Large language models have demonstrated impressive performance on commonsense tasks; however, these tasks are often posed as multiple-choice questions, allowing models to exploit systematic biases. Commonsense is also inherently probabilistic with multiple correct answers. The purpose of "boiling water" could be making tea and cooking, but it also could be killing germs. Existing tasks do not capture the probabilistic nature of common sense. To this end, we present commonsense frame completion (CFC), a new generative task that evaluates common sense via multiple open-ended generations. We also propose a method of probabilistic evaluation that strongly correlates with human judgments. Humans drastically outperform strong language model baselines on our dataset, indicating this approach is both a challenging and useful evaluation of machine common sense.

Community and core-periphery are two widely studied graph structures, with their coexistence observed in real-world graphs (Rombach, Porter, Fowler \& Mucha [SIAM J. App. Math. 2014, SIAM Review 2017]). However, the nature of this coexistence is not well understood and has been pointed out as an open problem (Yanchenko \& Sengupta [Statistics Surveys, 2023]). Especially, the impact of inferring the core-periphery structure of a graph on understanding its community structure is not well utilized. In this direction, we introduce a novel quantification for graphs with ground truth communities, where each community has a densely connected part (the core), and the rest is more sparse (the periphery), with inter-community edges more frequent between the peripheries. Built on this structure, we propose a new algorithmic concept that we call relative centrality to detect the cores. We observe that core-detection algorithms based on popular centrality measures such as PageRank and degree centrality can show some bias in their outcome by selecting very few vertices from some cores. We show that relative centrality solves this bias issue and provide theoretical and simulation support, as well as experiments on real-world graphs. Core detection is known to have important applications with respect to core-periphery structures. In our model, we show a new application: relative-centrality-based algorithms can select a subset of the vertices such that it contains sufficient vertices from all communities, and points in this subset are better separable into their respective communities. We apply the methods to 11 biological datasets, with our methods resulting in a more balanced selection of vertices from all communities such that clustering algorithms have better performance on this set.

Data Mining is a promising field and is applied in multiple domains for its predictive capabilities. Data in the real world cannot be readily used for data mining as it suffers from the problems of multidimensionality, unbalance and missing values. It is difficult to use its predictive capabilities by novice users. It is difficult for a beginner to find the relevant set of attributes from a large pool of data available. The paper presents a Robust Prediction Model that finds a relevant set of attributes; resolves the problems of unbalanced and multidimensional real-life datasets and helps in finding patterns for informed decision making. Model is tested upon five different datasets in the domain of Health Sector, Education, Business and Fraud Detection. The results showcase the robust behaviour of the model and its applicability in various domains.

This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper proves that, under some mild condition on the cluster-structure, the clusters of the final graph $G_T$ of $n_T$ vertices at time $T$ can be well approximated by a dynamic variant of the spectral clustering algorithm. The algorithm runs in amortised update time $O(1)$ and query time $o(n_T)$. Experimental studies on both synthetic and real-world datasets further confirm the practicality of our designed algorithm.

Financial organisations such as brokers face a significant challenge in servicing the investment needs of thousands of their traders worldwide. This task is further compounded since individual traders will have their own risk appetite and investment goals. Traders may look to capture short-term trends in the market which last only seconds to minutes, or they may have longer-term views which last several days to months. To reduce the complexity of this task, client trades can be clustered. By examining such clusters, we would likely observe many traders following common patterns of investment, but how do these patterns vary through time? Knowledge regarding the temporal distributions of such clusters may help financial institutions manage the overall portfolio of risk that accumulates from underlying trader positions. This study contributes to the field by demonstrating that the distribution of clusters derived from the real-world trades of 20k Foreign Exchange (FX) traders (from 2015 to 2017) is described in accordance with Ewens' Sampling Distribution. Further, we show that the Aggregating Algorithm (AA), an on-line prediction with expert advice algorithm, can be applied to the aforementioned real-world data in order to improve the returns of portfolios of trader risk. However we found that the AA 'struggles' when presented with too many trader ``experts'', especially when there are many trades with similar overall patterns. To help overcome this challenge, we have applied and compared the use of Statistically Validated Networks (SVN) with a hierarchical clustering approach on a subset of the data, demonstrating that both approaches can be used to significantly improve results of the AA in terms of profitability and smoothness of returns.

