Computing distances on Riemannian manifolds is a challenging problem with numerous applications, from physics, through statistics, to machine learning. In this paper, we introduce the metric-constrained Eikonal solver to obtain continuous, differentiable representations of distance functions (geodesics) on manifolds. The differentiable nature of these representations allows for the direct computation of globally length-minimising paths on the manifold. We showcase the use of metric-constrained Eikonal solvers for a range of manifolds and demonstrate the applications. First, we demonstrate that metric-constrained Eikonal solvers can be used to obtain the Fréchet mean on a manifold, employing the definition of a Gaussian mixture model, which has an analytical solution to verify the numerical results. Second, we demonstrate how the obtained distance function can be used to conduct unsupervised clustering on the manifold - a task for which existing approaches are computationally prohibitive. This work opens opportunities for distance computations on manifolds.

Solving multimodal optimization problems (MMOP) requires finding all optimal solutions, which is challenging in limited function evaluations. Although existing works strike the balance of exploration and exploitation through hand-crafted adaptive strategies, they require certain expert knowledge, hence inflexible to deal with MMOP with different properties. In this paper, we propose RLEMMO, a Meta-Black-Box Optimization framework, which maintains a population of solutions and incorporates a reinforcement learning agent for flexibly adjusting individual-level searching strategies to match the up-to-date optimization status, hence boosting the search performance on MMOP. Concretely, we encode landscape properties and evolution path information into each individual and then leverage attention networks to advance population information sharing. With a novel reward mechanism that encourages both quality and diversity, RLEMMO can be effectively trained using a policy gradient algorithm. The experimental results on the CEC2013 MMOP benchmark underscore the competitive optimization performance of RLEMMO against several strong baselines.

There is a limitation in the literature of data-driven analyses for the ex-post evaluation of community risk and resilience, particularly using features related to the performance of coupled human-infrastructure systems. To address this gap, in this study we created a machine learning-based method for the ex-post assessment of community risk and resilience and their interplay based on features related to the coupled human-infrastructure systems performance. Utilizing feature groups related to population protective actions, infrastructure/building performance features, and recovery features, we examined the risk and resilience performance of communities in the context of the 2017 Hurricane Harvey in Harris County, Texas. These features related to the coupled human-infrastructure systems performance were processed using the K-means clustering method to classify census block groups into four distinct clusters then, based on feature analysis, these clusters were labeled and designated into four quadrants of risk-resilience archetypes. Finally, we analyzed the disparities in risk-resilience status of spatial areas across different clusters as well as different income groups. The findings unveil the risk-resilience status of spatial areas shaped by their coupled human-infrastructure systems performance and their interactions. The results also inform about features that contribute to high resilience in high-risk areas. For example, the results indicate that in high-risk areas, evacuation rates contributed to a greater resilience, while in low-risk areas, preparedness contributed to greater resilience.

In this paper, we advocate a novel measure for the purpose of checking the quality of a cluster partition for a sample into several distinct classes, and thus, determine the unknown value for the true number of clusters prevailing the provided set of data. Our objective leads us to the development of an approach through applying the multinomial distribution to the distances of data members, clustered in a group, from their respective cluster representatives. This procedure is carried out independently for each of the clusters, and the concerned statistics are combined together to design our targeted measure. Individual clusters separately possess the category-wise probabilities which correspond to different positions of its members in the cluster with respect to a typical member, in the form of cluster-centroid, medoid or mode, referred to as the corresponding cluster representative. Our method is robust in the sense that it is distribution-free, since this is devised irrespective of the parent distribution of the underlying sample. It fulfills one of the rare coveted qualities, present in the existing cluster accuracy measures, of having the capability to investigate whether the assigned sample owns any inherent clusters other than a single group of all members or not. Our measure's simple concept, easy algorithm, fast runtime, good performance, and wide usefulness, demonstrated through extensive simulation and diverse case-studies, make it appealing.

Indoor positioning systems based on Ultra-wideband (UWB) technology are gaining recognition for their ability to provide cm-level localization accuracy. However, these systems often encounter challenges caused by dense multi-path fading, leading to positioning errors. To address this issue, in this letter, we propose a novel methodology for unsupervised anchor node selection using deep embedded clustering (DEC). Our approach uses an Auto Encoder (AE) before clustering, thereby better separating UWB features into separable clusters of UWB input signals. We furthermore investigate how to rank these clusters based on their cluster quality, allowing us to remove untrustworthy signals. Experimental results show the efficiency of our proposed method, demonstrating a significant 23.1% reduction in mean absolute error (MAE) compared to without anchor exclusion. Especially in the dense multi-path area, our algorithm achieves even more significant enhancements, reducing the MAE by 26.6% and the 95th percentile error by 49.3% compared to without anchor exclusion.

