Topic
Perfect map
About: Perfect map is a research topic. Over the lifetime, 64 publications have been published within this topic receiving 1858 citations.
Papers published on a yearly basis
Papers
TL;DR: This paper proves the so-called "Meek Conjecture", which shows that if a DAG H is an independence map of another DAG G, then there exists a finite sequence of edge additions and covered edge reversals in G such that H remains anindependence map of G and after all modifications G =H.
Abstract: In this paper we prove the so-called "Meek Conjecture". In particular, we show that if a DAG H is an independence map of another DAG G, then there exists a finite sequence of edge additions and covered edge reversals in G such that (1) after each edge modification H remains an independence map of G and (2) after all modifications G =H. As shown by Meek (1997), this result has an important consequence for Bayesian approaches to learning Bayesian networks from data: in the limit of large sample size, there exists a two-phase greedy search algorithm that---when applied to a particular sparsely-connected search space---provably identifies a perfect map of the generative distribution if that perfect map is a DAG. We provide a new implementation of the search space, using equivalence classes as states, for which all operators used in the greedy search can be scored efficiently using local functions of the nodes in the domain. Finally, using both synthetic and real-world datasets, we demonstrate that the two-phase greedy approach leads to good solutions when learning with finite sample sizes.
1,848 citations
26 Mar 1999
TL;DR: This paper proves that a solution to the SLAM problem is indeed possible and shows that it is possible for an autonomous vehicle to start in anunknown location in an unknown environment and, using relative observations only, incrementally build a perfect map of the world and simultaneously to compute a bounded estimate of vehicle location.
Abstract: The simultaneous localisation and map building (SLAM) problem asks if it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and then to incrementally build a map of this environment while simultaneously using this map to compute absolute vehicle location. Starting from the estimation-theoretic foundations of this problem developed in [5, 4, 2], this paper proves that a solution to the SLAM problem is indeed possible. The underlying structure of the SLAM problem is first elucidated. A proof that the estimated map converges monotonically to a relative map with zero uncertainty is then developed. It is then shown that the absolute accuracy of the map and the vehicle location reach a lower bound defined only by the initial vehicle uncertainty. Together, these results show that it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and, using relative observations only, incrementally build a perfect map of the world and simultaneously to compute a bounded estimate of vehicle location.
120 citations
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TL;DR: In this article, the existence question for perfect maps is settled by giving constructions for all parameter sets subject to certain simple necessary conditions, which are expressed as bounds on the linear complexities of the periodic sequences formed from the rows and columns of perfect maps.
Abstract: Given positive integers r, s, u, and /spl upsi/, an (r, s; u, /spl upsi/) perfect map (PM) is defined to be a periodic r/spl times/s binary array in which every u/spl times//spl upsi/ binary array appears exactly once as a periodic subarray. Perfect maps are the natural extension of the de Bruijn sequences to two dimensions. In the paper the existence question for perfect maps is settled by giving constructions for perfect maps for all parameter sets subject to certain simple necessary conditions. Extensive use is made of previously known constructions by finding new conditions which guarantee their repeated application. These conditions are expressed as bounds on the linear complexities of the periodic sequences formed from the rows and columns of perfect maps. >
66 citations
TL;DR: It is shown how those components of map accuracy that are most pertinent to a particular user may be optimized.
Abstract: The utility of a map of terrain classes may be measured by ditTerent components of accuracy, estimated from an error matrix. A systematic classification of the questions that such a map is required to answer is proposed. In each case the utility of the map is best measured by a ditTerent subset of the components of accuracy. It follows that no one map will be optimal from the point of view of every user (given that the perfect map cannot be made). It is shown how those components of map accuracy that are most pertinent to a particular user may be optimized.
53 citations
Proceedings Article•
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TL;DR: This paper makes extensive use of previously known constructions by finding new conditions guaranteeing their repeated application on the linear complexities of the periodic sequences formed from the rows and columns of Perfect Maps.
Abstract: Given positive integers r, s, u and v, an (r, s; u, v) Perfect Map (PM) is defined to be a periodic r x s binary array in which every u x v binary array appears exactly once as a subarray. Perfect Maps are the natural extention of the de Bruijin sequences to two dimensions. In this paper we settle the existence question for Perfect Maps by proving the following result. Let r, s, u, v be positive integers. Then there exists an (r, s; u, v) PM if and only if the following three conditions hold: i) rs = 2/sup uv/, ii) r > u or r = u = 1, iii) s > v or s = u = 1. We make extensive use of previously known constructions by finding new conditions guaranteeing their repeated application. These conditions are expressed as bounds on the linear complexities of the periodic sequences formed from the rows and columns of Perfect Maps.
48 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2019 | 2 |
| 2018 | 1 |
| 2016 | 1 |
| 2015 | 1 |
| 2013 | 2 |