Journal of Signal Processing Systems

, Volume 91, Issue 2, pp 191–215 | Cite as

Multi-Output Tree Chaining: An Interpretative Modelling and Lightweight Multi-Target Approach

  • Saulo Martiello MasteliniEmail author
  • Victor Guilherme Turrisi da Costa
  • Everton Jose Santana
  • Felipe Kenji Nakano
  • Rodrigo Capobianco Guido
  • Ricardo Cerri
  • Sylvio BarbonJr.


Multi-target regression (MTR) regards predictive problems with multiple numerical targets. To solve this, machine learning techniques can model solutions treating each target as a separated problem based only on the input features. Nonetheless, modelling inter-target correlation can improve predictive performance. When performing MTR tasks using the statistical dependencies of targets, several approaches put aside the evaluation of each pair-wise correlation between those targets, which may differ for each problem. Besides that, one of the main drawbacks of the current leading MTR method is its high memory cost. In this paper, we propose a novel MTR method called Multi-output Tree Chaining (MOTC) to overcome the mentioned disadvantages. Our method provides an interpretative internal tree-based structure which represents the relationships between targets denominated Chaining Trees (CT). Different from the current techniques, we compute the outputs dependencies, one-by-one, based on the Random Forest importance metric. Furthermore, we proposed a memory friendly approach which reduces the number of required regression models when compared to a leading method, reducing computational cost. We compared the proposed algorithm against three MTR methods (Single-target - ST; Multi-Target Regressor Stacking - MTRS; and Ensemble of Regressor Chains - ERC) on 18 benchmark datasets with two base regression algorithms (Random Forest and Support Vector Regression). The obtained results show that our method is superior to the ST approach regarding predictive performance, whereas, having no significant difference from ERC and MTRS. Moreover, the interpretative tree-based structures built by MOTC pose as great insight on the relationships among targets. Lastly, the proposed solution used significantly less memory than ERC being very similar in predictive performance.


Multi-target regression Multi-output Memory-friendly algorithm Interpretative tree structure Machine learning 



The authors would like to thank CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) and FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) for financial support.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Saulo Martiello Mastelini
    • 1
    Email author
  • Victor Guilherme Turrisi da Costa
    • 1
  • Everton Jose Santana
    • 2
  • Felipe Kenji Nakano
    • 3
  • Rodrigo Capobianco Guido
    • 4
  • Ricardo Cerri
    • 3
  • Sylvio BarbonJr.
    • 1
  1. 1.Computer Science DepartmentState University of Londrina. Rodovia Celso Garcia Cid, Km 380, s/n - Campus UniversitárioLondrinaBrazil
  2. 2.Electrical Engineering DepartmentState University of Londrina. Rodovia Celso Garcia Cid, Km 380, s/n - Campus UniversitárioLondrinaBrazil
  3. 3.Department of Computer ScienceFederal University of São Carlos, Rodovia Washington LuísSão CarlosBrazil
  4. 4.Instituto de Biociências, Letras e Ciências ExatasUnesp - Univ Estadual Paulista (São Paulo State University)São José do Rio PretoBrazil

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