The von Mises-Fisher distribution as an exponential family can be expressed in terms of either its natural or its mean parameters. Unfortunately, however, the normalization function for the distribution in terms of its mean parameters is not available in closed form, limiting the practicality of the mean parametrization and complicating maximum-likelihood estimation more generally. We derive a second-order ordinary differential equation, the solution to which yields the mean-parameter normalizer along with its first two derivatives, as well as the variance function of the family. We also provide closed-form approximations to the solution of the differential equation. This allows rapid evaluation of both densities and natural parameters in terms of mean parameters. We show applications to topic modeling with mixtures of von Mises-Fisher distributions using Bregman Clustering.

Single-cell RNA sequencing (scRNA-seq) is essential for unraveling cellular heterogeneity and diversity, offering invaluable insights for bioinformatics advancements. Despite its potential, traditional clustering methods in scRNA-seq data analysis often neglect the structural information embedded in gene expression profiles, crucial for understanding cellular correlations and dependencies. Existing strategies, including graph neural networks, face challenges in handling the inefficiency due to scRNA-seq data's intrinsic high-dimension and high-sparsity. Addressing these limitations, we introduce scCDCG (single-cell RNA-seq Clustering via Deep Cut-informed Graph), a novel framework designed for efficient and accurate clustering of scRNA-seq data that simultaneously utilizes intercellular high-order structural information. scCDCG comprises three main components: (i) A graph embedding module utilizing deep cut-informed techniques, which effectively captures intercellular high-order structural information, overcoming the over-smoothing and inefficiency issues prevalent in prior graph neural network methods. (ii) A self-supervised learning module guided by optimal transport, tailored to accommodate the unique complexities of scRNA-seq data, specifically its high-dimension and high-sparsity. (iii) An autoencoder-based feature learning module that simplifies model complexity through effective dimension reduction and feature extraction. Our extensive experiments on 6 datasets demonstrate scCDCG's superior performance and efficiency compared to 7 established models, underscoring scCDCG's potential as a transformative tool in scRNA-seq data analysis. Our code is available at: https://github.com/XPgogogo/scCDCG.

Clustering in dynamic environments is of increasing importance, with broad applications ranging from real-time data analysis and online unsupervised learning to dynamic facility location problems. While meta-heuristics have shown promising effectiveness in static clustering tasks, their application for tracking optimal clustering solutions or robust clustering over time in dynamic environments remains largely underexplored. This is partly due to a lack of dynamic datasets with diverse, controllable, and realistic dynamic characteristics, hindering systematic performance evaluations of clustering algorithms in various dynamic scenarios. This deficiency leads to a gap in our understanding and capability to effectively design algorithms for clustering in dynamic environments. To bridge this gap, this paper introduces the Dynamic Dataset Generator (DDG). DDG features multiple dynamic Gaussian components integrated with a range of heterogeneous, local, and global changes. These changes vary in spatial and temporal severity, patterns, and domain of influence, providing a comprehensive tool for simulating a wide range of dynamic scenarios.

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the topological structure of the data. In this paper, we explore several aspects that affect the quality of a vertex embedding of graph-structured data. To this effect, we first present a family of flexible distance functions that faithfully capture the topological distance between different vertices. Secondly, we analyze vertex embeddings as resulting from a fitted transformation of the distance matrix rather than as a direct result of optimization. Finally, we evaluate the effectiveness of our proposed embedding constructions by performing community detection on a host of benchmark datasets. The reported results are competitive with classical algorithms that operate on the entire graph while benefitting from a substantially reduced computational complexity due to the reduced dimensionality of the representations.

Epidemic outbreaks can cause critical health concerns and severe global economic crises. For countries or regions with new infectious disease outbreaks, it is essential to generate preventive strategies by learning lessons from others with similar risk profiles. A Strategy Transfer and Decision Support Approach (STDSA) is proposed based on the profile similarity evaluation. There are four steps in this method: (1) The similarity evaluation indicators are determined from three dimensions, i.e., the Basis of National Epidemic Prevention & Control, Social Resilience, and Infection Situation. (2) The data related to the indicators are collected and preprocessed. (3) The first round of screening on the preprocessed dataset is conducted through an improved collaborative filtering algorithm to calculate the preliminary similarity result from the perspective of the infection situation. (4) Finally, the K-Means model is used for the second round of screening to obtain the final similarity values. The approach will be applied to decision-making support in the context of COVID-19. Our results demonstrate that the recommendations generated by the STDSA model are more accurate and aligned better with the actual situation than those produced by pure K-means models. This study will provide new insights into preventing and controlling epidemics in regions that lack experience.