Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or communities. Our method implements discrete Ricci curvatures and their associated geometric flows, under which the edge weights of the graph evolve to reveal its community structure. We consider several discrete curvature notions and analyze the utility of the resulting algorithms. In contrast to prior literature, we study not only single-membership community detection, where each node belongs to exactly one community, but also mixed-membership community detection, where communities may overlap. For the latter, we argue that it is beneficial to perform community detection on the line graph, i.e., the graph's dual. We provide both theoretical and empirical evidence for the utility of our curvature-based clustering algorithms. In addition, we give several results on the relationship between the curvature of a graph and that of its dual, which enable the efficient implementation of our proposed mixed-membership community detection approach and which may be of independent interest for curvature-based network analysis.

Since late 2022, Large Language Models (LLMs) have become very prominent with LLMs like ChatGPT and Bard receiving millions of users. Hundreds of new LLMs are announced each week, many of which are deposited to Hugging Face, a repository of machine learning models and datasets. To date, nearly 16,000 Text Generation models have been uploaded to the site. Given the huge influx of LLMs, it is of interest to know which LLM backbones, settings, training methods, and families are popular or trending. However, there is no comprehensive index of LLMs available. We take advantage of the relatively systematic nomenclature of Hugging Face LLMs to perform hierarchical clustering and identify communities amongst LLMs using n-grams and term frequency-inverse document frequency. Our methods successfully identify families of LLMs and accurately cluster LLMs into meaningful subgroups. We present a public web application to navigate and explore Constellation, our atlas of 15,821 LLMs. Constellation rapidly generates a variety of visualizations, namely dendrograms, graphs, word clouds, and scatter plots. Constellation is available at the following link: https://constellation.sites.stanford.edu/.

In this paper, we propose a novel fully unsupervised framework that learns action representations suitable for the action segmentation task from the single input video itself, without requiring any training data. Our method is a deep metric learning approach rooted in a shallow network with a triplet loss operating on similarity distributions and a novel triplet selection strategy that effectively models temporal and semantic priors to discover actions in the new representational space. Under these circumstances, we successfully recover temporal boundaries in the learned action representations with higher quality compared with existing unsupervised approaches. The proposed method is evaluated on two widely used benchmark datasets for the action segmentation task and it achieves competitive performance by applying a generic clustering algorithm on the learned representations.

Representative Selection (RS) is the problem of finding a small subset of exemplars from a dataset that is representative of the dataset. In this paper, we study RS for attributed graphs, and focus on finding representative nodes that optimize the accuracy of a model trained on the selected representatives. Theoretically, we establish a new hardness result for RS (in the absence of a graph structure) by proving that a particular, highly practical variant of it (RS for Learning) is hard to approximate in polynomial time within any reasonable factor, which implies a significant potential gap between the optimum solution of widely-used surrogate functions and the actual accuracy of the model. We then study the setting where a (homophilous) graph structure is available, or can be constructed, between the data points. We show that with an appropriate modeling approach, the presence of such a structure can turn a hard RS (for learning) problem into one that can be effectively solved. To this end, we develop RS-GNN, a representation learning-based RS model based on Graph Neural Networks. Empirically, we demonstrate the effectiveness of RS-GNN on problems with predefined graph structures as well as problems with graphs induced from node feature similarities, by showing that RS-GNN achieves significant improvements over established baselines on a suite of eight benchmarks.

We introduce the nested stochastic block model (NSBM) to cluster a collection of networks while simultaneously detecting communities within each network. NSBM has several appealing features including the ability to work on unlabeled networks with potentially different node sets, the flexibility to model heterogeneous communities, and the means to automatically select the number of classes for the networks and the number of communities within each network. This is accomplished via a Bayesian model, with a novel application of the nested Dirichlet process (NDP) as a prior to jointly model the between-network and within-network clusters. The dependency introduced by the network data creates nontrivial challenges for the NDP, especially in the development of efficient samplers. For posterior inference, we propose several Markov chain Monte Carlo algorithms including a standard Gibbs sampler, a collapsed Gibbs sampler, and two blocked Gibbs samplers that ultimately return two levels of clustering labels from both within and across the networks. Extensive simulation studies are carried out which demonstrate that the model provides very accurate estimates of both levels of the clustering structure. We also apply our model to two social network datasets that cannot be analyzed using any previous method in the literature due to the anonymity of the nodes and the varying number of nodes in each network.

