Ives Rene Venturini Pola

Slicing the metric space to provide quick indexing of complex data in the main memory

Searching in a dataset for elements that are similar to a given query element is a core problem in applications that manage complex data, and has been aided by metric access methods (MAMs). A growing number of applications require indices that must be built faster and repeatedly, also providing faster response for similarity queries. The increase in the main memory capacity and its lowering costs also motivate using memory-based MAMs. In this paper, we propose the Onion-tree, a new and robust dynamic memory-based MAM that slices the metric space into disjoint subspaces to provide quick indexing of complex data. It introduces three major characteristics: (i) a partitioning method that controls the number of disjoint subspaces generated at each node; (ii) a replacement technique that can change the leaf node pivots in insertion operations; and (iii) range and k-NN extended query algorithms to support the new partitioning method, including a new visit order of the subspaces in k-NN queries. Performance tests with both real-world and synthetic datasets showed that the Onion-tree is very compact. Comparisons of the Onion-tree with the MM-tree and a memory-based version of the Slim-tree showed that the Onion-tree was always faster to build the index. The experiments also showed that the Onion-tree significantly improved range and k-NN query processing performance and was the most efficient MAM, followed by the MM-tree, which in turn outperformed the Slim-tree in almost all the tests.

The MM-tree: a memory-based metric tree without overlap between nodes

Advanced database systems offer similarity queries on complex data. Searching by similarity on complex data is accelerated through the use of metric access methods (MAM). These access methods organize data in order to reduce the number of comparison between elements when answering queries. MAM can be categorized in two types: disk-based and memory-based. The disk-based structures limit the partitioning of space forcing nodes to have multiple elements according to disk page sizes. However, memory-based trees allows more flexibility, producing trees faster to build and to perform queries. Although recent developments target disk-based methods on tree structures, several applications benefits from a faster way to build indexes on main memory. This paper presents a memory-based metric tree, the MM-tree, which successively partitions the space into non-overlapping regions. We present experiments comparing MM-tree with existing high performance MAM, including the disk-based Slim-tree. The experiments reveal that MM-tree requires up to one fifth of the number of distance calculations to be constructed when compared with Slim-tree, performs range queries requiring 64% less distance calculations and KNN queries requiring 74% less distance calculations.

Three Dimensional Finite Element Analyses of Oral Structures by Computerized Tomography

Our aim was to document the benefits of three dimensional finite element model generations from computed tomography data as well as the realistic creation of all oral structures in a patient. The stresses resulting from the applied load in our study did not exceed the structure limitations, suggesting a clinically acceptable physiological condition.

The Onion-Tree: Quick Indexing of Complex Data in the Main Memory

Searching for elements in a dataset that are similar to a given query element is a core problem in applications that use complex data, and has been carried out aided by a metric access method (MAM). A growing number of these applications require indices that can be built faster and for several times, in addition to providing smaller response times for similarity queries. Besides, the increase in the main memory capacity and its lowering costs also motivate using memory-based MAMs. In this paper, we propose the Onion-tree , a new and robust dynamic memory-based MAM that performs a hierarchical division of the metric space into disjoint subspaces. The Onion-tree is very compact, requiring a small fraction of the main memory (e.g., at most 4.8%). Comparisons of the Onion-tree , a memory-based version of the Slim-tree, and the memory-based MM-tree showed that the Onion-tree always produced the smallest elapsed time to build the index. Our experiments also showed that the Onion-tree produced the best query performance results, followed by the MM-tree, which in turn outperformed the Slim-tree. With regard to the MM-tree, the Onion-tree provided a reduction in the number of distance calculations that ranged from 1% to 11% in range queries and from 16% up to 64% in k -NN queries. The Onion-tree also significantly improved the required elapsed time, which ranged from 12% to 39% in range query processing and from 40% up to 70% in k -NN query processing, as compared to the MM-tree, its closest competitor. The Onion-tree source code is available at http://gbd.dc.ufscar.br/download/Onion-tree .

The NOBH-tree

In order to speed up similarity query evaluation, index structures divide the target dataset into subsets aimed at finding the answer without examining the entire dataset. As the complexity of the data types handled by modern applications keeps growing, searching by similarity becomes increasingly interesting, that makes the Metric Space Theory as the theoretical base to build the structures employed to index complex data. Also, as the main memory capacity grows and the price decreases, increasingly larger databases can be completely indexed in the main-memory. Thus, more and more applications require the data base management systems to quickly build indexes that can take advantage of memory-based indexes. In this paper, we propose a new family of metric access methods, called NOBH-trees that allow a non-overlapping division of the data space, combining Voronoi-shaped with ball-shaped regions to partition the metric space. We show how to query the subspaces divided by the hyperplanes and how the distance from any element to the hyperplane can be evaluated. The results obtained from the experiments show that the new MAM achieves better performance than the existing ones during both the construction and querying phases.

Improving Metric Access Methods with Bucket Files

Modern applications deal with complex data, where retrieval by similarity plays an important role in most of them. Complex data whose primary comparison mechanisms are similarity predicates are usually immersed in metric spaces. Metric Access Methods MAMs exploit the metric space properties to divide the metric space into regions and conquer efficiency on the processing of similarity queries, like range and k-nearest neighbor queries. Existing MAM use homogeneous data structures to improve query execution, pursuing the same techniques employed by traditional methods developed to retrieve scalar and multidimensional data. In this paper, we combine hashing and hierarchical ball partitioning approaches to achieve a hybrid index that is tuned to improve similarity queries targeting complex data sets, with search algorithms that reduce total execution time by aggressively reducing the number of distance calculations. We applied our technique in the Slim-tree and performed experiments over real data sets showing that the proposed technique is able to reduce the execution time of both range and k-nearest queries to at least half of the Slim-tree. Moreover, this technique is general to be applied over many existing MAM.

Distance Functions Association for Content-Based Image Retrieval using Multiple Comparison Criteria

The comparison operators available in traditional database management systems (DBMS) are not adequate to handle complex data such as images, rather comparing them using similarity operators is the option of choice. Similarity operators need a way to measure the similarity between pairs of objects. Although there are many interesting works dealing with similarity queries and functions to measure similarity, they all rely on a single similarity function that must be applicable over the whole dataset. However, images from medical exams often require several ways to measure similarity, depending on many factors, such as the particular pathological condition being searched, or the existence of specific clinical condition revealed in the images compared. Therefore, the ability to handle several ways to compare images by similarity is important in medical software handling images. This work develop a technique to allow several similarity functions to be combined when indexing a large set of images, allowing queries to probe the dataset regarding distinct comparison criteria. This technique also allows a flexible way to pose queries supporting fast retrieval of the answers