5,914 research outputs found
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
Bolt: Accelerated Data Mining with Fast Vector Compression
Vectors of data are at the heart of machine learning and data mining.
Recently, vector quantization methods have shown great promise in reducing both
the time and space costs of operating on vectors. We introduce a vector
quantization algorithm that can compress vectors over 12x faster than existing
techniques while also accelerating approximate vector operations such as
distance and dot product computations by up to 10x. Because it can encode over
2GB of vectors per second, it makes vector quantization cheap enough to employ
in many more circumstances. For example, using our technique to compute
approximate dot products in a nested loop can multiply matrices faster than a
state-of-the-art BLAS implementation, even when our algorithm must first
compress the matrices.
In addition to showing the above speedups, we demonstrate that our approach
can accelerate nearest neighbor search and maximum inner product search by over
100x compared to floating point operations and up to 10x compared to other
vector quantization methods. Our approximate Euclidean distance and dot product
computations are not only faster than those of related algorithms with slower
encodings, but also faster than Hamming distance computations, which have
direct hardware support on the tested platforms. We also assess the errors of
our algorithm's approximate distances and dot products, and find that it is
competitive with existing, slower vector quantization algorithms.Comment: Research track paper at KDD 201
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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