We present BALDUR, a novel Bayesian algorithm designed to deal with multi-modal datasets and small sample sizes in high-dimensional settings while providing explainable solutions. To do so, the proposed model combines within a common latent space the different data views to extract the relevant information to solve the classification task and prune out the irrelevant/redundant features/data views. Furthermore, to provide generalizable solutions in small sample size scenarios, BALDUR efficiently integrates dual kernels over the views with a small sample-to-feature ratio. Finally, its linear nature ensures the explainability of the model outcomes, allowing its use for biomarker identification. This model was tested over two different neurodegeneration datasets, outperforming the state-of-the-art models and detecting features aligned with markers already described in the scientific literature.