Issue
EPL
Volume 87, Number 4, August 2009
Article Number 48003
Number of page(s) 5
Section Interdisciplinary Physics and Related Areas of Science and Technology
DOI http://dx.doi.org/10.1209/0295-5075/87/48003
Published online 02 September 2009
EPL, 87 (2009) 48003
DOI: 10.1209/0295-5075/87/48003

Universal behavior in large-scale aggregation of independent noisy observations

T. Murayama and P. Davis

NTT Communication Science Laboratories, NTT Corporation - Kyoto 619-0237, Japan

murayama@cslab.kecl.ntt.co.jp

received 21 May 2009; accepted in final form 31 July 2009; published August 2009
published online 2 September 2009

Abstract
Aggregation of noisy observations involves a difficult tradeoff between observation quality, which can be increased by increasing the number of observations, and aggregation quality which decreases if the number of observations is too large. We clarify this behavior for a prototypical system in which arbitrarily large numbers of observations exceeding the system capacity can be aggregated using lossy data compression. We show the existence of a scaling relation between the collective error and the system capacity, and show that large-scale lossy aggregation can outperform lossless aggregation above a critical level of observation noise. Further, we show that universal results for scaling and critical value of noise can be obtained when the system capacity increases toward infinity.

PACS
89.70.-a - Information and communication theory.
64.60.-i - General studies of phase transitions.
75.10.Nr - Spin-glass and other random models.

© EPLA 2009