30,273 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
R-Forest for Approximate Nearest Neighbor Queries in High Dimensional Space
Searching high dimensional space has been a challenge and an area of intense research for many years. The dimensionality curse has rendered most existing index methods all but useless causing people to research other techniques. In my dissertation I will try to resurrect one of the best known index structures, R-Tree, which most have given up on as a viable method of answering high dimensional queries. I have pointed out the various advantages of R-Tree as a method for answering approximate nearest neighbor queries, and the advantages of locality sensitive hashing and locality sensitive B-Tree, which are the most successful methods today. I started by looking at improving the maintenance of R-Tree by the use of bulk loading and insertion. I proposed and implemented a new method that bulk loads the index which was an improvement of standard method. I then turned my attention to nearest neighbor queries, which is a much more challenging problem especially in high dimensional space. Initially I developed a set of heuristics, easily implemented in R-Tree, which improved the efficiency of high dimensional approximate nearest neighbor queries. To further refine my method I took another approach, by developing a new model, known as R-Forest, which takes advantage of space partitioning while still using R-Tree as its index structure. With this new approach I was able to implement new heuristics and can show that R-Forest, comprised of a set of R-Trees, is a viable solution tohigh dimensional approximate nearest neighbor queries when compared to established methods
Graph-Based Time-Space Trade-Offs for Approximate Near Neighbors
We take a first step towards a rigorous asymptotic analysis of graph-based methods for finding (approximate) nearest neighbors in high-dimensional spaces, by analyzing the complexity of randomized greedy walks on the approximate nearest neighbor graph. For random data sets of size n = 2^{o(d)} on the d-dimensional Euclidean unit sphere, using near neighbor graphs we can provably solve the approximate nearest neighbor problem with approximation factor c > 1 in query time n^{rho_{q} + o(1)} and space n^{1 + rho_{s} + o(1)}, for arbitrary rho_{q}, rho_{s} >= 0 satisfying (2c^2 - 1) rho_{q} + 2 c^2 (c^2 - 1) sqrt{rho_{s} (1 - rho_{s})} >= c^4. Graph-based near neighbor searching is especially competitive with hash-based methods for small c and near-linear memory, and in this regime the asymptotic scaling of a greedy graph-based search matches optimal hash-based trade-offs of Andoni-Laarhoven-Razenshteyn-Waingarten [Andoni et al., 2017]. We further study how the trade-offs scale when the data set is of size n = 2^{Theta(d)}, and analyze asymptotic complexities when applying these results to lattice sieving
Multiple query points parallel search algorithm (Comb Algorithm) for multimedia database systems
In this project, we introduce and present a new search method for fast nearest-neighbor search in high-dimensional feature space, which is called Comb algorithm . Most similarity search techniques map the data objects into high-dimensional feature space. The similarity search corresponds to a nearest-neighbor search in the feature space. Fagin and Threshold algorithms are two known methods that perform for nearest-neighbor search with one query point. On the other hand, the method we present works on parallel systems that are identical. We provide an alternative solution with several query points searching in parallel identical systems in as many copies as query points are defined. The algorithm is a trade-off between space storage (multiple copies of the multidimensional system), computation resources, and query execution time
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
Scalable Image Retrieval by Sparse Product Quantization
Fast Approximate Nearest Neighbor (ANN) search technique for high-dimensional
feature indexing and retrieval is the crux of large-scale image retrieval. A
recent promising technique is Product Quantization, which attempts to index
high-dimensional image features by decomposing the feature space into a
Cartesian product of low dimensional subspaces and quantizing each of them
separately. Despite the promising results reported, their quantization approach
follows the typical hard assignment of traditional quantization methods, which
may result in large quantization errors and thus inferior search performance.
Unlike the existing approaches, in this paper, we propose a novel approach
called Sparse Product Quantization (SPQ) to encoding the high-dimensional
feature vectors into sparse representation. We optimize the sparse
representations of the feature vectors by minimizing their quantization errors,
making the resulting representation is essentially close to the original data
in practice. Experiments show that the proposed SPQ technique is not only able
to compress data, but also an effective encoding technique. We obtain
state-of-the-art results for ANN search on four public image datasets and the
promising results of content-based image retrieval further validate the
efficacy of our proposed method.Comment: 12 page
- …