No abstract

k nearest neighbours (kNN) queries are fundamental in many applications, ranging from data mining, recommendation system and Internet of Things, to Industry 4.0 framework applications. In mining, specifically, it can be used for the classification of human activities, iterative closest point registration and pattern recognition and has also been helpful for intrusion detection systems and fault detection. Due to the importance of kNN queries, many algorithms have been proposed in the literature, for both static and dynamic data. In this paper, we focus on exact kNN queries and present a comprehensive survey of exact kNN queries. In particular, we study two fundamental types of exact kNN queries: the kNN Search queries and the kNN Join queries. Our survey focuses on exact approaches over high-dimensional data space, which covers 20 kNN Search methods and 9 kNN Join methods. To the best of our knowledge, this is the first work of a comprehensive survey of exact kNN queries over high-dimensional datasets. We specifically categorise the algorithms based on indexing strategies, data and space partitioning strategies, clustering techniques and the computing paradigm. We provide useful insights for the evolution of approaches based on the various categorisation factors, as well as the possibility of further expansion. Lastly, we discuss some open challenges and future research directions.

Given a user dataset U and an object dataset I, a kNN join query in high-dimensional space returns the k nearest neighbors of each object in dataset U from the object dataset I. The kNN join is a basic and necessary operation in many applications, such as databases, data mining, computer vision, multi-media, machine learning, recommendation systems, and many more. In the real world, datasets frequently update dynamically as objects are added or removed. In this paper, we propose novel methods of continuous kNN join over dynamic high-dimensional data. We firstly propose the HDR+ Tree which supports more efficient insertion, deletion, and batch update. Further observed that the existing methods rely on globally correlated datasets for effective dimen-sionality reduction, we then propose the HDR Forest. It clusters the dataset and constructs multiple HDR Trees to capture local correlations among the data. As a result, our HDR Forest is able to process non-globally correlated dataset efficiently. Two novel optimisations are applied to the proposed HDR Forest, including the precomputation of the PCA states of data items and pruning-based kNN recomputation during item deletion. For the completeness of the work, we also present the proof of computing distances in reduced dimensions of PCA in HDR Tree. Extensive experiments on real-world datasets show that the proposed methods and optimisations outperform the baseline algorithms of naive RkNN join and HDR Tree.