In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worst-case efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used in practice.

To address the emerging needs of applications that require access to and retrieval of multimedia objects, we are developing the Multimedia Analysis and Retrieval System (MARS) [29]. In this paper, we concentrate on the retrieval subsystem of MARS and its support for content-based queries over image databases. Content-based retrieval techniques have been extensively studied for textual documents in the area of automatic information retrieval [40, 4]. This paper describes how these techniques can be adapted for ranked retrieval over image databases. Specifically, we discuss the ranking and retrieval algorithms developed in MARS based on the Boolean retrieval model and describe the results of our experiments that demonstrate the effectiveness of the developed model for image retrieval.

This paper is about metric data structures in high-dimensional or non-Euclidean space that permit cached sufficient statistics accelerations of learning algorithms.

This paper concerns approximate nearest neighbor searching algorithms, which have become increasingly important, especially in high dimensional perception areas such as computer vision, with dozens of publications in recent years. Much of this enthusiasm is due to a successful new approximate nearest neighbor approach called Locality Sensitive Hashing (LSH). In this paper we ask the question: can earlier spatial data structure approaches to exact nearest neighbor, such as metric trees, be altered to provide approximate answers to proximity queries and if so, how? We introduce a new kind of metric tree that allows overlap: certain datapoints may appear in both the children of a parent. We also introduce new approximate k-NN search algorithms on this structure. We show why these structures should be able to exploit the same randomprojection-based approximations that LSH enjoys, but with a simpler algorithm and perhaps with greater efficiency. We then provide a detailed empirical evaluation on five large, high dimensional datasets which show up to 31-fold accelerations over LSH. This result holds true throughout the spectrum of approximation levels.

We propose a new data structure to search in metric spaces. A metric space is formed by a collection of objects and a distance function defined among them, which satisfies the triangle inequality. The goal is, given a set of objects and a query, retrieve those objects close enough to the query. The complexity measure is the number of distances computed to achieve this goal. Our data structure, called sa-tree ("spatial approximation tree"), is based on approaching spatially the searched objects, that is, getting closer and closer to them, rather than the classical divide-and-conquer approach of other data structures. We analyze our method and show that the number of distance evaluations to search among n objects is sublinear. We show experimentally that the sa-tree is the best existing technique when the metric space is hard to search or the query has low selectivity. These are the most important unsolved cases in real applications. As a practical advantage, our data structure is one of the few that do not need to tune parameters, which makes it appealing for use by non-experts.

A frequent type of query in spatial networks (e.g., road networks) is to find the K nearest neighbors (KNN) of a given query object.

There are several aspects that might influence the performance achieved by existing learning systems. It has been reported that one of these aspects is related to class imbalance in which examples in training data belonging to one class heavily outnumber the examples in the other class. In this situation, which is found in real world data describing an infrequent but important event, the learning system may have di#culties to learn the concept related to the minority class. In this work we perform a broad experimental evaluation involving ten methods, three of them proposed by the authors, to deal with the class imbalance problem in thirteen UCI data sets. Our experiments provide evidence that class imbalance does not systematically hinder the performance of learning systems. In fact, the problem seems to be related to learning with too few minority class examples in the presence of other complicating factors, such as class overlapping. Two of our proposed methods, Smote + Tomek and Smote + ENN, deal with these conditions directly, allying a known over-sampling method with data cleaning methods in order to produce better-defined class clusters. Our comparative experiments show that, in general, over-sampling methods provide more accurate results than under-sampling methods considering the area under the ROC curve (AUC). This result seems to contradict results previously published in the literature. Smote + Tomek and Smote + ENN presented very good results for data sets with a small number of positive examples. Moreover, Random over-sampling, a very simple over-sampling method, is very competitive to more complex over-sampling methods. Since the over-sampling methods provided very good performance results, we also measured the syntactic complexity of decision trees induc...

In many database applications, one of the common queries is to find approximate matches to a given query item from a collection of data items. For example, given an image database, one may want to retrieve all images that are similar to a given query image. Distance based index structures are proposed for applications where the distance computations between objects of the data domain are expensive (such as high dimensional data), and the distance function used is metric. In this paper, we consider using distance-based index structures for similarity queries on large metric spaces. We elaborate on the approach of using reference points (vantage points) to partition the data space into spherical shell-like regions in a hierarchical manner. We introduce the multi-vantage point tree structure (mvp-tree) that uses more than one vantage points to partition the space into spherical cuts at each level. In answering similarity based queries, the mvp-tree also utilizes the pre-computed (at con...

We consider the use of wavelet transformations as a dimensionality reduction technique to permit efficient similarity search over high-dimensional time-series data. While numerous transformations have been proposed and studied, the only wavelet that has been shown to be effective for this application is the Haar wavelet. In this work, we observe that a large class of wavelet transformations (not only orthonormal wavelets but also bi-orthonormal wavelets)can be used to support similarity search. This class includes the most popular and most effective wavelets being used in image compression. We present a detailed performance study of the effects of using different wavelets on the performance of similarity search for time-series data. We include several wavelets that outperform both the Haar wavelet and the best known non-wavelet transformations for this application. To ensure our results are usable by an application engineer, we also show how to configure an indexing strategy for the best performing transformations. Finally, we identify classes of data that can be indexed efficiently using these wavelet transformations. 1.

. In many situations, users would readily accept an approximate query result if evaluation of the query becomes faster. In this article, we investigate approximate evaluation techniques based on the VA-File for Nearest-Neighbor Search (NN-Search). The VA-File contains approximations of feature points. These approximations frequently suffice to eliminate the vast majority of points in a first phase. Then, a second phase identifies the NN by computing exact distances of all remaining points. To develop approximate query-evaluation techniques, we proceed in two steps: first, we derive an analytic model for VA-File based NN-search. This is to investigate the relationship between approximation granularity, effectiveness of the filtering step and search performance. In more detail, we develop formulae for the distribution of the error of the bounds and the duration of the different phases of query evaluation. Based on these results, we develop different approximate query evaluat...