This paper develops an approximation to the (effective) $p$-resistance and applies it to multi-class clustering. Spectral methods based on the graph Laplacian and its generalization to the graph $p$-Laplacian have been a backbone of non-euclidean clustering techniques. The advantage of the $p$-Laplacian is that the parameter $p$ induces a controllable bias on cluster structure. The drawback of $p$-Laplacian eigenvector based methods is that the third and higher eigenvectors are difficult to compute. Thus, instead, we are motivated to use the $p$-resistance induced by the $p$-Laplacian for clustering. For $p$-resistance, small $p$ biases towards clusters with high internal connectivity while large $p$ biases towards clusters of small "extent," that is a preference for smaller shortest-path distances between vertices in the cluster. However, the $p$-resistance is expensive to compute. We overcome this by developing an approximation to the $p$-resistance. We prove upper and lower bounds on this approximation and observe that it is exact when the graph is a tree. We also provide theoretical justification for the use of $p$-resistance for clustering. Finally, we provide experiments comparing our approximated $p$-resistance clustering to other $p$-Laplacian based methods.

With Company2Vec, the paper proposes a novel application in representation learning. The model analyzes business activities from unstructured company website data using Word2Vec and dimensionality reduction. Company2Vec maintains semantic language structures and thus creates efficient company embeddings in fine-granular industries. These semantic embeddings can be used for various applications in banking. Direct relations between companies and words allow semantic business analytics (e.g. top-n words for a company). Furthermore, industry prediction is presented as a supervised learning application and evaluation method. The vectorized structure of the embeddings allows measuring companies similarities with the cosine distance. Company2Vec hence offers a more fine-grained comparison of companies than the standard industry labels (NACE). This property is relevant for unsupervised learning tasks, such as clustering. An alternative industry segmentation is shown with k-means clustering on the company embeddings. Finally, this paper proposes three algorithms for (1) firm-centric, (2) industry-centric and (3) portfolio-centric peer-firm identification.

Low-rank tensor analysis has received widespread attention with many practical applications. However, the tensor data are often contaminated by outliers or sample-specific corruptions. How to recover the tensor data that are corrupted by outliers and perform data clustering remains a challenging problem. This paper develops an outlier-robust tensor low-rank representation (OR-TLRR) method for simultaneous outlier detection and tensor data clustering based on the tensor singular value decomposition (t-SVD) algebraic framework. It is motivated by the recently proposed tensor-tensor product induced by invertible linear transforms that satisfy certain conditions. For tensor observations with arbitrary outlier corruptions, OR-TLRR has provable performance guarantee for exactly recovering the row space of clean data and detecting outliers under mild conditions. Moreover, an extension of OR-TLRR is also proposed to handle the case when parts of the data are missing. Finally, extensive experimental results on both synthetic and real data demonstrate the effectiveness of the proposed algorithms.

This paper introduces a novel self-consistency clustering algorithm ($K$-Tensors) designed for {partitioning a distribution of} positive-semidefinite matrices based on their eigenstructures. As positive semi-definite matrices can be represented as ellipsoids in $\mathbb R^p$, $p \ge 2$, it is critical to maintain their structural information to perform effective clustering. However, traditional clustering algorithms {applied to matrices} often {involve vectorization of} the matrices, resulting in a loss of essential structural information. To address this issue, we propose a distance metric {for clustering} that is specifically based on the structural information of positive semi-definite matrices. This distance metric enables the clustering algorithm to consider the differences between positive semi-definite matrices and their projections onto {a} common space spanned by \thadJulyTen{orthonormal vectors defined from a set of} positive semi-definite matrices. This innovative approach to clustering positive semi-definite matrices has broad applications in several domains including financial and biomedical research, such as analyzing functional connectivity data. By maintaining the structural information of positive semi-definite matrices, our proposed algorithm promises to cluster the positive semi-definite matrices in a more meaningful way, thereby facilitating deeper insights into the underlying data in various applications.

In this paper, we propose a framework to detect topics in social media based on Human Word Association. Identifying topics discussed in these media has become a critical and significant challenge. Most of the work done in this area is in English, but much has been done in the Persian language, especially microblogs written in Persian. Also, the existing works focused more on exploring frequent patterns or semantic relationships and ignored the structural methods of language. In this paper, a topic detection framework using HWA, a method for Human Word Association, is proposed. This method uses the concept of imitation of mental ability for word association. This method also calculates the Associative Gravity Force that shows how words are related. Using this parameter, a graph can be generated. The topics can be extracted by embedding this graph and using clustering methods. This approach has been applied to a Persian language dataset collected from Telegram. Several experimental studies have been performed to evaluate the proposed framework's performance. Experimental results show that this approach works better than other topic detection methods.