Scaling kNN queries using statistical learning

Cahsai, Atoshum Samuel (2020) Scaling kNN queries using statistical learning. PhD thesis, University of Glasgow.

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Abstract

The k-Nearest Neighbour (kNN) method is a fundamental building block for many sophisticated statistical learning models and has a wide application in different fields; for instance, in kNN regression, kNN classification, multi-dimensional items search, location-based services, spatial analytics, etc.
However, nowadays with the unprecedented spread of data generated by computing and communicating devices has resulted in a plethora of low-dimensional large-scale datasets and their users' community, the need for efficient and scalable kNN processing is pressing. To this end, several parallel and distributed approaches and methodologies for processing exact kNN in low-dimensional large-scale datasets have been proposed; for example Hadoop-MapReduce-based kNN query processing approaches such as Spatial-Hadoop (SHadoop), and Spark-based approaches like Simba. This thesis contributes with a variety of methodologies for kNN query processing based on statistical and machine learning techniques over large-scale datasets.

This study investigates the exact kNN query performance behaviour of the well-known Big Data Systems, SHadoop and Simba, that proposes building multi-dimensional Global and Local Indexes over low dimensional large-scale datasets. The rationale behind such methods is that when executing exact kNN query, the Global and Local indexes access a small subset of a large-scale dataset stored in a distributed file system. The Global Index is used to prune out irrelevant subsets of the dataset; while the multiple distributed Local Indexes are used to prune out unnecessary data elements of a partition (subset).

The kNN execution algorithm of SHadoop and Simba involves loading data elements that reside in the relevant partitions from disks/network points to memory. This leads to significantly high kNN query response times; so, such methods are not suitable for low-latency applications and services. An extensive literature review showed that not enough attention has been given to access relatively small-sized but relevant data using kNN query only. Based on this limitation, departing from the traditional kNN query processing methods, this thesis contributes two novel solutions: Coordinator With Index (COWI) and Coordinator with No Index(CONI) approaches. The essence of both approaches rests on adopting a coordinator-based distributed processing algorithm and a way to structure computation and index the stored datasets that ensures that only a very small number of pieces of data are retrieved from the underlying data centres, communicated over the network, and processed by the coordinator for every kNN query. The expected outcome is that scalability is ensured and kNN queries can be processed in just tens of milliseconds. Both approaches are implemented using a NoSQL Database (HBase) achieving up to three orders of magnitude of performance gain compared with state of the art methods -SHadoop and Simba.

It is common practice that the current state-of-the-art approaches for exact kNN query processing in low-dimensional space use Tree-based multi-dimensional Indexing methods to prune out irrelevant data during 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 methods becomes exceptionally high, especially when opted to partition a dataset into smaller chunks. In this context, this thesis contributes with a novel perspective on how to organise low-dimensional large-scale datasets based on data space transformations deriving a Space Transformation Organisation Structure (STOS). STOS facilitates kNN query processing as if underlying datasets were uniformly distributed in the space. Such an approach bears significant advantages: first, STOS enjoys a minute memory footprint that is many orders of magnitude smaller than Index-based approaches found in the literature. Second, the required memory for such meta-data information over large-scale datasets, unlike related work, increases very slowly with dataset size. Hence, STOS enjoys significantly higher scalability. Third, STOS is relatively efficient to compute, outperforming traditional multivariate Index building times, and comparable, if not better, query response times.

In the literature, the exact kNN query in a large-scale dataset was limited to low-dimensional space; this is because the query response time and memory space requirement of the Tree-based index methods increase with dimension. Unable to solve such exponential dependency on the dimension, researchers assume that no efficient solution exists and propose approximation kNN in high dimensional space. Unlike the approximated kNN query that tries to retrieve approximated nearest neighbours from large-scale datasets, in this thesis a new type of kNN query referred to as ‘estimated kNN query’ is proposed. The estimated kNN query processing methodology attempts to estimate the nearest neighbours based on the marginal cumulative distribution of underlying data using statistical copulas. This thesis showcases the performance trade-off of exact kNN and the estimate kNN queries in terms of estimation error and scalability. In contrast, kNN regression predicts that a value of a target variable based on kNN; but, particularly in a high dimensional large-scale dataset, a query response time of kNN regression, can be a significantly high due to the curse of dimensionality. In an effort to tackle this issue, a new probabilistic kNN regression method is proposed. The proposed method statistically predicts the values of a target variable of kNN without computing distance.

In different contexts, a kNN as missing value algorithm in high dimensional space in Pytha, a distributed/parallel missing value imputation framework, is investigated. In Pythia, a different way of indexing a high-dimensional large-scale dataset is proposed by the group (not the work of the author of this thesis); by using such indexing methods, scaling-out of kNN in high dimensional space was ensured. Pythia uses Adaptive Resonance Theory (ART) -a machine learning clustering algorithm- for building a data digest (aka signatures) of large-scale datasets distributed across several data machines. The major idea is that given an input vector, Pythia predicts the most relevant data centres to get involved in processing, for example, kNN. Pythia does not retrieve exact kNN. To this end, instead of accessing the entire dataset that resides in a data-node, in this thesis, accessing only relevant clusters that reside in appropriate data-nodes is proposed. As we shall see later, such method has comparable accuracy to that of the original design of Pythia but has lower imputation time. Moreover, the imputation time does not significantly grow with a size of a dataset that resides in a data node or with the number of data nodes in Pythia. Furthermore, as Pythia depends utterly on the data digest built by ART to predict relevant data centres, in this thesis, the performance of Pythia is investigated by comparing different signatures constructed by a different clustering algorithms, the Self-Organising Maps.

In this thesis, the performance advantages of the proposed approaches via extensive experimentation with multi-dimensional real and synthetic datasets of different sizes and context are substantiated and quantified.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Keywords: scaling k nearest neighbours, big data, indexing multi-dimensional data, large scale dataset, machine learning, HBase, Hadoop, Spark, Copulas, Pythia, Probabilistic Data Space Transformations, estimated kNN, approximate kNN regression, Adaptive resonance theory, Self Organising Maps, missing value imputation, gaussian mixture model, Sklar’s theorem, cumulative distribution function.
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Colleges/Schools: College of Science and Engineering > School of Computing Science
Supervisor's Name: Anagnostopoulos, Doctor Christos
Date of Award: 2020
Depositing User: MR Atoshum Samuel Cahsai
Unique ID: glathesis:2020-81523
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 31 Jul 2020 08:12
Last Modified: 31 Jul 2020 08:16
URI: http://theses.gla.ac.uk/id/eprint/81523

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