12 research outputs found
Efficient Nearest Neighbors Search for Large-Scale Landmark Recognition
The problem of landmark recognition has achieved excellent results in
small-scale datasets. When dealing with large-scale retrieval, issues that were
irrelevant with small amount of data, quickly become fundamental for an
efficient retrieval phase. In particular, computational time needs to be kept
as low as possible, whilst the retrieval accuracy has to be preserved as much
as possible. In this paper we propose a novel multi-index hashing method called
Bag of Indexes (BoI) for Approximate Nearest Neighbors (ANN) search. It allows
to drastically reduce the query time and outperforms the accuracy results
compared to the state-of-the-art methods for large-scale landmark recognition.
It has been demonstrated that this family of algorithms can be applied on
different embedding techniques like VLAD and R-MAC obtaining excellent results
in very short times on different public datasets: Holidays+Flickr1M, Oxford105k
and Paris106k
CoveringLSH: Locality-sensitive Hashing without False Negatives
We consider a new construction of locality-sensitive hash functions for Hamming space that is
covering
in the sense that is it guaranteed to produce a collision for every pair of vectors within a given radius
r
. The construction is
efficient
in the sense that the expected number of hash collisions between vectors at distance
cr
, for a given
c
>1, comes close to that of the best possible data independent LSH without the covering guarantee, namely, the seminal LSH construction of Indyk and Motwani (STOC’98). The efficiency of the new construction essentially
matches
their bound when the search radius is not too large—e.g., when
cr
=
o
(log (
n
)/ log log
n
), where
n
is the number of points in the dataset, and when
cr
= log (
n
)/
k
, where
k
is an integer constant. In general, it differs by at most a factor ln (4) in the exponent of the time bounds. As a consequence, LSH-based similarity search in Hamming space can avoid the problem of false negatives at little or no cost in efficiency.
</jats:p
Optimal Hashing-based Time-Space Trade-offs for Approximate Near Neighbors
[See the paper for the full abstract.]
We show tight upper and lower bounds for time-space trade-offs for the
-Approximate Near Neighbor Search problem. For the -dimensional Euclidean
space and -point datasets, we develop a data structure with space and query time for
every such that: \begin{equation} c^2 \sqrt{\rho_q} +
(c^2 - 1) \sqrt{\rho_u} = \sqrt{2c^2 - 1}. \end{equation}
This is the first data structure that achieves sublinear query time and
near-linear space for every approximation factor , improving upon
[Kapralov, PODS 2015]. The data structure is a culmination of a long line of
work on the problem for all space regimes; it builds on Spherical
Locality-Sensitive Filtering [Becker, Ducas, Gama, Laarhoven, SODA 2016] and
data-dependent hashing [Andoni, Indyk, Nguyen, Razenshteyn, SODA 2014] [Andoni,
Razenshteyn, STOC 2015].
Our matching lower bounds are of two types: conditional and unconditional.
First, we prove tightness of the whole above trade-off in a restricted model of
computation, which captures all known hashing-based approaches. We then show
unconditional cell-probe lower bounds for one and two probes that match the
above trade-off for , improving upon the best known lower bounds
from [Panigrahy, Talwar, Wieder, FOCS 2010]. In particular, this is the first
space lower bound (for any static data structure) for two probes which is not
polynomially smaller than the one-probe bound. To show the result for two
probes, we establish and exploit a connection to locally-decodable codes.Comment: 62 pages, 5 figures; a merger of arXiv:1511.07527 [cs.DS] and
arXiv:1605.02701 [cs.DS], which subsumes both of the preprints. New version
contains more elaborated proofs and fixed some typo
Efficient processing of similarity queries with applications
Today, a myriad of data sources, from the Internet to business operations to scientific instruments, produce large and different types of data. Many application scenarios, e.g., marketing analysis, sensor networks, and medical and biological applications, call for identifying and processing similarities in big data. As a result, it is imperative to develop new similarity query processing approaches and systems that scale from low dimensional data to high dimensional data, from single machine to clusters of hundreds of machines, and from disk-based to memory-based processing. This dissertation introduces and studies several similarity-aware query operators, analyzes and optimizes their performance.
The first contribution of this dissertation is an SQL-based Similarity Group-by operator (SGB, for short) that extends the semantics of the standard SQL Group-by operator to group data with similar but not necessarily equal values. We realize these SGB operators by extending the Standard SQL Group-by and introduce two new SGB operators for multi-dimensional data. We implement and test the new SGB operators and their algorithms inside an open-source centralized database server (PostgreSQL).
In the second contribution of this dissertation, we study how to efficiently process Hamming-distance-based similarity queries (Hamming-distance select and Hamming-distance join) that are crucial to many applications. We introduce a new index, termed the HA-Index, that speeds up distance comparisons and eliminates redundancies when performing the two flavors of Hamming distance range queries (namely, the selects and joins).
In the third and last contribution of this dissertation, we develop a system for similarity query processing and optimization in an in-memory and distributed setup for big spatial data. We propose a query scheduler and a distributed query optimizer that use a new cost model to optimize the cost of similarity query processing in this in-memory distributed setup. The scheduler and query optimizer generates query execution plans that minimize the effect of query skew. The query scheduler employs new spatial indexing techniques based on bloom filters to forward queries to the appropriate local sites. The proposed query processing and optimization techniques are prototyped inside Spark, a distributed main-memory computation system