods can be broadly categorized into two paradigms: topic model-based approaches and deep representation learning-based approaches. This task is inherently challenging due to the sparse, large-scale, and high-dimensional characteristics of the short text data. Furthermore, the computational intensity required by representation learning significantly increases the running time. T o address these issues, we propose a collapsed Gibbs Sampling algorithm for the Dirichlet Multinomial Mixture model (GSDMM), which effectively handles the sparsity and high dimensionality of short texts while identifying representative words for each cluster . Based on several aspects of GSDMM that warrant further refinement, we propose an improved approach, GSDMM+, designed to further optimize its performance. GSDMM+ reduces initialization noise and adap-tively adjusts word weights based on entropy, achieving fine-grained clustering that reveals more topic-related information. Additionally, strategic cluster merging is employed to refine clustering granularity, better aligning the predicted distribution with the true category distribution. We conduct extensive experiments, comparing our methods with both classical and state-of-the-art approaches. The experimental results demonstrate the efficiency and effectiveness of our methods. The source code for our model is publicly available at https://github.com/chehaoa/VEMC. HE proliferation of mobile internet has led to an exponential increase in user-generated data on online platforms, including video, text, and image data. Intelligent processing of such data can significantly enhance the quality of life across society and generate substantial economic benefits. Short text data are a prevalent and important form of user-generated data, consisting of concise texts such as microblogs and comments.

Clustering based on belief functions has been gaining increasing attention in the machine learning community due to its ability to effectively represent uncertainty and/or imprecision. However, none of the existing algorithms can be applied to complex data, such as mixed data (numerical and categorical) or non-tabular data like time series. Indeed, these types of data are, in general, not represented in a Euclidean space and the aforementioned algorithms make use of the properties of such spaces, in particular for the construction of barycenters. In this paper, we reformulate the Evidential C-Means (ECM) problem for clustering complex data. We propose a new algorithm, Soft-ECM, which consistently positions the centroids of imprecise clusters requiring only a semi-metric. Our experiments show that Soft-ECM present results comparable to conventional fuzzy clustering approaches on numerical data, and we demonstrate its ability to handle mixed data and its benefits when combining fuzzy clustering with semi-metrics such as DTW for time series data.

We study the problem of clustering ranking vectors, where each vector represents preferences as an ordered list of distinct integers. Specifically, we focus on the k-centroids ranking vectors clustering problem (KRC), which aims to partition a set of ranking vectors into k clusters and identify the centroid of each cluster. Unlike classical k-means clustering (KMC), KRC constrains both the observations and centroids to be ranking vectors. We establish the NP-hardness of KRC and characterize its feasible set. For the single-cluster case, we derive a closed-form analytical solution for the optimal centroid, which can be computed in linear time. To address the computational challenges of KRC, we develop an efficient approximation algorithm, KRCA, which iteratively refines initial solutions from KMC, referred to as the baseline solution. Additionally, we introduce a branch-and-bound (BnB) algorithm for efficient cluster reconstruction within KRCA, leveraging a decision tree framework to reduce computational time while incorporating a controlling parameter to balance solution quality and efficiency. We establish theoretical error bounds for KRCA and BnB. Through extensive numerical experiments on synthetic and real-world datasets, we demonstrate that KRCA consistently outperforms baseline solutions, delivering significant improvements in solution quality with fast computational times. This work highlights the practical significance of KRC for personalization and large-scale decision making, offering methodological advancements and insights that can be built upon in future studies.