Semantic segmentation is a fundamental problem in computer vision. It is considered as a pixel-wise classification problem in practice, and most segmentation models use a pixel-wise loss as their optimization criterion. However, the pixel-wise loss ignores the dependencies between pixels in an image. Several ways to exploit the relationship between pixels have been investigated, \eg, conditional random fields (CRF) and pixel affinity based methods. Nevertheless, these methods usually require additional model branches, large extra memories, or more inference time.

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We introduce resampled mutual information (ResMI), a novel measure of clustering similarity that combines insights from information theoretic and pair counting approaches to clustering and community detection. Similar to chance-corrected measures, ResMI satisfies the constant baseline property, but it has the advantages of not requiring adjustment terms and being fully interpretable in the language of information theory. Experiments on synthetic datasets demonstrate that ResMI is robust to common biases exhibited by existing measures, particularly in settings with high cluster counts and asymmetric cluster distributions. Additionally, we show that ResMI identifies meaningful community structures in two real contact tracing networks.

Semantic segmentation is a fundamental problem in computer vision. It is considered as a pixel-wise classification problem in practice, and most segmentation models use a pixel-wise loss as their optimization criterion. However, the pixel-wise loss ignores the dependencies between pixels in an image. Several ways to exploit the relationship between pixels have been investigated, \eg, conditional random fields (CRF) and pixel affinity based methods. Nevertheless, these methods usually require additional model branches, large extra memories, or more inference time.

Community detection, which involves partitioning nodes within a network, has widespread applications across computational sciences. Modularity-based algorithms identify communities by attempting to maximize the modularity function across network node partitions. Our study assesses the performance of various modularity-based algorithms in obtaining optimal partitions. Our analysis utilizes 104 networks, including both real-world instances from diverse contexts and modular graphs from two families of synthetic benchmarks. We analyze ten inexact modularity-based algorithms against the exact integer programming baseline that globally optimizes modularity. Our comparative analysis includes eight heuristics, two variants of a graph neural network algorithm, and nine variations of the Bayan approximation algorithm. Our findings reveal that the average modularity-based heuristic yields optimal partitions in only 43.9% of the 104 networks analyzed. Graph neural networks and approximate Bayan, on average, achieve optimality on 68.7% and 82.3% of the networks respectively. Additionally, our analysis of three partition similarity metrics exposes substantial dissimilarities between high-modularity sub-optimal partitions and any optimal partition of the networks. We observe that near-optimal partitions are often disproportionately dissimilar to any optimal partition. Taken together, our analysis points to a crucial limitation of the commonly used modularity-based methods: they rarely produce an optimal partition or a partition resembling an optimal partition even on networks with modular structures. If modularity is to be used for detecting communities, we recommend approximate optimization algorithms for a more methodologically sound usage of modularity within its applicability limits.

This document is in supplement to the paper titled "Multi-Robot Relative Pose Estimation and IMU Preintegration Using Passive UWB Transceivers", available at [1]. The purpose of this document is to show how IMU biases can be incorporated into the framework presented in [1], while maintaining the differential Sylvester equation form of the process model.

This work analyzes and parallelizes LearnedSort, the novel algorithm that sorts using machine learning models based on the cumulative distribution function. LearnedSort is analyzed under the lens of algorithms with predictions, and it is argued that LearnedSort is a learning-augmented SampleSort. A parallel LearnedSort algorithm is developed combining LearnedSort with the state-of-the-art SampleSort implementation, IPS4o. Benchmarks on synthetic and real-world datasets demonstrate improved parallel performance for parallel LearnedSort compared to IPS4o and other sorting algorithms.

Semantic segmentation is a fundamental problem in computer vision. It is considered as a pixel-wise classification problem in practice, and most segmentation models use a pixel-wise loss as their optimization criterion. However, the pixel-wise loss ignores the dependencies between pixels in an image. Several ways to exploit the relationship between pixels have been investigated, \eg, conditional random fields (CRF) and pixel affinity based methods. Nevertheless, these methods usually require additional model branches, large extra memories, or more inference time.

Semantic segmentation is a fundamental problem in computer vision. It is considered as a pixel-wise classification problem in practice, and most segmentation models use a pixel-wise loss as their optimization criterion. However, the pixel-wise loss ignores the dependencies between pixels in an image. Several ways to exploit the relationship between pixels have been investigated, \eg, conditional random fields (CRF) and pixel affinity based methods. Nevertheless, these methods usually require additional model branches, large extra memories, or more inference time. In this paper, we develop a region mutual information (RMI) loss to model the dependencies among pixels more simply and efficiently. In contrast to the pixel-wise loss which treats the pixels as independent samples, RMI uses one pixel and its neighbour pixels to represent this pixel. Then for each pixel in an image, we get a multi-dimensional point that encodes the relationship between pixels, and the image is cast into a multi-dimensional distribution of these high-dimensional points. The prediction and ground truth thus can achieve high order consistency through maximizing the mutual information (MI) between their multi-dimensional distributions. Moreover, as the actual value of the MI is hard to calculate, we derive a lower bound of the MI and maximize the lower bound to maximize the real value of the MI. RMI only requires a few extra computational resources in the training stage, and there is no overhead during testing. Experimental results demonstrate that RMI can achieve substantial and consistent improvements in performance on PASCAL VOC 2012 and CamVid datasets. The code is available at \url{https://github.com/ZJULearning/RMI}.