Hollow-tree: a metric access method for data with missing values

  • Safia BrinisEmail author
  • Caetano TrainaJr.
  • Agma J. M. Traina


Similarity search is fundamental to store and retrieve large volumes of complex data required by many real world applications. A useful mechanism for such concept is the query-by-similarity. Based on their topological properties, metric similarity functions can be used to index sets of data which can be queried effectively and efficiently by the so-called metric access methods. However, data produced by various application domains and the varying data types handled often lead to missing data, hence, they do not follow the metric similarity requirements. As a consequence, missing data cause distortions in the index structure and yield bias in the query answer. In this paper, we propose the Hollow-tree, a novel access method aimed at successfully retrieving data with missing attribute values. It employs new strategies for indexing and searching data elements, capable of handling the missing data issues when the cause of missingness is ignorable. The indexing strategy is based on a family of distance functions that allow measuring the distance between elements with missing values, along with a set of policies able to organize the elements in the index without causing distortions to its internal structure. The searching strategy employs fractal dimension property of the data to achieve accurate query answer while considering data with missing values part of the response. Results from experiments performed on a variety of real and synthetic data sets showed that, while other metric access methods deteriorate with small amounts of missing values, the Hollow-tree maintains a remarkable performance with almost 100% of precision and recall for range queries and more than 90% for k-nearest neighbor queries, for up to 40% of missing values.


Missing values Missing at random Similarity search Fractal dimension 



This research was financed, in part, by the grant number 2016/17078-0 from the Sao Paulo Research Foundation (FAPESP), by the grant number 1406799 from the Coordination for the Improvement of Higher Education Personnel (CAPES), and by the grant numbers 150626/2017-7, 433328/2018-5, 309061/2017-2, 307615/2017-0, and 437420/2018-3 from the National Council for Scientific and Technological Development (CNPq).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Computer Science Department, Institute of Mathematics and Computer SciencesUniversity of São PauloSão CarlosBrazil

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