Speeding up spatial approximation search in metric spaces

Iberoamerican Congress on Pattern Recognition CIARP, 2009

Many pattern recognition tasks can be modeled as proximity searching. Here the common task is to quickly find all the elements close to a given query without sequentially scanning a very large database. A recent shift in the searching paradigm has been established by using permutations instead of distances to predict proximity. Every object in the database record how the set of reference objects (the permutants) is seen, i.e. only the relative positions are used. When a query arrives the relative displacements in the permutants between the query and a particular object is measured. This approach turned out to be the most efficient and scalable, at the expense of loosing recall in the answers. The permutation of every object is represented with κ short integers in practice, producing bulky indexes of 16 κn bits. In this paper we show how to represent the permutation as a binary vector, using just one bit for each permutant (instead of logκ in the plain representation). The Hamming distance in the binary signature is used then to predict proximity between objects in the database. We tested this approach with many real life metric databases obtaining faster queries with a recall close to the Spearman ρ using 16 times less space.

Lecture Notes in Computer Science, 2005

Kernel based methods (such as k-nearest neighbors classifiers) for AI tasks translate the classification problem into a proximity search problem, in a space that is usually very high dimensional. Unfortunately, no proximity search algorithm does well in high dimensions. An alternative to overcome this problem is the use of approximate and probabilistic algorithms, which trade time for accuracy. In this paper we present a new probabilistic proximity search algorithm. Its main idea is to order a set of samples based on their distance to each element. It turns out that the closeness between the order produced by an element and that produced by the query is an excellent predictor of the relevance of the element to answer the query. The performance of our method is unparalleled. For example, for a full 128-dimensional dataset, it is enough to review 10% of the database to obtain 90% of the answers, and to review less than 1% to get 80% of the correct answers. The result is more impressive if we realize that a full 128dimensional dataset may span thousands of dimensions of clustered data. Furthermore, the concept of proximity preserving order opens a totally new approach for both exact and approximated proximity searching.

Multimedia Tools and Applications, 2001

Pivot-based algorithms are effective tools for proximity searching in metric spaces. They allow trading space overhead for number of distance evaluations performed at query time. With additional search structures (that pose extra space overhead) they can also reduce the amount of side computations. We introduce a new data structure, the Fixed Queries Array (FQA), whose novelties are (1) it permits sublinear extra CPU time without any extra data structure;(2) it permits trading number of pivots for their precision so as to make better use ...

Lecture Notes in Computer Science, 2012

Proximity searching consists in retrieving the most similar objects to a given query. This kind of searching is a basic tool in many fields of artificial intelligence, because it can be used as a search engine to solve problems like kNN searching. A common technique to solve proximity queries is to use an index. In this paper, we show a variant of the permutation based index, which, in his original version, has a great predicting power about which are the objects worth to compare with the query (avoiding the exhaustive comparison). We have noted that when two permutants are close, they can produce small differences in the order in which objects are revised, which could be responsible of finding the true answer or missing it. In this paper we pretend to mitigate this effect. As a matter of fact, our technique allows us both to reduce the index size and to improve the query cost up to 30%.

Lecture Notes in Computer Science, 2015

Proximity searching consists in retrieving objects out of a database similar to a given query. Nowadays, when multimedia databases are growing up, this is an elementary task. The permutation based index (PBI) and its variants are excellent techniques to solve proximity searching in high dimensional spaces, however they have been surmountable in low dimensional ones. Another PBI's drawback is that the distance between permutations cannot allow to discard elements safely when solving similarity queries. In the following, we introduce an improvement on the PBI that allows to produce a better promissory order using less space than the basic permutation technique and also gives us information to discard some elements. To do so, besides the permutations, we quantize distance information by defining distance rings around each permutant, and we also keep this data. The experimental evaluation shows we can dramatically improve upon specialized techniques in low dimensional spaces. For instance, in the real world dataset of NASA images, our boosted PBI uses up to 90% less distances evaluations than AESA, the state-of-the-art searching algorithm with the best performance in this particular space.

ACM Transactions on Information Systems, 2003

Similarity search structures for metric data typically bound object partitions by ball regions. Since regions can overlap, a relevant issue is to estimate the proximity of regions in order to predict the number of objects in the regions' intersection. This paper analyzes the problem using a probabilistic approach and provides a solution that effectively computes the proximity through realistic heuristics that only require small amounts of auxiliary data. An extensive simulation to validate the technique is provided. An application is developed to demonstrate how the proximity measure can be successfully applied to the approximate similarity search. Search speedup is achieved by ignoring data regions whose proximity to the query region is smaller than a user-defined threshold. This idea is implemented in a metric tree environment for the similarity range and "nearest neighbors" queries. Several measures of efficiency and effectiveness are applied to evaluate proposed approximate search algorithms on real-life data sets. An analytical model is developed to relate proximity parameters and the quality of search. Improvements of two orders of magnitude are achieved for moderately approximated search results. We demonstrate that the precision of proximity measures can significantly influence the quality of approximated algorithms.

