# On evolutionary subspace clustering with symbiosis

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## Abstract

Subspace clustering identifies the attribute support for each cluster as well as identifying the location and number of clusters. In the most general case, attributes associated with each cluster could be unique. A multi-objective evolutionary method is proposed to identify the unique attribute support of each cluster while detecting its data instances. The proposed algorithm, symbiotic evolutionary subspace clustering (S-ESC) borrows from ‘symbiosis’ in the sense that each clustering solution is defined in terms of a host (single member of the host population) and a number of coevolved cluster centroids (or symbionts in an independent symbiont population). Symbionts define clusters and therefore attribute subspaces, whereas hosts define sets of clusters to constitute a non-degenerate solution. The symbiotic representation of S-ESC is the key to making it scalable to high-dimensional datasets, while an integrated subsampling process makes it scalable to tasks with a large number of data items. Benchmarking is performed against a test suite of 59 subspace clustering tasks with four well known comparator algorithms from both the full-dimensional and subspace clustering literature: EM, MINECLUS, PROCLUS, STATPC. Performance of the S-ESC algorithm was found to be robust across a wide cross-section of properties with a common parameterization utilized throughout. This was not the case for the comparator algorithms. Specifically, performance could be sensitive to the particular data distribution or parameter sweeps might be necessary to provide comparable performance. An additional evaluation is performed against a non-symbiotic GA, with S-ESC still returning superior clustering solutions.

### Keywords

Subspace clustering Evolutionary multi-objective optimization Symbiosis## Notes

### Acknowledgment

The authors gratefully acknowledge support from the NSERC Discovery grant, NSERC RTI and CFI New Opportunities programs (Canada).

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