TY - GEN
T1 - Low dimensional embeddings of doubling metrics
AU - Neiman, Ofer
PY - 2014/1/1
Y1 - 2014/1/1
N2 - We study several embeddings of doubling metrics into low dimensional normed spaces, in particular into ℓ2 and ℓ∞. Doubling metrics are a robust class of metric spaces that have low intrinsic dimension, and often occur in applications. Understanding the dimension required for a concise representation of such metrics is a fundamental open problem in the area of metric embedding. Here we show that the n-vertex Laakso graph can be embedded into constant dimensional ℓ2 with the best possible distortion, which has implications for possible approaches to the above problem. Since arbitrary doubling metrics require high distortion for embedding into ℓ2 and even into ℓ1, we turn to the ℓ∞ space that enables us to obtain arbitrarily small distortion. We show embeddings of doubling metrics and their "snowflakes" into low dimensional ℓ∞ space that simplify and extend previous results.
AB - We study several embeddings of doubling metrics into low dimensional normed spaces, in particular into ℓ2 and ℓ∞. Doubling metrics are a robust class of metric spaces that have low intrinsic dimension, and often occur in applications. Understanding the dimension required for a concise representation of such metrics is a fundamental open problem in the area of metric embedding. Here we show that the n-vertex Laakso graph can be embedded into constant dimensional ℓ2 with the best possible distortion, which has implications for possible approaches to the above problem. Since arbitrary doubling metrics require high distortion for embedding into ℓ2 and even into ℓ1, we turn to the ℓ∞ space that enables us to obtain arbitrarily small distortion. We show embeddings of doubling metrics and their "snowflakes" into low dimensional ℓ∞ space that simplify and extend previous results.
UR - http://www.scopus.com/inward/record.url?scp=84903584590&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-319-08001-7_2
DO - https://doi.org/10.1007/978-3-319-08001-7_2
M3 - Conference contribution
SN - 9783319080000
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 12
EP - 23
BT - Approximation and Online Algorithms - 11th International Workshop, WAOA 2013, Revised Selected Papers
PB - Springer Verlag
T2 - 11th International Workshop on Approximation and Online Algorithms, WAOA 2013
Y2 - 5 September 2013 through 6 September 2013
ER -