22,341 research outputs found
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
Ptolemaic Indexing
This paper discusses a new family of bounds for use in similarity search,
related to those used in metric indexing, but based on Ptolemy's inequality,
rather than the metric axioms. Ptolemy's inequality holds for the well-known
Euclidean distance, but is also shown here to hold for quadratic form metrics
in general, with Mahalanobis distance as an important special case. The
inequality is examined empirically on both synthetic and real-world data sets
and is also found to hold approximately, with a very low degree of error, for
important distances such as the angular pseudometric and several Lp norms.
Indexing experiments demonstrate a highly increased filtering power compared to
existing, triangular methods. It is also shown that combining the Ptolemaic and
triangular filtering can lead to better results than using either approach on
its own
To Index or Not to Index: Optimizing Exact Maximum Inner Product Search
Exact Maximum Inner Product Search (MIPS) is an important task that is widely
pertinent to recommender systems and high-dimensional similarity search. The
brute-force approach to solving exact MIPS is computationally expensive, thus
spurring recent development of novel indexes and pruning techniques for this
task. In this paper, we show that a hardware-efficient brute-force approach,
blocked matrix multiply (BMM), can outperform the state-of-the-art MIPS solvers
by over an order of magnitude, for some -- but not all -- inputs.
In this paper, we also present a novel MIPS solution, MAXIMUS, that takes
advantage of hardware efficiency and pruning of the search space. Like BMM,
MAXIMUS is faster than other solvers by up to an order of magnitude, but again
only for some inputs. Since no single solution offers the best runtime
performance for all inputs, we introduce a new data-dependent optimizer,
OPTIMUS, that selects online with minimal overhead the best MIPS solver for a
given input. Together, OPTIMUS and MAXIMUS outperform state-of-the-art MIPS
solvers by 3.2 on average, and up to 10.9, on widely studied
MIPS datasets.Comment: 12 pages, 8 figures, 2 table
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
DROP: Dimensionality Reduction Optimization for Time Series
Dimensionality reduction is a critical step in scaling machine learning
pipelines. Principal component analysis (PCA) is a standard tool for
dimensionality reduction, but performing PCA over a full dataset can be
prohibitively expensive. As a result, theoretical work has studied the
effectiveness of iterative, stochastic PCA methods that operate over data
samples. However, termination conditions for stochastic PCA either execute for
a predetermined number of iterations, or until convergence of the solution,
frequently sampling too many or too few datapoints for end-to-end runtime
improvements. We show how accounting for downstream analytics operations during
DR via PCA allows stochastic methods to efficiently terminate after operating
over small (e.g., 1%) subsamples of input data, reducing whole workload
runtime. Leveraging this, we propose DROP, a DR optimizer that enables speedups
of up to 5x over Singular-Value-Decomposition-based PCA techniques, and exceeds
conventional approaches like FFT and PAA by up to 16x in end-to-end workloads
Perspects in astrophysical databases
Astrophysics has become a domain extremely rich of scientific data. Data
mining tools are needed for information extraction from such large datasets.
This asks for an approach to data management emphasizing the efficiency and
simplicity of data access; efficiency is obtained using multidimensional access
methods and simplicity is achieved by properly handling metadata. Moreover,
clustering and classification techniques on large datasets pose additional
requirements in terms of computation and memory scalability and
interpretability of results. In this study we review some possible solutions
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