Random Forest regression for manifold-valued responses

Dimosthenis Tsagkrasoulis, Giovanni Montana

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)
219 Downloads (Pure)


An increasing array of biomedical and computer vision applications requires the predictive modeling of complex data, for example images and shapes. The main challenge when predicting such objects lies in the fact that they do not comply to the assumptions of Euclidean geometry. Rather, they occupy non-linear spaces, a.k.a. manifolds, where it is difficult to define concepts such as coordinates, vectors and expected values. In this work, we construct a non-parametric predictive methodology for manifold-valued objects, based on a distance modification of the Random Forest algorithm. Our method is versatile and can be applied both in cases where the response space is a well-defined manifold, but also when such knowledge is not available. Model fitting and prediction phases only require the definition of a suitable distance function for the observed responses. We validate our methodology using simulations and apply it on a series of illustrative image completion applications, showcasing superior predictive performance, compared to various established regression methods.
Original languageEnglish
Early online date7 Nov 2017
Publication statusE-pub ahead of print - 7 Nov 2017


  • Manifold regression
  • Random Forest
  • Distance-based data analysis


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