Background and objective. In medical imaging, population studies have to overcome the differences that exist between individuals to identify invariant image features that can be used for diagnosis purposes. In functional neu-roimaging, an appealing solution to identify neural coding principles that hold at the population level is inter-subject pattern analysis, i.e. to learn a predictive model on data from multiple subjects and evaluate its generalization performance on new subjects. Although it has gained popularity in recent years, its widespread adoption is still hampered by the blatant lack of a formal definition in the literature. In this paper, we precisely introduce the first principled formalization of inter-subject pattern analysis targeted at multivariate group analysis of functional neuroimaging. Methods. We propose to frame inter-subject pattern analysis as a multi-source transductive transfer question, thus grounding it within several well defined machine learning settings and broadening the spectrum of usable algorithms. We describe two sets of inter-subject brain decoding experiments that use several open datasets: a magneto-encephalography study with 16 subjects and a functional magnetic resonance imaging paradigm with 100 subjects. We assess the relevance of our framework by performing model comparisons, where one brain decoding model exploits our formalization while others do not. Results. The first set of experiments demonstrates the superiority of a brain decoder that uses subject-by-subject standardization compared to state of the art models that use other standardization schemes, making the case for the interest of the transductive and the multi-source components of our formalization The second set of experiments quantitatively shows that, even after such transformation, it is more difficult for a brain decoder to generalize to new participants rather than to new data from participants available in the training phase, thus highlighting the transfer gap that needs to be overcome. Conclusion. This paper describes the first formalization of inter-subject pattern analysis as a multi-source trans-ductive transfer learning problem. We demonstrate the added value of this formalization using proof-of-concept experiments on several complementary functional neuroimaging datasets. This work should contribute to popularize inter-subject pattern analysis for functional neuroimaging population studies and pave the road for future methodolog-ical innovations.