Metric (mathematics)

About: Metric (mathematics) is a research topic. Over the lifetime, 42617 publications have been published within this topic receiving 836571 citations. The topic is also known as: distance function & metric.

A peer-to-peer information system based on the XOR metric

Abstract: We describe a peer-to-peer distributed hash table with provable consistency and performance in a fault-prone environment. Our system routes queries and locates nodes using a novel XOR-based metric topology that simplifies the algorithm and facilitates our proof. The topology has the property that every message exchanged conveys or reinforces useful contact information. The system exploits this information to send parallel, asynchronous query messages that tolerate node failures without imposing timeout delays on users.

RISE: Randomized Input Sampling for Explanation of Black-box Models

Abstract: Deep neural networks are being used increasingly to automate data analysis and decision making, yet their decision-making process is largely unclear and is difficult to explain to the end users. In this paper, we address the problem of Explainable AI for deep neural networks that take images as input and output a class probability. We propose an approach called RISE that generates an importance map indicating how salient each pixel is for the model's prediction. In contrast to white-box approaches that estimate pixel importance using gradients or other internal network state, RISE works on black-box models. It estimates importance empirically by probing the model with randomly masked versions of the input image and obtaining the corresponding outputs. We compare our approach to state-of-the-art importance extraction methods using both an automatic deletion/insertion metric and a pointing metric based on human-annotated object segments. Extensive experiments on several benchmark datasets show that our approach matches or exceeds the performance of other methods, including white-box approaches. Project page: this http URL

Evaluating the scalability of distributed systems

Abstract: Many distributed systems must be scalable, meaning that they must be economically deployable in a wide range of sizes and configurations. This paper presents a scalability metric based on cost-effectiveness, where the effectiveness is a function of the system's throughput and its quality of service. It is part of a framework which also includes a sealing strategy for introducing changes as a function of a scale factor, and an automated virtual design optimization at each scale factor. This is an adaptation of concepts for scalability measures in parallel computing. Scalability is measured by the range of scale factors that give a satisfactory value of the metric, and good scalability is a joint property of the initial design and the scaling strategy. The results give insight into the scaling capacity of the designs, and into how to improve the design. A rapid simple bound on the metric is also described. The metric is demonstrated in this work by applying it to some well-known idealized systems, and to real prototypes of communications software.

Merging Occupancy Grid Maps From Multiple Robots

Abstract: Mapping can potentially be speeded up in a significant way by using multiple robots exploring different parts of the environment. But the core question of multirobot mapping is how to integrate the data of the different robots into a single global map. A significant amount of research exists in the area of multirobot mapping that deals with techniques to estimate the relative robots poses at the start or during the mapping process. With map merging, the robots in contrast individually build local maps without any knowledge about their relative positions. The goal is then to identify regions of overlap at which the local maps can be joined together. A concrete approach to this idea is presented in form of a special similarity metric and a stochastic search algorithm. Given two maps m and m', the search algorithm transforms m' by rotations and translations to find a maximum overlap between m and m'. In doing so, the heuristic similarity metric guides the search algorithm toward optimal solutions. Results from experiments with up to six robots are presented based on simulated as well as real-world map data

Mahalanobis Distance Learning for Person Re-Identification

Abstract: Recently, Mahalanobis metric learning has gained a considerable interest for single-shot person re-identification. The main idea is to build on an existing image representation and to learn a metric that reflects the visual camera-to-camera transitions, allowing for a more powerful classification. The goal of this chapter is twofold. We first review the main ideas of Mahalanobis metric learning in general and then give a detailed study on different approaches for the task of single-shot person re-identification, also comparing to the state of the art. In particular, for our experiments, we used Linear Discriminant Metric Learning (LDML), Information Theoretic Metric Learning (ITML), Large Margin Nearest Neighbor (LMNN), Large Margin Nearest Neighbor with Rejection (LMNN-R), Efficient Impostor-based Metric Learning (EIML), and KISSME. For our evaluations we used four different publicly available datasets (i.e., VIPeR, ETHZ, PRID 2011, and CAVIAR4REID). Additionally, we generated the new, more realistic PRID 450S dataset, where we also provide detailed segmentations. For the latter one, we also evaluated the influence of using well-segmented foreground and background regions. Finally, the corresponding results are presented and discussed.