Abstract-Recently parallel / distributed processing approaches have been proposed for processing k-Nearest Neighbours (kNN) queries over very large (multi-dimensional) datasets aiming to ensure scalability. However, this is typically achieved at the expense of efficiency. With this paper we offer a novel approach that alleviates the performance problems associated with state of the art methods. The essence of our approach, which differentiates it from related research, rests on (i) adopting a coordinator-based distributed processing algorithm, instead of those employed over data-parallel execution engines (such as Hadoop/MapReduce or Spark), and (ii) on a way to organize data, to structure computation, and to index the stored datasets that ensures that only a very small number of data items are retrieved from the underlying data store, communicated over the network, and processed by the coordinator for every kNN query. Our approach also pays special attention to ensuring scalability in addition to low query processing times. Overall, kNN queries can be processed in just tens of milliseconds (as opposed to the (tens of) seconds required by state of the art. We have implemented our approach, using a NoSQL DB (HBase) as the data store, and we compare it against the state-of-the-art: the Hadoop-based Spatial Hadoop (SHadoop) and the Spark-based Simba methods. We employ different datasets of various sizes, showcasing the contributed performance advantages. Our approach outperforms the state of the art, by 2-3 orders of magnitude, and consistently for dataset sizes ranging from hundreds of millions to hundreds of billions of data points. We also show that the key constituent performance overheads incurred during query processing (such as the number of data items retrieved from the data store, the required network bandwidth, and the processing time at the coordinator) scale very well, ensuring the overall scalability of the approach.
The state-of-the-art approaches for scalable kNN query processing utilise big data parallel/distributed platforms (e.g., Hadoop and Spark) and storage engines (e.g, HDFS, NoSQL, etc.), upon which they build (tree based) indexing methods for efficient query processing. However, as data sizes continue to increase (nowadays it is not uncommon to reach several Petabytes), the storage cost of tree-based index structures becomes exceptionally high. In this work, we propose a novel perspective to organise multivariate (mv) datasets. The main novel idea relies on data space probabilistic transformations and derives a Space Transformation Organisation Structure (STOS) for mv data organisation. STOS facilitates query processing as if underlying datasets were uniformly distributed. This approach bears significant advantages. First, STOS enjoys a minute memory footprint that is many orders of magnitude smaller than indexes in related work. Second, the required memory, unlike related work, increases very slowly with dataset size and, thus, enjoys significantly higher scalability. Third, the STOS structure is relatively efficient to compute, outperforming traditional index building times. The new approach comes bundled with a distributed coordinatorbased query processing method so that, overall, lower query processing times are achieved compared to the state-of-the-art index-based methods. We conducted extensive experimentation with real and synthetic datasets of different sizes to substantiate and quantify the performance advantages of our proposal.
Solving the missing-value (MV) problem with small estimation errors in large-scale data environments is a notoriously resource-demanding task. The most widely used MV imputation approaches are computationally expensive because they explicitly depend on the volume and the dimension of the data. Moreover, as datasets and their user community continuously grow, the problem can only be exacerbated. In an attempt to deal with such a problem, in our previous work, we introduced a novel framework coined Pythia, which employs a number of distributed data nodes (cohorts), each of which contains a partition of the original dataset. To perform MV imputation, the Pythia, based on specific machine and statistical learning structures (signatures), selects the most appropriate subset of cohorts to perform locally a missing value substitution algorithm (MVA). This selection relies on the principle that particular subset of cohorts maintains the most relevant partition of the dataset. In addition to this, as Pythia uses only part of the dataset for imputation and accesses different cohorts in parallel, it improves efficiency, scalability, and accuracy compared to a single machine (coined Godzilla), which uses the entire massive dataset to compute imputation requests. Although this article is an extension of our previous work, we particularly investigate the robustness of the Pythia framework and show that the Pythia is independent from any MVA and signature construction algorithms. In order to facilitate our research, we considered two well-known MVAs (namely K-nearest neighbor and expectation-maximization imputation algorithms), as well as two machine and neural computational learning signature construction algorithms based on adaptive vector quantization and competitive learning. We prove comprehensive experiments to assess the performance of the Pythia against Godzilla and showcase the benefits stemmed from this framework.
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