Skip to main content

Shape Clustering Using K-Medoids in Architectural Form Finding

Part of the Communications in Computer and Information Science book series (CCIS,volume 1028)


As the number of design candidates in generative systems is often high, there is a need for an articulation mechanism that assists designers in exploring the generated design set. This research aims to condense the solution set yet enhance heterogeneity in generative design systems. Specifically, this work accomplishes the following: (1) introduces a new design articulation approach, a Shape Clustering using K-Medoids (SC-KM) method that is capable of grouping a dataset of shapes with similitude in one cluster and retrieving a representative for each cluster, and (2) incorporate the developed clustering method in architectural form finding. The articulated (condensed) set of shapes can be presented to designers to assist in their decision making. The research methods include formulating an algorithmic set with the implementation of K-Medoids and other algorithms. The results, visualized and discussed in the paper, show accurate clustering in comparison with the expected reference clustering sets.


  • Generative design systems
  • Clustering
  • Form finding
  • K-Medoids

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-981-13-8410-3_32
  • Chapter length: 15 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-981-13-8410-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   139.99
Price excludes VAT (USA)
Fig. 1.

(image courtesy of Kalvelagen [6]).

Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.


  1. Woodbury, R.: Elements of parametric design (2010)

    Google Scholar 

  2. Malkawi, A.M.: Performance simulation: research and tools. In: Performative Architecture: Beyond Instrumentality, pp. 85–96. Spon Press, New York (2005)

    Google Scholar 

  3. Wortmann, T., Nannicini, G.: Introduction to architectural design optimization. In: Karakitsiou, A., Migdalas, A., Rassia, S.T., Pardalos, P.M. (eds.) City Networks. SOIA, vol. 128, pp. 259–278. Springer, Cham (2017).

    CrossRef  Google Scholar 

  4. Aish, R., Woodbury, R.: Multi-level interaction in parametric design. In: Butz, A., Fisher, B., Krüger, A., Olivier, P. (eds.) SG 2005. LNCS, vol. 3638, pp. 151–162. Springer, Heidelberg (2005).

    CrossRef  Google Scholar 

  5. Rodrigues, E., Sousa-Rodrigues, D., de Sampayo, M.T., Gaspar, A.R., Gomes, Á., Antunes, C.H.: Clustering of architectural floor plans: a comparison of shape representations. Autom. Constr. 80, 48–65 (2017)

    CrossRef  Google Scholar 

  6. Kalvelagen, E.: Visualization of large multi-criteria result sets with

  7. Radford, A.D., Gero, J.S.: Design by Optimization in Architecture, Building, and Construction. Wiley, Hoboken (1987)

    Google Scholar 

  8. Brown, N.C., Mueller, C.T.: Quantifying diversity in parametric design: a comparison of possible metrics. AI EDAM 33, 1–14 (2018)

    CrossRef  Google Scholar 

  9. Yousif, S., Clayton, M., Yan, W.: Towards integrating aesthetic variables in architectural design optimization. Presented at the 106th ACSA Annual Meeting, the Ethical Imperative, the Association of Collegiate Schools of Architecture (ACSA) (2018)

    Google Scholar 

  10. Han, J., Pei, J., Kamber, M.: Data Mining: Concepts and Techniques. Elsevier, New York (2011)

    MATH  Google Scholar 

  11. Velmurugan, T., Santhanam, T.: Computational complexity between K-means and K-medoids clustering algorithms for normal and uniform distributions of data points. J. Comput. Sci. 6, 363 (2010)

    CrossRef  Google Scholar 

  12. Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Comput. Surv. (CSUR) 31, 264–323 (1999)

    CrossRef  Google Scholar 

  13. Ward Jr., J.H.: Hierarchical grouping to optimize an objective function. J. Am. Stat. Assoc. 58, 236–244 (1963)

    MathSciNet  CrossRef  Google Scholar 

  14. Zhang, D., Lu, G.: Review of shape representation and description techniques. Pattern Recogn. 37, 1–19 (2004)

    CrossRef  Google Scholar 

  15. Cha, M.Y., Gero, J.S.: Shape pattern recognition using a computable pattern representation. In: Gero, J.S., Sudweeks, F. (eds.) Artificial Intelligence in Design 1998, pp. 169–187. Springer, Dordrecht (1998).

    CrossRef  Google Scholar 

  16. de las Heras, L.-P., Fernández, D., Fornés, A., Valveny, E., Sánchez, G., Lladós, J.: Runlength histogram image signature for perceptual retrieval of architectural floor plans. In: Lamiroy, B., Ogier, J.-M. (eds.) GREC 2013. LNCS, vol. 8746, pp. 135–146. Springer, Heidelberg (2014).

    CrossRef  Google Scholar 

  17. Dutta, A., Lladós, J., Bunke, H., Pal, U.: A product graph based method for dual subgraph matching applied to symbol spotting. In: Lamiroy, B., Ogier, J.-M. (eds.) GREC 2013. LNCS, vol. 8746, pp. 11–24. Springer, Heidelberg (2014).

    CrossRef  Google Scholar 

  18. Brière-Côté, A., Rivest, L., Maranzana, R.: Comparing 3D CAD models: uses, methods, tools and perspectives. Comput.-Aided Des. Appl. 9, 771–794 (2012)

    CrossRef  Google Scholar 

  19. Mills-Tettey, G.A., Stentz, A., Dias, M.B.: The Dynamic Hungarian Algorithm for the Assignment Problem with Changing Costs. Robotics Institute, Pittsburgh (2007)

    Google Scholar 

  20. Wagstaff, K., Cardie, C., Rogers, S., Schrödl, S.: Constrained k-means clustering with background knowledge. Presented at the ICML (2001)

    Google Scholar 

  21. Jin, X., Han, J.: K-Medoids clustering. In: Sammut, C., Webb, G.I. (eds.) Encyclopedia of Machine Learning and Data Mining, pp. 1–3. Springer, Boston (2016).

    CrossRef  Google Scholar 

  22. Yousif, S., Yan, W.: Clustering forms for enhancing architectural design optimization. Presented at the Learning, Adapting and Prototyping, the 23rd Conference of the Association for Computer-Aided Architectural Design Research in Asia (CAADRIA) (2018)

    Google Scholar 

  23. Yousif, S., Yan, W., Culp, C.: Incorporating form diversity into architectural design optimization. Presented at the ACADIA 2017: DISCIPLINES & DISRUPTION [Proceedings of the 37th Annual Conference of the Association for Computer Aided Design in Architecture (ACADIA) (2017)

    Google Scholar 

  24. Funkhouser, T., Kazhdan, M., Min, P., Shilane, P.: Shape-based retrieval and analysis of 3D models. Commun. ACM 48, 58–64 (2005).

    CrossRef  Google Scholar 

  25. Bauckhage, C.: Numpy/Scipy Recipes for Data Science: k-Medoids Clustering, February 2015.

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Shermeen Yousif .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Yousif, S., Yan, W. (2019). Shape Clustering Using K-Medoids in Architectural Form Finding. In: Lee, JH. (eds) Computer-Aided Architectural Design. "Hello, Culture". CAAD Futures 2019. Communications in Computer and Information Science, vol 1028. Springer, Singapore.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-8409-7

  • Online ISBN: 978-981-13-8410-3

  • eBook Packages: Computer ScienceComputer Science (R0)