It is challenging to characterize and classify normal and abnormal brain development during early childhood. To reduce the complexity of heterogeneous data population, manifold learning techniques are increasingly applied, which find a low-dimensional representation of the data, while preserving all relevant information. The neighborhood definition used for constructing manifold representations of the population is crucial for preserving the similarity structure and it is highly application dependent. The recently proposed neighborhood approximation forests learn a neighborhood structure in a dataset based on a user-defied distance. We propose a framework to learn multiple pairwise distances in a population of brain images and to combine them in an unsupervised manner optimally in a manifold learning step. Unlike other methods that only use a univariate distance measure, our method allows for a natural combination of multiple distances from heterogeneous sources. As a result, it yields a representation of the population that preserves the multiple distances. Furthermore, our method also selects the most predictive features associated with the distances. We evaluate our method in neonatal magnetic resonance images of three groups (term controls, patients affected by intrauterine growth restriction and mild isolated ventriculomegaly). We show that combining multiple distances related to the condition improves the overall characterization and classifcation of the three clinical groups compared to the use of single distances and classical unsupervised manifold learning.

V. A. Zimmer is supported by the grant FI-DGR 2013 (2013 FI B00159) from the Generalitat de Catalunya. This research was partially funded by the Spanish Ministry of Economy and Competitiveness (TIN2012-35874). This study was also supported by Instituto de Salud Carlos III (PI16/00861), integrated in the Plan Nacional de I+D+I and co-financed by ISCIII-Subdirección General de Evaluación and Fondo Europeo de Desarrollo Regional (FEDER) \Una manera de hacer Europa"; additionally, the research leading to these results has received funding from \la Caixa" Foundation.