High-dimensional data indexing with applications
Schuh, Michael Arthur.
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The indexing of high-dimensional data remains a challenging task amidst an active and storied area of computer science research that impacts many far-reaching applications. At the crossroads of databases and machine learning, modern data indexing enables information retrieval capabilities that would otherwise be impractical or near impossible to attain and apply. One such useful retrieval task in our increasingly data-driven world is the k-nearest neighbor (k-NN) search, which returns the k most similar items in a dataset to the search query provided. While the k-NN concept was popularized in every-day use through the sorted (ranked) results of online text-based search engines like Google, multimedia applications are rapidly becoming the new frontier of research. This dissertation advances the current state of high-dimensional data indexing with the creation of a novel index named ID* (\ID Star"). Based on extensive theoretical and empirical analyses, we discuss important challenges associated with high dimensional data and identify several shortcomings of existing indexing approaches and methodologies. By further mitigating against the negative effects of the curse of dimensionality, we are able to push the boundary of effective k-NN retrieval to a higher number of dimensions over much larger volumes of data. As the foundations of the ID* index, we developed an open-source and extensible distance-based indexing framework predicated on the basic concepts of the popular iDistance index, which utilizes an internal B+-tree for efficient one-dimensional data indexing. Through the addition of several new heuristic-guided algorithmic improvements and hybrid indexing extensions, we show that our new ID* index can perform significantly better than several other popular alternative indexing techniques over a wide variety of synthetic and real-world data. In addition, we present applications of our ID* index through the use of k-NN queries in Content-Based Image Retrieval (CBIR) systems and machine learning classification. An emphasis is placed on the NASA sponsored interdisciplinary research goal of developing a CBIR system for large-scale solar image repositories. Since such applications rely on fast and effective k-NN queries over increasingly large-scale and high-dimensional datasets, it is imperative to utilize an efficient data indexing strategy such as the ID* index.