Supporting KDD Applications by the k-Nearest Neighbor Join

Abstract

Abstract. The similarity join has become an important database primitive to support similarity search and data mining. A similarity join combines two sets of complex objects such that the result contains all pairs of similar objects. Well-known are two types of the similarity join, the distance range join where the user defines a distance threshold for the join, and the closest point query or k-distance join which retrieves the k most similar pairs. In this paper, we propose an important, third similarity join operation called k-nearest neighbor join which combines each point of one point set with its k nearest neighbors in the other set. We discover that many standard algorithms of Knowledge Discovery in Databases (KDD) such as k-means and k-medoid clustering, nearest neighbor classification, data cleansing, postprocessing of sampling-based data mining etc. can be implemented on top of the k-nn join operation to achieve performance improvements without affecting the quality of the result of these algorithms. Our list of possible applications includes standard methods for all stages of the KDD process including preprocessing, data mining, and postprocessing. Thus, our method is turbo charging the complete KDD process.

Processing Distance Join Queries with Constraints

“…A clustering algorithm based on closest pairs has been proposed in [13]. In [2,3] the authors study applications of the k-NN join operation to knowledge discovery, which is a direct extension of the k-Semi-Closest-Pair query. More specifically, the authors discuss the application of k-NN join to clustering, classification and sampling tasks in data mining operations, and they illustrate how these tasks can be performed more efficiently.…”

Efficient Evaluation of All-Nearest-Neighbor Queries

“…A related problem, called AkNN, which reports the kNN for each data point, is directly used in the JarvisPatrick Clustering algorithm [16]. AkNN is also used in a number of other clustering algorithms including the kmeans and the k-medoid clustering algorithms [4].…”

“…In many applications that use ANN, especially large scientific applications, the datasets are growing rapidly and often the ANN computation is one of the main computational bottlenecks. Recognizing this problem, there has been a lot of interest in the database community in developing efficient external ANN algorithms [4,5,9,13,32]. All of these methods build R*-tree indices [3] on one or both datasets, and evaluate the ANN by traversing the index.…”

“…Previous index-based ANN methods [4,5,9,13,32] have exclusively focused on the "ubiquitous" R*-tree index structure. In this paper, we show that for ANN queries there is a much better choice for an index structure, the MBRQT index.…”

Closest Pair Queries with Spatial Constraints

“…A clustering algorithm based on closest pairs has been proposed in [12]. In [2,3] the authors study applications of the k-NN join operation to knowledge discovery, which is a direct extension of the k-semi-closest-pair query. More specifically, the authors discuss the application of k-NN join to clustering, classification and sampling tasks in data mining operations, and they illustrate how these tasks can be performed more efficiently.…”