Projective Clustering Algorithm

A Projective Clustering Algorithm is a Subspace Clustering Algorithm that is based on project clusters.

• AKA: Projected Cluster Algorithm.
• Context:
  • It can be implemented by a Projective Clustering System to solve a Projective Clustering Task.
• Example(s):
  • BIRCH Algorithm,
  • DBSCAN Algorithm,
  • EPCH Algorithm,
  • OPTICS Algorithm,
  • ORCLU Algorithm,
  • PROCLUS Algorithm.
  • …
• Counter-Example(s):
  • k-Means Clustering Algorithm,
  • KD-Tree Clustering Algorithm,
  • DBSCAN Clustering Algorithm,
  • E-M Algorithm.
• See: Clustering Algorithm, Projective Clustering Ensemble, Projection, Projected Set.

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References

2020

• (Maalouf et al., 2020) ⇒ Alaa Maalouf, Harry Lang, Daniela Rus, and Dan Feldman (2020). "Deep Learning Meets Projective Clustering". In: arXiv preprint arXiv:2010.04290.

2013

• (Gullo et al., 2013) ⇒ Francesco Gullo, Carlotta Domeniconi, and Andrea Tagarelli (2013). "Projective Clustering Ensembles". In: Data Mining and Knowledge Discovery, 26(3), 452-511.
  • QUOTE: Traditional feature selection and extraction methods aim to reduce the number of dimensions, but they treat the dataset as a whole; consequently, some dimensions potentially relevant for part of the data may be filtered out. Projective clustering (...) aims to discover clusters which correspond to subsets of the input data and have different (possibly overlapping) dimensional subspaces associated to them. Projected clusters tend to be less noisy — because each group of data is represented over a subspace which does not contain irrelevant dimensions — and more understandable — because the exploration of a cluster is easier as fewer dimensions are involved.

2008

• (Moise et al., 2008) ⇒ Gabriela Moise, Jorg Sander, and Martin Ester (2008). "Robust Projected Clustering". In: Knowledge and Information Systems, 14(3), 273-298.
  • QUOTE: Existing projected clustering algorithms are either based on the computation of k initial clusters in full dimensional space, or leverage the idea that clusters with as many relevant attributes as possible are preferable. Consequently, these algorithms are likely to be less effective in the practically most interesting case of projected clusters with very few relevant attributes, because the members of such clusters are likely to have low similarity in full dimensional space. Furthermore, a re-occurring weakness of these algorithms is that their performance depends greatly on a series of parameters whose appropriate values are difficult to anticipate by the users (e.g., the true number of projected clusters or the average dimensionality of subspaces where clusters exist). Finally, projected clusters are, by definition, disjoint. However, a data point may satisfy the signature of more than one projected cluster. Projected clustering is not able to capture this type of information.

2005a

• (Ng et al., 2005) ⇒ Eric Ka Ka Ng, Ada Wai-chee Fu, and Raymond Chi-Wing Wong (2005). "Projective Clustering by Histograms". In: IEEE Transactions on Knowledge and Data Engineering, 17(3), 369-383.
  • QUOTE: Projective clustering algorithms such as PROCLUS in (...), and ORCLUS in (...) have been shown to give good quality result, and continue to attract new ideas, such as those in (...). PROCLUS and ORCLUS aim at discovering projected clusters with different properties. PROCLUS discovers groups of data objects located closely in each of the related dimensions in its associated subspace.

2005b

• (Yiu & Mamoulis, 2005) ⇒ Man Lung Yiu, and Nikos Mamoulis (2005). "Iterative Projected Clustering by Subspace Mining". In: IEEE Transactions on Knowledge and Data Engineering, 17(2), 176-189.

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