6,747 research outputs found
Analysis of approximate nearest neighbor searching with clustered point sets
We present an empirical analysis of data structures for approximate nearest
neighbor searching. We compare the well-known optimized kd-tree splitting
method against two alternative splitting methods. The first, called the
sliding-midpoint method, which attempts to balance the goals of producing
subdivision cells of bounded aspect ratio, while not producing any empty cells.
The second, called the minimum-ambiguity method is a query-based approach. In
addition to the data points, it is also given a training set of query points
for preprocessing. It employs a simple greedy algorithm to select the splitting
plane that minimizes the average amount of ambiguity in the choice of the
nearest neighbor for the training points. We provide an empirical analysis
comparing these two methods against the optimized kd-tree construction for a
number of synthetically generated data and query sets. We demonstrate that for
clustered data and query sets, these algorithms can provide significant
improvements over the standard kd-tree construction for approximate nearest
neighbor searching.Comment: 20 pages, 8 figures. Presented at ALENEX '99, Baltimore, MD, Jan
15-16, 199
High-dimensional approximate nearest neighbor: k-d Generalized Randomized Forests
We propose a new data-structure, the generalized randomized kd forest, or
kgeraf, for approximate nearest neighbor searching in high dimensions. In
particular, we introduce new randomization techniques to specify a set of
independently constructed trees where search is performed simultaneously, hence
increasing accuracy. We omit backtracking, and we optimize distance
computations, thus accelerating queries. We release public domain software
geraf and we compare it to existing implementations of state-of-the-art methods
including BBD-trees, Locality Sensitive Hashing, randomized kd forests, and
product quantization. Experimental results indicate that our method would be
the method of choice in dimensions around 1,000, and probably up to 10,000, and
pointsets of cardinality up to a few hundred thousands or even one million;
this range of inputs is encountered in many critical applications today. For
instance, we handle a real dataset of images represented in 960
dimensions with a query time of less than sec on average and 90\% responses
being true nearest neighbors
Approximate Nearest Neighbor Search for Low Dimensional Queries
We study the Approximate Nearest Neighbor problem for metric spaces where the
query points are constrained to lie on a subspace of low doubling dimension,
while the data is high-dimensional. We show that this problem can be solved
efficiently despite the high dimensionality of the data.Comment: 25 page
HD-Index: Pushing the Scalability-Accuracy Boundary for Approximate kNN Search in High-Dimensional Spaces
Nearest neighbor searching of large databases in high-dimensional spaces is
inherently difficult due to the curse of dimensionality. A flavor of
approximation is, therefore, necessary to practically solve the problem of
nearest neighbor search. In this paper, we propose a novel yet simple indexing
scheme, HD-Index, to solve the problem of approximate k-nearest neighbor
queries in massive high-dimensional databases. HD-Index consists of a set of
novel hierarchical structures called RDB-trees built on Hilbert keys of
database objects. The leaves of the RDB-trees store distances of database
objects to reference objects, thereby allowing efficient pruning using distance
filters. In addition to triangular inequality, we also use Ptolemaic inequality
to produce better lower bounds. Experiments on massive (up to billion scale)
high-dimensional (up to 1000+) datasets show that HD-Index is effective,
efficient, and scalable.Comment: PVLDB 11(8):906-919, 201
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