Skip to main content

Cascade–Correlation

  • Living reference work entry
  • Latest version View entry history
  • First Online:
Encyclopedia of Machine Learning and Data Science

Synonyms

Cascor; CC

Definition

Cascade–correlation (often abbreviated as “Cascor” or “CC”) is a supervised learning algorithm for artificial neural networks. It is related to the back-propagation algorithm (“backprop”). CC differs from backprop in that a CC network begins with no hidden units and then adds units one by one, as needed during learning.

Each new hidden unit is trained to correlate with residual error in the network built so far. When it is added to the network, the new unit is frozen, in the sense that its input weights are fixed. The hidden units form a cascade: each new unit receives weighted input from all the original network inputs and from the output of every previously created hidden unit. This cascading creates a network that is as deep as the number of hidden units. Stated another way, the CC algorithm is capable of efficiently creating complex, higher-order nonlinear basis functions – the hidden units – which are then combined to form the desired outputs.

The...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Recommended Reading

  • Baluja S, Fahlman SE (1994) Reducing network depth in the cascade-correlation learning architecture. School of Computer Science, Carnegie Mellon University, Pittsburgh

    Google Scholar 

  • Buckingham D, Shultz TR (2000) The developmental course of distance, time, and velocity concepts: a generative connectionist model. J Cogn Dev 1:305–345

    Article  Google Scholar 

  • Dandurand F, Berthiaume V, Shultz TR (2007) A systematic comparison of flat and standard cascade-correlation using a student-teacher network approximation task. Connect Sci 19:223–244

    Article  Google Scholar 

  • Denison S, Xu F (2010) Twelve- to 14-month-old infants can predict single-event probability with large set sizes. Dev Sci 13(5):798–803

    Article  Google Scholar 

  • Denison S, Xu F (2014) The origins of probabilistic inference in human infants. Cognition 130(3):335–347

    Article  Google Scholar 

  • Denison S, Reed C, Xu F (2013) The emergence of probabilistic reasoning in very young infants: evidence from 4.5- and 6-month-olds. Dev Psychol 49(2):243–249

    Article  Google Scholar 

  • Fahlman SE (1988) Faster-learning variations on back-propagation: an empirical study. In: Touretzky DS, Hinton GE, Sejnowski TJ (eds) Proceedings of the 1988 connectionist models summer school. Morgan Kaufmann, Los Altos, pp 38–51

    Google Scholar 

  • Fahlman SE (1991) The recurrent cascade-correlation architecture. In: Touretzky DS (ed) Advances in neural information processing systems, vol 3. Morgan Kaufmann, Los Altos

    Google Scholar 

  • Fahlman SE, Lebiere C (1990) The cascade-correlation learning architecture. In: Touretzky DS (ed) Advances in neural information processing systems, vol 2. Morgan Kaufmann, Los Altos, pp 524–532

    Google Scholar 

  • Gerken L, Balcomb F, Minton J (2011) Infants avoid “labouring in vain” by attending more to learnable than unlearnable linguistic patterns. Dev Sci 14(5):972–979

    Article  Google Scholar 

  • Justesen N, Bontrager P, Togelius J, Risi S (2019) Deep learning for video game playing. IEEE Trans on Games 12(1):1–20

    Article  Google Scholar 

  • Kharratzadeh M, Shultz T (2016) Neural implementation of probabilistic models of cognition. Cogn Syst Res 40:99–113

    Article  Google Scholar 

  • Mareschal D, Shultz TR (1999) Development of children’s seriation: a connectionist approach. Connect Sci 11:149–186

    Article  Google Scholar 

  • Marquez E, Hare J, Niranjan M (2018) Deep cascade learning. IEEE Trans Neural Networks Learn Syst 29(11):5475–5485

    Article  MathSciNet  Google Scholar 

  • Nobandegani AS, Shultz TR (2017) Converting cascade-correlation neural nets into probabilistic generative models. Proceedings of the 39th Annual Meeting Cognitive Science Society, pp 1029–1034

