Author Summary Human brain connectome studies aim at both exploring healthy brains, and analyzing relevant features associated to pathologies of interest. This consists in modeling the brain connectome as a graph and in using graph metrics as features. Such data analysis problems fall in the high-dimension low sample size framework. Our goal is to provide a machine learning technique that exhibits flexibility, gives the investigator grip on the features and covariates, allows visualization, and yields insight into the biological phenomena at stake. The retained approach is dimension reduction in a manifold learning methodology, the originality lying in that several reduced variables be chosen by the investigator. The method sheds light on the differences between brain connectivity graphs using graph metrics and potential clinical interpretations of theses differences. Abstract Human brain connectome studies aim to both explore healthy brains, and extract and analyze relevant features associated with pathologies of interest. Usually this consists of modeling the brain connectome as a graph and using graph metrics as features. A fine brain description requires graph metrics computation at the node level. Given the relatively reduced number of patients in standard cohorts, such data analysis problems fall in the high-dimension, low-sample-size framework. In this context, our goal is to provide a machine learning technique that exhibits flexibility, gives the investigator an understanding of the features and covariates, allows visualization and exploration, and yields insight into the data and the biological phenomena at stake. The retained approach is dimension reduction in a manifold learning methodology; the originality is that the investigator chooses one (or several) reduced variables. The proposed method is illustrated in two studies. The first one addresses comatose patients; the second one compares young and elderly populations. The method sheds light on the differences between brain connectivity graphs using graph metrics and potential clinical interpretations of these differences.

We present a low-dimensional morphospace of fMRI brain networks, where axes are defined in a data-driven manner based on the network motifs. The morphospace allows us to identify the key variations in healthy fMRI networks in terms of their underlying motifs, and we observe that two principal components (PCs) can account for 97% of the motif variability. The first PC of the motif distribution is correlated with efficiency and inversely correlated with transitivity. Hence this axis approximately conforms to the well-known economical small-world trade-off between integration and segregation in brain networks. Finally, we show that the economical clustering generative model proposed by Vértes et al. ( 2012 ) can approximately reproduce the motif morphospace of the real fMRI brain networks, in contrast to other generative models. Overall, the motif morphospace provides a powerful way to visualize the relationships between network properties and to investigate generative or constraining factors in the formation of complex human brain functional networks. Author Summary Motifs have been described as the building blocks of complex networks. Meanwhile, a morphospace allows networks to be placed in a common space and can reveal the relationships between different network properties and elucidate the driving forces behind network topology. We combine the concepts of motifs and morphospaces to create the first motif morphospace of fMRI brain networks. Crucially, the morphospace axes are defined by the motifs, in a data-driven manner. We observe strong correlations between the networks’ positions in morphospace and their global topological properties, suggesting that motif morphospaces are a powerful way to capture the topology of networks in a low-dimensional space and to compare generative models of brain networks. Motif morphospaces could also be used to study other complex networks’ topologies.