Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Performance Guarantees for Spectral Initialization in Rotation Averaging
  and Pose-Graph SLAM   In this work we present the first initialization methods equipped with
explicit performance guarantees adapted to the pose-graph simultaneous
localization and mapping (SLAM) and rotation averaging (RA) problems. SLAM and
rotation averaging are typically formalized as large-scale nonconvex point
estimation problems, with many bad local minima that can entrap the smooth
optimization methods typically applied to solve them; the performance of
standard SLAM and RA algorithms thus crucially depends upon the quality of the
estimates used to initialize this local search. While many initialization
methods for SLAM and RA have appeared in the literature, these are typically
obtained as purely heuristic approximations, making it difficult to determine
whether (or under what circumstances) these techniques can be reliably
deployed. In contrast, in this work we study the problem of initialization
through the lens of spectral relaxation. Specifically, we derive a simple
spectral relaxation of SLAM and RA, the form of which enables us to exploit
classical linear-algebraic techniques (eigenvector perturbation bounds) to
control the distance from our spectral estimate to both the (unknown)
ground-truth and the global minimizer of the estimation problem as a function
of measurement noise. Our results reveal the critical role that spectral
graph-theoretic properties of the measurement network play in controlling
estimation accuracy; moreover, as a by-product of our analysis we obtain new
bounds on the estimation error for the maximum likelihood estimators in SLAM
and RA, which are likely to be of independent interest. Finally, we show
experimentally that our spectral estimator is very effective in practice,
producing initializations of comparable or superior quality at lower
computational cost compared to existing state-of-the-art techniques.

30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an