    Google Scholar 

  • Nobandegani AS, Shultz TR (2018) Example generation under constraints using cascade correlation neural nets. Proceedings of the 40th Annual Meeting Cognitive Science Society, pp 2385–2390

    Google Scholar 

  • Oshima-Takane Y, Takane Y, Shultz TR (1999) The learning of first and second pronouns in English: network models and analysis. J Child Lang 26:545–575

    Article  Google Scholar 

  • Schlimm D, Shultz TR (2009) Learning the structure of abstract groups. In: Taatgen NA, Rijn HV (eds) Proceedings of the 31st annual conference of the cognitive science society. Cognitive Science Society, Austin, pp 2950–2955

    Google Scholar 

  • Shultz TR (1998) A computational analysis of conservation. Dev Sci 1:103–126

    Article  Google Scholar 

  • Shultz TR (2003) Computational developmental psychology. MIT, Cambridge

    Google Scholar 

  • Shultz TR (2006) Constructive learning in the modeling of psychological development. In: Munakata Y, Johnson MH (eds) Processes of change in brain and cognitive development: attention and performance XXI. Oxford University Press, Oxford, pp 61–86

    Google Scholar 

  • Shultz TR, Bale AC (2006) Neural networks discover a near-identity relation to distinguish simple syntactic forms. Mind Mach 16:107–139

    Article  Google Scholar 

  • Shultz TR, Cohen LB (2004) Modeling age differences in infant category learning. Infancy 5:153–171

    Article  Google Scholar 

  • Shultz TR, Doty E (2014) Knowing when to quit on unlearnable problems: another step towards autonomous learning. In: Mayor J, Gomez P (eds) Computational models of cognitive processes. World Scientific, London, pp 211–221

    Chapter  Google Scholar 

  • Shultz TR, Nobandegani AS (2021) A computational model of infant learning and reasoning with probabilities. Psychol Rev. https://doi.org/10.1037/rev0000322

  • Shultz TR, Rivest F (2001) Knowledge-based cascade-correlation: using knowledge to speed learning. Connect Sci 13:1–30

    Article  Google Scholar 

  • Shultz TR, Takane Y (2007) Rule following and rule use in simulations of the balance-scale task. Cognition 103:460–472

    Article  Google Scholar 

  • Shultz TR, Vogel A (2004) A connectionist model of the development of transitivity. In: Proceedings of the twenty-sixth annual conference of the cognitive science society. Erlbaum, Mahwah, pp 1243–1248.

    Google Scholar 

  • Shultz TR, Mareschal D, Schmidt WC (1994) Modeling cognitive development on balance scale phenomena. Mach Learn 16:57–86

    Google Scholar 

  • Shultz TR, Rivest F, Egri L, Thivierge J-P, Dandurand F (2007) Could knowledge-based neural learning be useful in developmental robotics? The case of KBCC. Int J Humanoid Robot 4:245–279

    Article  Google Scholar 

  • Sirois S, Shultz TR (1998) Neural network modeling of developmental effects in discrimination shifts. J Exp Child Psychol 71:235–274

    Article  Google Scholar 

  • Xu F, Garcia V (2008) Intuitive statistics by 8-month-old infants. Proc Natl Acad Sci 105(13):5012–5015

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Thomas R. Shultz .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Science+Business Media, LLC, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Shultz, T.R., Nobandegani, A.S., Fahlman, S.E. (2022). Cascade–Correlation. In: Phung, D., Webb, G.I., Sammut, C. (eds) Encyclopedia of Machine Learning and Data Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-7502-7_33-2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-7502-7_33-2

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4899-7502-7

  • Online ISBN: 978-1-4899-7502-7

  • eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Chapter history

  1. Latest

    Cascade–Correlation
    Published:
    27 April 2022

    DOI: https://doi.org/10.1007/978-1-4899-7502-7_33-2

  2. Original

    Cascade-Correlation
    Published:
    17 February 2015

    DOI: https://doi.org/10.1007/978-1-4899-7502-7_33-1