TY - GEN

T1 - Reference point hyperplane trees

AU - Connor, Richard

N1 - The final publication is available at Springer via http://https:doi.org/10.1007/978-3-319-46759-7

PY - 2016/10/24

Y1 - 2016/10/24

N2 - We make the simple observation that, the deeper a data item is within the tree, the higher the probability of that item being excluded from a search. Assuming a fixed and independent probability p of any subtree being excluded at query time, the probability of an individual data item being accessed is (1-p)d for a node at depth d. In a balanced binary tree half of the data will be at the maximum depth of the tree so this effect should be significant and observable. We test this hypothesis with two experiments on partition trees. First, we force a balance by adjusting the partition/exclusion criteria, and compare this with unbalanced trees where the mean data depth is greater. Second, we compare a generic hyperplane tree with a monotone hyperplane tree, where also the mean depth is greater. In both cases the tree with the greater mean data depth performs better in high-dimensional spaces. We then experiment with increasing the mean depth of nodes by using a small, fixed set of reference points to make exclusion decisions over the whole tree, so that almost all of the data resides at the maximum depth. Again this can be seen to reduce the overall cost of indexing. Furthermore, we observe that having already calculated reference point distances for all data, a final filtering can be applied if the distance table is retained. This reduces further the number of distance calculations required, whilst retaining scalability. The final structure can in fact be viewed as a hybrid between a generic hyperplane tree and a LAESA search structure.

AB - We make the simple observation that, the deeper a data item is within the tree, the higher the probability of that item being excluded from a search. Assuming a fixed and independent probability p of any subtree being excluded at query time, the probability of an individual data item being accessed is (1-p)d for a node at depth d. In a balanced binary tree half of the data will be at the maximum depth of the tree so this effect should be significant and observable. We test this hypothesis with two experiments on partition trees. First, we force a balance by adjusting the partition/exclusion criteria, and compare this with unbalanced trees where the mean data depth is greater. Second, we compare a generic hyperplane tree with a monotone hyperplane tree, where also the mean depth is greater. In both cases the tree with the greater mean data depth performs better in high-dimensional spaces. We then experiment with increasing the mean depth of nodes by using a small, fixed set of reference points to make exclusion decisions over the whole tree, so that almost all of the data resides at the maximum depth. Again this can be seen to reduce the overall cost of indexing. Furthermore, we observe that having already calculated reference point distances for all data, a final filtering can be applied if the distance table is retained. This reduces further the number of distance calculations required, whilst retaining scalability. The final structure can in fact be viewed as a hybrid between a generic hyperplane tree and a LAESA search structure.

KW - metric search

KW - partition tree

KW - reference point

KW - monotonic hyperplane tree

KW - LAESA

UR - http://www.sisap.org/2016/

UR - http://www.springer.com/gb/computer-science/lncs

UR - http://www.springer.com/

U2 - 10.1007/978-3-319-46759-7

DO - 10.1007/978-3-319-46759-7

M3 - Conference contribution book

SN - 978-3-319-46758-0

VL - 9939

T3 - Lecture Notes in Computing Science

SP - 65

EP - 78

BT - 9th International Conference on Similarity Search and Applications

A2 - Amsaleg, Laurent

A2 - Houle, Michael E.

A2 - Shubert, Erich

PB - Springer-Verlag

CY - New York

T2 - SISAP 2016 - 9th International Conference on Similarity Searches and Applications

Y2 - 24 October 2016 through 26 October 2016

ER -