# On Exploring Complex Relationships of Correlation Clusters

@article{Achtert2007OnEC, title={On Exploring Complex Relationships of Correlation Clusters}, author={Elke Achtert and C. B{\"o}hm and Hans-Peter Kriegel and Peer Kr{\"o}ger and Arthur Zimek}, journal={19th International Conference on Scientific and Statistical Database Management (SSDBM 2007)}, year={2007}, pages={7-7} }

In high dimensional data, clusters often only exist in arbitrarily oriented subspaces of the feature space. In addition, these so-called correlation clusters may have complex relationships between each other. For example, a correlation cluster in a 1-D subspace (forming a line) may be enclosed within one or even several correlation clusters in 2-D superspaces (forming planes). In general, such relationships can be seen as a complex hierarchy that allows multiple inclusions, i.e. clusters may be… Expand

#### 58 Citations

Local graph based correlation clustering

- Computer Science
- Knowl. Based Syst.
- 2017

Local Graph Based Correlation Clustering (LGBACC) is an efficient and scalable approach that produces high-quality clusters in high-dimensional and large data spaces and uses graph models to visualize the results. Expand

Finding the Optimal Subspace for Clustering

- Mathematics, Computer Science
- 2014 IEEE International Conference on Data Mining
- 2014

This paper develops the mathematical foundation ORT (Optimal Rigid Transform) to determine an arbitrarily-oriented subspace, suitable for a given cluster structure, and proposes FOSSCLU (Finding the Optimal Sub Space for Clustering), a new iterative clustering algorithm. Expand

Subspace clustering for complex data

- Computer Science
- BTW
- 2012

This work introduces novel methods for effective subspace clustering on various types of complex data: vector data, imperfect data, and graph data and proposes models whose solutions contain only non-redundant and, thus, valuable clusters. Expand

Detecting clusters in moderate-to-high dimensional data: subspace clustering, pattern-based clustering, and correlation clustering

- Computer Science
- Proc. VLDB Endow.
- 2008

This tutorial tries to clarify the different problem definitions related to subspace clustering in general, the specific difficulties encountered in this field of research, the varying assumptions, heuristics, and intuitions forming the basis of different approaches, and how several prominent solutions essentially tackle different problems. Expand

Hierarchical Subspace Clustering

- Computer Science
- 2007

The goal of this dissertation is to develop new efficient and effective methods for hierarchical subspace clustering by identifying novel challenges for the hierarchical approach and proposing innovative and solid solutions for these challenges. Expand

Hierarchical Subspace Clustering

- Mathematics
- 2007

It is well-known that traditional clustering methods considering all dimensions of the feature space usually fail in terms of efficiency and effectivity when applied to high-dimensional data. This… Expand

Clustering high-dimensional data: A survey on subspace clustering, pattern-based clustering, and correlation clustering

- Mathematics, Computer Science
- TKDD
- 2009

This survey tries to clarify the different problem definitions related to subspace clustering in general; the specific difficulties encountered in this field of research; the varying assumptions, heuristics, and intuitions forming the basis of different approaches; and how several prominent solutions tackle different problems. Expand

Subspace correlation clustering: finding locally correlated dimensions in subspace projections of the data

- Mathematics, Computer Science
- KDD
- 2012

This work introduces the novel paradigm of subspace correlation clustering, which allows multiple overlapping clusters in general but simultaneously avoids redundant clusters deducible from already known correlations, and introduces the algorithm SSCC that exploits different pruning techniques to efficiently generate a subspace correlations clustering. Expand

KLNCC: A new nonlinear correlation clustering algorithm based on KL-divergence

- Computer Science
- 2008 8th IEEE International Conference on Computer and Information Technology
- 2008

KLNCC, a novel nonlinear correlation clustering algorithm which adopts a dynamic two-phase approach and adopts the KL-divergence as the distance between two microclusters when using the EM clustering algorithms to find the microcl clusters. Expand

Detecting Arbitrarily Oriented Subspace Clusters in Data Streams Using Hough Transform

- Computer Science
- PAKDD
- 2020

The CashStream algorithm is proposed that unites state-of-the-art stream processing techniques and additionally relies on the Hough transform to detect arbitrarily oriented subspace clusters in high-dimensional data streams. Expand

#### References

SHOWING 1-10 OF 25 REFERENCES

Mining Hierarchies of Correlation Clusters

- Computer Science
- 18th International Conference on Scientific and Statistical Database Management (SSDBM'06)
- 2006

The algorithm HiCO (hierarchical correlation ordering), the first hierarchical approach to correlation clustering, is proposed, which determines the cluster hierarchy, and visualizes it using correlation diagrams. Expand

Detection and Visualization of Subspace Cluster Hierarchies

- Computer Science
- DASFAA
- 2007

The algorithm DiSH (Detecting Subspace cluster Hierarchies) is proposed that improves in the following points over existing approaches: first, DiSH can detect clusters in subspaces of significantly different dimensionality, and second, it uncovers complex hierarchies of nested subspace clusters, i.e. clusters in lower-dimensional subspace that are embedded within higher-dimensionalSubspace clusters. Expand

CURLER: finding and visualizing nonlinear correlation clusters

- Computer Science
- SIGMOD '05
- 2005

An algorithm for finding and visualizing nonlinear correlation clusters in the subspace of high-dimensional databases using a novel concept called co-sharing level which captures both spatial proximity and cluster orientation when judging similarity between clusters. Expand

Computing Clusters of Correlation Connected objects

- Computer Science
- SIGMOD '04
- 2004

This paper proposes a method called 4C (Computing Correlation Connected Clusters), based on a combination of PCA and density-based clustering, to identify local subgroups of the data objects sharing a uniform but arbitrarily complex correlation. Expand

OP-cluster: clustering by tendency in high dimensional space

- Mathematics, Computer Science
- Third IEEE International Conference on Data Mining
- 2003

A flexible yet powerful clustering model, namely OP-cluster (Order Preserving Cluster), which is essential in revealing significant gene regulatory networks and its effectiveness and efficiency in detecting coregulated patterns is demonstrated. Expand

Density-Connected Subspace Clustering for High-Dimensional Data

- Mathematics, Computer Science
- SDM
- 2004

SUBCLU (density-connected Subspace Clustering), an effective and efficient approach to the subspace clustering problem, based on a formal clustering notion using the concept of density-connectivity underlying the algorithm DBSCAN [EKSX96]. Expand

/spl delta/-clusters: capturing subspace correlation in a large data set

- Computer Science
- Proceedings 18th International Conference on Data Engineering
- 2002

The /spl delta/-cluster model takes the bicluster model as a special case, where the FLOC algorithm performs far superior to the bICluster algorithm, and is devised to efficiently produce a near-optimal clustering results. Expand

Finding generalized projected clusters in high dimensional spaces

- SIGMOD '00
- 2000

High dimensional data has always been a challenge for clustering algorithms because of the inherent sparsity of the points. Recent research results indicate that in high dimensional data, even the… Expand

Finding Generalized Projected Clusters In High Dimensional Spaces

- Computer Science
- SIGMOD Conference
- 2000

Very general techniques for projected clustering are discussed which are able to construct clusters in arbitrarily aligned subspaces of lower dimensionality, which is substantially more general and realistic than currently available techniques. Expand

Clustering by pattern similarity in large data sets

- Computer Science
- SIGMOD '02
- 2002

This paper introduces an effective algorithm to detect clusters of genes that are essential in revealing significant connections in gene regulatory networks, and performs tests on several real and synthetic data sets to show its effectiveness. Expand