Effective resistance is a distance between vertices of a graph that is both theoretically interesting and useful in applications. We study a variant of effective resistance called the biharmonic distance. While the effective resistance measures how well-connected two vertices are, we prove several theoretical results supporting the idea that the biharmonic distance measures how important an edge is to the global topology of the graph. Our theoretical results connect the biharmonic distance to well-known measures of connectivity of a graph like its total resistance and sparsity. Based on these results, we introduce two clustering algorithms using the biharmonic distance. Finally, we introduce a further generalization of the biharmonic distance that we call the $k$-harmonic distance. We empirically study the utility of biharmonic and $k$-harmonic distance for edge centrality and graph clustering.

Knowledge Graph Embedding (KGE) techniques are crucial in learning compact representations of entities and relations within a knowledge graph, facilitating efficient reasoning and knowledge discovery. While existing methods typically focus either on training KGE models solely based on graph structure or fine-tuning pre-trained language models with classification data in KG, KG-FIT leverages LLM-guided refinement to construct a semantically coherent hierarchical structure of entity clusters. By incorporating this hierarchical knowledge along with textual information during the fine-tuning process, KG-FIT effectively captures both global semantics from the LLM and local semantics from the KG. Extensive experiments on the benchmark datasets FB15K-237, YAGO3-10, and PrimeKG demonstrate the superiority of KG-FIT over state-of-the-art pre-trained language model-based methods, achieving improvements of 14.4%, 13.5%, and 11.9% in the Hits@10 metric for the link prediction task, respectively. Furthermore, KG-FIT yields substantial performance gains of 12.6%, 6.7%, and 17.7% compared to the structure-based base models upon which it is built. These results highlight the effectiveness of KG-FIT in incorporating open-world knowledge from LLMs to significantly enhance the expressiveness and informativeness of KG embeddings.

Self-supervised learning (SSL) has attracted great interest in recent years across almost every machine learning sub-field, due to the promise of being able to harness large quantities of unlabelled data and obtaining generic feature embeddings useful for a variety of downstream tasks (Balestriero et al., 2023). This has, for example, led to the development of impressive large language models (Brown et al., 2020) and computer vision systems trained on 1 billion images (Goyal et al., 2021). However, while the embeddings from an SSL-trained encoder can perform well on downstream tasks after fine-tuning the network, there has been less investigation into the utility of the embeddings without fine-tuning. Prior work (Vaze et al., 2022; Zhou and Zhang, 2022) suggests SSL feature encoders generate embeddings suitable for clustering, but nonetheless adjust the feature encoders through fine-tuning. Yet, widespread interest in the application of large pretrained models on custom datasets, combined with prohibitive cost of compute, make this question important and increasingly urgent. We find that to date there has been no investigation into whether SSL-trained feature encoders can serve as a foundation for clustering, yielding informative groupings of embeddings on real-world datasets that were totally unseen to the encoder during its training. Vaze et al. (2023) showed that features from SSL encoders are typically biased toward shape features and not color, texture, or count when clustered using K-Means. However, this was conducted using a synthetic dataset, where very specific object attributes could be disentangled.

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description of the global structure of the point cloud. However, common machine learning applications like classification require point-level information and features to be available. In this paper, we bridge this gap and propose a novel method to extract node-level topological features from complex point clouds using discrete variants of concepts from algebraic topology and differential geometry. We verify the effectiveness of these topological point features (TOPF) on both synthetic and real-world data and study their robustness under noise.

Deep image clustering methods are typically evaluated on small-scale balanced classification datasets while feature-based $k$-means has been applied on proprietary billion-scale datasets. In this work, we explore the performance of feature-based deep clustering approaches on large-scale benchmarks whilst disentangling the impact of the following data-related factors: i) class imbalance, ii) class granularity, iii) easy-to-recognize classes, and iv) the ability to capture multiple classes. Consequently, we develop multiple new benchmarks based on ImageNet21K. Our experimental analysis reveals that feature-based $k$-means is often unfairly evaluated on balanced datasets. However, deep clustering methods outperform $k$-means across most large-scale benchmarks. Interestingly, $k$-means underperforms on easy-to-classify benchmarks by large margins. The performance gap, however, diminishes on the highest data regimes such as ImageNet21K. Finally, we find that non-primary cluster predictions capture meaningful classes (i.e. coarser classes).