内在的次元に基づく探索手法の設計と解析

学位の種別:課程博士University of Tokyo(東京大学

Dimensionnalité intrinsèque dans les espaces de représentation des termes et des documents

National audienceExamining the properties of representation spaces for documents or words in IR (typically R n with n large) brings precious insights to help the retrieval process. Recently, several authors have studied the real dimensionality of the datasets, called intrinsic dimensionality, in specific parts of these spaces (Houle et al., 2012a). In this paper, we propose to revisit this notion through a coefficient called α in the specific case of IR and to study its use in IR tasks. More precisely, we show how to estimate α from IR similarities and to use it in representation spaces used for documents and words (Mikolov et al., 2013 ; Claveau et al., 2014). Indeed, we prove that α may be used to characterize difficult queries; moreover we show that this intrinsic dimensionality notion, applied to words, can help to choose terms to use for query expansion.L'examen des propriétés des espaces de représentation des documents ou des mots en RI (typiquement, R n avec n très grand) fournit de précieuses indications pour aider la re-cherche. Récemment, plusieurs travaux ont montré qu'il était possible d'étudier la dimensionnalité réelle des données, appelée dimensionnalité intrinsèque, en certains points de ces espaces (Houle et al., 2012a). Dans cet article, nous proposons de revisiter cette notion de dimension intrinsèque sous la forme d'un indice noté α dans le cas particulier de la RI et d'étudier son utilisation pratique en RI. Plus précisément, nous montrons comment son estimation à partir de similarités de type RI, peut être utilisée dans les espaces de représentations des documents et les espaces de représentations de mots (Mikolov et al., 2013 ; Claveau et al., 2014). Ainsi, nous montrons d'une part que l'indice α aide à caractériser les requêtes difficiles ; d'autre part, dans une tâche d'extension de requête, nous montrons comment cette notion de dimensionnalité intrinsèque appliquée à des mots permet de choisir au mieux les termes à étendre et leurs extensions

Indexing Metric Spaces for Exact Similarity Search

With the continued digitalization of societal processes, we are seeing an explosion in available data. This is referred to as big data. In a research setting, three aspects of the data are often viewed as the main sources of challenges when attempting to enable value creation from big data: volume, velocity and variety. Many studies address volume or velocity, while much fewer studies concern the variety. Metric space is ideal for addressing variety because it can accommodate any type of data as long as its associated distance notion satisfies the triangle inequality. To accelerate search in metric space, a collection of indexing techniques for metric data have been proposed. However, existing surveys each offers only a narrow coverage, and no comprehensive empirical study of those techniques exists. We offer a survey of all the existing metric indexes that can support exact similarity search, by i) summarizing all the existing partitioning, pruning and validation techniques used for metric indexes, ii) providing the time and storage complexity analysis on the index construction, and iii) report on a comprehensive empirical comparison of their similarity query processing performance. Here, empirical comparisons are used to evaluate the index performance during search as it is hard to see the complexity analysis differences on the similarity query processing and the query performance depends on the pruning and validation abilities related to the data distribution. This article aims at revealing different strengths and weaknesses of different indexing techniques in order to offer guidance on selecting an appropriate indexing technique for a given setting, and directing the future research for metric indexes

Design and analysis of algorithms for similarity search based on intrinsic dimension

One of the most fundamental operations employed in data mining tasks such as classification, cluster analysis, and anomaly detection, is that of similarity search. It has been used in numerous fields of application such as multimedia, information retrieval, recommender systems and pattern recognition. Specifically, a similarity query aims to retrieve from the database the most similar objects to a query object, where the underlying similarity measure is usually expressed as a distance function. The cost of processing similarity queries has been typically assessed in terms of the representational dimension of the data involved, that is, the number of features used to represent individual data objects. It is generally the case that high representational dimension would result in a significant increase in the processing cost of similarity queries. This relation is often attributed to an amalgamation of phenomena, collectively referred to as the curse of dimensionality. However, the observed effects of dimensionality in practice may not be as severe as expected. This has led to the development of models quantifying the complexity of data in terms of some measure of the intrinsic dimensionality. The generalized expansion dimension (GED) is one of such models, which estimates the intrinsic dimension in the vicinity of a query point q through the observation of the ranks and distances of pairs of neighbors with respect to q. This dissertation is mainly concerned with the design and analysis of search algorithms, based on the GED model. In particular, three variants of similarity search problem are considered, including adaptive similarity search, flexible aggregate similarity search, and subspace similarity search. The good practical performance of the proposed algorithms demonstrates the effectiveness of dimensionality-driven design of search algorithms

Local selection of features and its applications to image search and annotation

In multimedia applications, direct representations of data objects typically involve hundreds or thousands of features. Given a query object, the similarity between the query object and a database object can be computed as the distance between their feature vectors. The neighborhood of the query object consists of those database objects that are close to the query object. The semantic quality of the neighborhood, which can be measured as the proportion of neighboring objects that share the same class label as the query object, is crucial for many applications, such as content-based image retrieval and automated image annotation. However, due to the existence of noisy or irrelevant features, errors introduced into similarity measurements are detrimental to the neighborhood quality of data objects. One way to alleviate the negative impact of noisy features is to use feature selection techniques in data preprocessing. From the original vector space, feature selection techniques select a subset of features, which can be used subsequently in supervised or unsupervised learning algorithms for better performance. However, their performance on improving the quality of data neighborhoods is rarely evaluated in the literature. In addition, most traditional feature selection techniques are global, in the sense that they compute a single set of features across the entire database. As a consequence, the possibility that the feature importance may vary across different data objects or classes of objects is neglected. To compute a better neighborhood structure for objects in high-dimensional feature spaces, this dissertation proposes several techniques for selecting features that are important to the local neighborhood of individual objects. These techniques are then applied to image applications such as content-based image retrieval and image label propagation. Firstly, an iterative K-NN graph construction method for image databases is proposed. A local variant of the Laplacian Score is designed for the selection of features for individual images. Noisy features are detected and sparsified iteratively from the original standardized feature vectors. This technique is incorporated into an approximate K-NN graph construction method so as to improve the semantic quality of the graph. Secondly, in a content-based image retrieval system, a generalized version of the Laplacian Score is used to compute different feature subspaces for images in the database. For online search, a query image is ranked in the feature spaces of database images. Those database images for which the query image is ranked highly are selected as the query results. Finally, a supervised method for the local selection of image features is proposed, for refining the similarity graph used in an image label propagation framework. By using only the selected features to compute the edges leading from labeled image nodes to unlabeled image nodes, better annotation accuracy can be achieved. Experimental results on several datasets are provided in this dissertation, to demonstrate the effectiveness of the proposed techniques for the local selection of features, and for the image applications under consideration