BM + -Tree: A Hyperplane-Based Index Method for High-Dimensional Metric Spaces

The density based clustering method Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is a popular method for outlier recognition and has received tremendous attention from many different areas. A major issue of the original DBSCAN is that the time complexity could be as large as quadratic. Most of existing DBSCAN algorithms focus on developing efficient index structures to speed up the procedure in low-dimensional Euclidean space. However, the research of DBSCAN in high-dimensional Euclidean space or general metric spaces is still quite limited, to the best of our knowledge. In this paper, we consider the metric DBSCAN problem under the assumption that the inliers (excluding the outliers) have a low doubling dimension. We apply a novel randomized k-center clustering idea to reduce the complexity of range query, which is the most time consuming step in the whole DBSCAN procedure. Our proposed algorithms do not need to build any complicated data structures and are easy to implement in practice. The experimental results show that our algorithms can significantly outperform the existing DBSCAN algorithms in terms of running time.

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PAC nearest neighbor queries: Approximate and controlled search in high-dimensional and metric spaces

Proceedings of 16th International Conference on Data Engineering (Cat. No.00CB37073) ◽

10.1109/icde.2000.839417 ◽

2002 ◽

Cited By ~ 42

Author(s):

P. Ciaccia ◽

M. Patella

Keyword(s):

Metric Spaces ◽

Nearest Neighbor ◽

High Dimensional ◽

Nearest Neighbor Queries

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Distance-driven adaptive trees in biological metric spaces: uninformed accretion does not prevent convergence

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2009.0146 ◽

2009 ◽

Vol 367 (1908) ◽

pp. 4967-4986 ◽

Cited By ~ 3

Author(s):

Yannick Louis Kergosien

Keyword(s):

Metric Spaces ◽

Binary Search ◽

Artificial Vision ◽

High Dimensional ◽

Target Point ◽

Stochastic Algorithm ◽

Self Organizing Maps ◽

Branching Points ◽

Darwinian Paradigm ◽

Biological Modelling

We present several variants of a stochastic algorithm which all evolve tree-structured sets adapted to the geometry of general target subsets in metric spaces, and we briefly discuss their relevance to biological modelling. In all variants, one repeatedly draws random points from the target (step 1), each time selecting from the tree to be grown the point which is closest to the point just randomly drawn (step 2), then adding to the tree a new point in the vicinity of that closest point (step 3 or accretion step). The algorithms differ in their accretion rule, which can use the position of the target point drawn, or not. The informed case relates to the early behaviour of self-organizing maps that mimic somatotopy. It is simple enough to be studied analytically near its branching points, which generally follow some unsuccessful bifurcations. Further modifying step 2 leads to a fast version of the algorithm that builds oblique binary search trees, and we show how to use it in high-dimensional spaces to address a problem relevant to interventional medical imaging and artificial vision. In the case of an uninformed accretion rule, some adaptation also takes place, the behaviour near branching points is computationally very similar to the informed case, and we discuss its interpretations within the Darwinian paradigm.

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A Novel High-Dimensional Index Method Based on the Mathematical Features

Big Data Computing and Communications - Lecture Notes in Computer Science ◽

10.1007/978-3-319-42553-5_22 ◽

2016 ◽

pp. 257-271

Author(s):

Yu Zhang ◽

Jiayu Li ◽

Ye Yuan

Keyword(s):

High Dimensional ◽

Index Method

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