Distance-based indexing for high-dimensional metric spaces

1997 ◽  
Vol 26 (2) ◽  
pp. 357-368 ◽  
Author(s):  
Tolga Bozkaya ◽  
Meral Ozsoyoglu
Keyword(s):  
Metric Spaces ◽  
High Dimensional

XM-tree: data driven computational model by using metric extended nodes with non-overlapping in high-dimensional metric spaces

2018 ◽  
Vol 25 (2) ◽  
pp. 196-223
Author(s):  
Zineddine Kouahla ◽  
Adeel Anjum ◽  
Sheeraz Akram ◽  
Tanzila Saba ◽  
José Martinez
Keyword(s):  
Computational Model ◽  
Metric Spaces ◽  
Data Driven ◽  
High Dimensional ◽  
Tree Data

scholarly journals On Metric DBSCAN with Low Doubling Dimension

2020 ◽  
Author(s):  
Hu Ding ◽  
Fan Yang ◽  
Mingyue Wang
Keyword(s):  
Euclidean Space ◽  
Metric Spaces ◽  
Spatial Clustering ◽  
High Dimensional ◽  
Dimensional Euclidean Space ◽  
Index Structures ◽  
Doubling Dimension ◽  
Density Based Clustering ◽  
Speed Up ◽  
Low Dimensional

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.

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

2009 ◽  
Vol 367 (1908) ◽  
pp. 4967-4986 ◽  
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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