A Distance Measure for Random Permutation Set: From the Layer-2 Belief Structure Perspective

• URL: http://arxiv.org/abs/2510.10596v1
• Date: Sun, 12 Oct 2025 13:29:23 GMT
• Title: A Distance Measure for Random Permutation Set: From the Layer-2 Belief Structure Perspective
• Authors: Ruolan Cheng, Yong Deng, Serafín Moral, José Ramón Trillo,
• Abstract summary: Measuring the distance between permutation mass functions is a key research topic in Random Permutation Set theory (RPST)<n>This paper conducts an in-depth analysis of distances between RPSs from two different perspectives: random finite set (RFS) and transferable belief model (TBM)<n>Adopting the layer-2 belief structure interpretation of RPS, we regard RPST as a refinement of TBM, where the order in the ordered focus set represents qualitative propensity.
• Score: 8.397744571823038
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Random permutation set (RPS) is a recently proposed framework designed to represent order-structured uncertain information. Measuring the distance between permutation mass functions is a key research topic in RPS theory (RPST). This paper conducts an in-depth analysis of distances between RPSs from two different perspectives: random finite set (RFS) and transferable belief model (TBM). Adopting the layer-2 belief structure interpretation of RPS, we regard RPST as a refinement of TBM, where the order in the ordered focus set represents qualitative propensity. Starting from the permutation, we introduce a new definition of the cumulative Jaccard index to quantify the similarity between two permutations and further propose a distance measure method for RPSs based on the cumulative Jaccard index matrix. The metric and structural properties of the proposed distance measure are investigated, including the positive definiteness analysis of the cumulative Jaccard index matrix, and a correction scheme is provided. The proposed method has a natural top-weightiness property: inconsistencies between higher-ranked elements tend to result in greater distance values. Two parameters are provided to the decision-maker to adjust the weight and truncation depth. Several numerical examples are used to compare the proposed method with the existing method. The experimental results show that the proposed method not only overcomes the shortcomings of the existing method and is compatible with the Jousselme distance, but also has higher sensitivity and flexibility.

Related papers

• MS-ISSM: Objective Quality Assessment of Point Clouds Using Multi-scale Implicit Structural Similarity [65.85858856481131]
  unstructured and irregular nature of point clouds poses a significant challenge for objective quality assessment (PCQA)<n>We propose the Multi-scale Implicit Structural Similarity Measurement (MS-ISSM)
  arXiv  Detail & Related papers  (2026-01-03T14:58:52Z)
• Edge-wise Topological Divergence Gaps: Guiding Search in Combinatorial Optimization [58.54587318370824]
  We introduce a topological feedback mechanism for the Travelling Salesman Problem (TSP) by analyzing the divergence between a tour and the minimum spanning tree (MST)
  arXiv  Detail & Related papers  (2025-12-16T20:04:25Z)
• A Non-overlap-based Conflict Measure for Random Permutation Sets [27.24948998441027]
  Measuring the conflict between two pieces of evidence represented by permutation mass functions remains an urgent research topic in order-structured uncertain information fusion.<n>We first define an inconsistency measure between permutations inspired by the rank-biased overlap(RBO) measure and further propose a non-overlap-based conflict measure method for RPSs.<n>Some numerical examples are used to demonstrate the behavior and properties of the proposed conflict measure.
  arXiv  Detail & Related papers  (2025-10-14T09:35:03Z)
• Shuffled Linear Regression via Spectral Matching [6.24954299842136]
  Shuffled linear regression seeks to estimate latent features through a linear transformation.<n>This problem extends traditional least-squares (LS) and Least Absolute Shrinkage and Selection Operator (LASSO) approaches.<n>We propose a spectral matching method that efficiently resolves permutations.
  arXiv  Detail & Related papers  (2024-09-30T16:26:40Z)
• Decomposed Global Optimization for Robust Point Matching with Low-Dimensional Branching [41.05165517541873]
  We introduce a novel global optimization method for align partially overlapping point sets.<n>Our method exhibits superior robustness to non-rigid deformations, positional noise and outliers.<n> Experiments on 2D and 3D synthetic and real-world data demonstrate that our method, compared to state-of-the-art approaches, exhibits superior robustness to outliers.
  arXiv  Detail & Related papers  (2024-05-14T13:28:57Z)
• Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstruction [40.73187749820041]
  Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. A prevalent approach in current deep learning is the set-based approach which measures the discrepancy between two surfaces by comparing two randomly sampled point-clouds from the two meshes with Chamfer pseudo-distance. We propose a novel metric for learning mesh deformation, defined by sliced Wasserstein distance on meshes represented as probability measures that generalize the set-based approach.
  arXiv  Detail & Related papers  (2023-05-27T19:10:19Z)
• Sharp Variance-Dependent Bounds in Reinforcement Learning: Best of Both Worlds in Stochastic and Deterministic Environments [48.96971760679639]
  We study variance-dependent regret bounds for Markov decision processes (MDPs) We propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm. In particular, this bound is simultaneously minimax optimal for both and deterministic MDPs.
  arXiv  Detail & Related papers  (2023-01-31T06:54:06Z)
• An approach to robust ICP initialization [77.45039118761837]
  We propose an approach to initialize the Iterative Closest Point (ICP) algorithm to match unlabelled point clouds related by rigid transformations. We derive bounds on the robustness of our approach to noise and numerical experiments confirm our theoretical findings.
  arXiv  Detail & Related papers  (2022-12-10T16:27:25Z)
• Random Forest Weighted Local Fréchet Regression with Random Objects [18.128663071848923]
  We propose a novel random forest weighted local Fr'echet regression paradigm.<n>Our first method uses these weights as the local average to solve the conditional Fr'echet mean.<n>Second method performs local linear Fr'echet regression, both significantly improving existing Fr'echet regression methods.
  arXiv  Detail & Related papers  (2022-02-10T09:10:59Z)
• Learning Bayesian Networks through Birkhoff Polytope: A Relaxation Method [0.0]
  We establish a novel framework for learning a directed acyclic graph (DAG) when data are generated from a Gaussian, linear structural equation model. For permutation matrix estimation, we propose a relaxation technique that avoids the NP-hard problem of order estimation. Our framework recovers DAGs without the need for an expensive verification of the acyclicity constraint or enumeration of possible parent sets.
  arXiv  Detail & Related papers  (2021-07-04T15:04:02Z)
• Improving Metric Dimensionality Reduction with Distributed Topology [68.8204255655161]
  DIPOLE is a dimensionality-reduction post-processing step that corrects an initial embedding by minimizing a loss functional with both a local, metric term and a global, topological term. We observe that DIPOLE outperforms popular methods like UMAP, t-SNE, and Isomap on a number of popular datasets.
  arXiv  Detail & Related papers  (2021-06-14T17:19:44Z)
• Joint Total Variation ESTATICS for Robust Multi-Parameter Mapping [0.0]
  ESTATICS performs a joint loglinear fit of multiple echo series to extract R2* and multiple extrapolated intercepts. We evaluate the proposed algorithm by predicting left-out echoes in a rich single-subject dataset.
  arXiv  Detail & Related papers  (2020-05-28T19:08:42Z)
• Augmented Parallel-Pyramid Net for Attention Guided Pose-Estimation [90.28365183660438]
  This paper proposes an augmented parallel-pyramid net with attention partial module and differentiable auto-data augmentation. We define a new pose search space where the sequences of data augmentations are formulated as a trainable and operational CNN component. Notably, our method achieves the top-1 accuracy on the challenging COCO keypoint benchmark and the state-of-the-art results on the MPII datasets.
  arXiv  Detail & Related papers  (2020-03-17T03:52:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.