Connectivity of the mutual k-nearest-neighbor graph in clustering and outlier detection

Brito, M. R.; Chávez, Edgar; Quiróz, Adolfo J.; Yukich, J. E.

doi:10.1016/s0167-7152(96)00213-1

Cited by 208 publications

(144 citation statements)

References 6 publications

Supporting

Mentioning

139

Contrasting

Unclassified

Order By: Relevance

“…Remark According to a referee, a challenging question is whether one can obtain similar results by using only the connected components of the standard ε-nearest and k-nearest neighbor graphs, for example by adapting methods of Brito, Chavez, Quiroz and Yukich [2] and Penrose [15].…”

Section: Resultsmentioning

confidence: 99%

A graph-based estimator of the number of clusters

2007

View full text Add to dashboard Cite

Assessing the number of clusters of a statistical population is one of the essential issues of unsupervised learning. Given n independent observations X 1 , . . . , X n drawn from an unknown multivariate probability density f , we propose a new approach to estimate the number of connected components, or clusters, of the t-level set L(t) = {x : f (x) ≥ t}. The basic idea is to form a rough skeleton of the set L(t) using any preliminary estimator of f , and to count the number of connected components of the resulting graph. Under mild analytic conditions on f , and using tools from differential geometry, we establish the consistency of our method.

show abstract

Section: Resultsmentioning

confidence: 99%

A graph-based estimator of the number of clusters

2007

View full text Add to dashboard Cite

show abstract

“…Note that k (n) cannot be smaller than the smallest k required for connectivity of the undirected kNNG. Because the lower bound for the smallest necessary k in undirected kNNGs is at least 0.3043· log(n) (whp) [6], together with the finding in [11], we have k (n) = (log(n)).…”

Section: Graph Connectivitymentioning

confidence: 96%

“…In other words, mutual selection is required, as in our proposed model. The smallest k necessary for graph connectivity of a mutual kNNG, denoted by k (n), is shown to be O(log(n)) [11]. Note that k (n) cannot be smaller than the smallest k required for connectivity of the undirected kNNG.…”

Section: Graph Connectivitymentioning

confidence: 99%

See 1 more Smart Citation

A New Random Graph Model with Self-Optimizing Nodes: Connectivity and Diameter

Kabkab

2015

Internet Mathematics

View full text Add to dashboard Cite

We introduce a new random graph model. In our model, n, n ≥ 2, vertices choose a subset of potential edges by considering the (estimated) benefits or utilities of the edges. More precisely, each vertex selects k, k ≥ 1, incident edges it wishes to set up, and an undirected edge between two vertices is present in the graph if and only if both of the end vertices choose the edge. First, we examine the scaling law of the smallest k needed for graph connectivity with increasing n and prove that it is (log(n)). Second, we study the diameter of the random graph and demonstrate that, under certain conditions on k, the diameter is close to log(n)/ log(log(n)) with high probability. In addition, as a byproduct of our findings, we show that, for all sufficiently large n, if k > β log(n), where β ≈ 2.4626, there exists a connected Erdös-Rényi random graph that is embedded in our random graph, with high probability.

show abstract

“…Various methods have been studied in considerable detail by both the statistics and database communities [1,4,15,29]. Detailed survey on clustering methods can be found in Refs.…”

Section: Different Approaches To Clusteringmentioning

confidence: 99%

Finding groups in data: Cluster analysis with ants

Boryczka¹

2009

Applied Soft Computing

View full text Add to dashboard Cite

Connectivity of the mutual k-nearest-neighbor graph in clustering and outlier detection

Cited by 208 publications

References 6 publications

A graph-based estimator of the number of clusters

A graph-based estimator of the number of clusters

A New Random Graph Model with Self-Optimizing Nodes: Connectivity and Diameter

Finding groups in data: Cluster analysis with ants

Contact Info

Product

Resources

About