1999

In this paper we introduce a new paradigm for similarity search, called PAC-NN (probably approximately correct nearest neighbor) queries, aiming to break the "dimensionality curse" which inhibits current approaches to be applied in high-dimensional spaces. PAC-NN queries return, with probability at least 1 − δ, a (1 +)-approximate NN-an object whose distance from the query q is less than (1 +) times the distance between q and its NN. We describe how the distance distribution of the query object can be used to determine a suitable stopping condition with probabilistic guarantees on the quality of the result, and then analyze performance of both sequential and index-based PAC-NN algorithms. This shows that PAC-NN queries can be efficiently processed even on very high-dimensional spaces and that control can be exerted in order to tradeoff between the accuracy of the result and the cost.

1999

We investigate the problem of approximate similarity (nearest neighbor) search in high-dimensional metric spaces, and describe how the distance distribution of the query object can be exploited so as to provide probabilistic guarantees on the quality of the result. This leads to a new paradigm for similarity search, called PAC-NN (probably approximately correct nearest neighbor) queries, aiming to break the "dimensionality curse". PAC-NN queries return, with probability at least 1 ; , a (1 + )-approximate NN -an object whose distance from the query q is less than (1 + ) times the distance between q and its NN. Analytical and experimental results obtained for sequential and index-based algorithms show that PAC-NN queries can be efficiently processed even on very high-dimensional spaces and that control can be exerted in order to tradeoff the accuracy of the result and the cost.

Lecture Notes in Computer Science, 2014

The permutation based index has shown to be very effective in medium and high dimensional metric spaces, even in difficult problems such as solving reverse k-nearest neighbor queries. Nevertheless, currently there is no study about which are the desirable features one can ask to a permutant set, or how to select good permutants. Similar to the case of pivots, our experimental results show that, compared with a randomly chosen set, a good permutant set yields to fast query response or to reduce the amount of space used by the index. In this paper, we start by characterizing permutants and studying their predictive power; then we propose an effective heuristic to select a good set of permutant candidates. We also show empirical evidence that supports our technique.

—We introduce a new probabilistic proximity search algorithm for range and K-nearest neighbor (K-NN) searching in both coordinate and metric spaces. Although there exist solutions for these problems, they boil down to a linear scan when the space is intrinsically high dimensional, as is the case in many pattern recognition tasks. This, for example, renders the K-NN approach to classification rather slow in large databases. Our novel idea is to predict closeness between elements according to how they order their distances toward a distinguished set of anchor objects. Each element in the space sorts the anchor objects from closest to farthest to it and the similarity between orders turns out to be an excellent predictor of the closeness between the corresponding elements. We present extensive experiments comparing our method against state-of-the-art exact and approximate techniques, both in synthetic and real, metric and nonmetric databases, measuring both CPU time and distance computations. The experiments demonstrate that our technique almost always improves upon the performance of alternative techniques, in some cases by a wide margin.

ing.utalca.cl

The permutation index has shown to be very effective in medium and high dimensional metric spaces, even in difficult problems, for instance, when solving reverse knearest neighbor queries. Nevertheless, currently there is no study about which are the desirable features one can ask to a permutant set, or how to select good permutants. Similar to the case of pivots, our experimental results show that, compared with a randomly chosen set, a good permutant set yields to fast query response or to reduce the amount of space used by the index. In this paper we start by characterizing permutants and studying their discrimination power, and then we propose an effective heuristic to select a good permutant candidate set. We also show empirical evidence that supports our technique.

2005

Proximity queries (the searching problem generalized beyond exact match) is mostly modeled as metric space. A metric space consists of a collection of objects and a distance function defined among them. The goal is to preprocess the data set (a slow procedure) to quickly answer proximity queries. This problem have received a lot of attention recently, specially in the pattern recognition community. The Excluded Middle Vantage Point Forest (VP–forest) is a data structure designed to search in high dimensional vector spaces. A VP ...

Lecture Notes in Computer Science, 2012

Some metric indexes, like the pivot based family, can natively trade space for query time. Other indexes may have a small memory footprint and still outperform the pivot based approach; but are unable to increase the memory usage to boost the query time. In this paper we propose a new metric indexing technique with an algorithmic mechanism to lift the performance of otherwise rigid metric indexes. We selected the well known List of Clusters (LC) as the base data structure, obtaining an index which is orders of magnitude faster to build, with memory usage adaptable to the intrinsic dimension of the data, and faster at query time than the original LC. We also present a nearest neighbor algorithm, of independent interest, which is optimal in the sense that requires the same number of distance computations as a range query with the radius of the nearest neighbor. We present exhaustive experimental evidence supporting our claims, for both synthetic and real world datasets.

Modeling proximity searching problems in a metric space allows one to approach many problems in different areas, e.g. pattern recognition, multimedia search, or clustering. Recently there was proposed the permutation based approach, a novel technique that is unbeatable in practice but difficult to compress. In this article we introduce an improvement on that metric space search data structure. Our technique shows that we can compress the permutation based algorithm without loosing precision. We show experimentally that our technique is competitive with the original idea and improves it up to 46% in real databases.