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Discriminative analysis in neuroimaging by means of deep/machine learning techniques is usually tested with validation techniques, whereas the associated statistical significance remains largely under-developed due to their computational complexity. In this work, a non-parametric framework is proposed that estimates the statistical significance of classifications using deep learning architectures. In particular, a combination of autoencoders (AE) and support vector machines (SVM) is applied to: (i) a one-condition, within-group designs often of normal controls (NC) and; (ii) a two-condition, between-group designs which contrast, for example, Alzheimer's disease (AD) patients with NC (the extension to multi-class analyses is also included). A random-effects inference based on a label permutation test is proposed in both studies using cross-validation (CV) and resubstitution with upper bound correction (RUB) as validation methods. This allows both false positives and classifier overfitting to be detected as well as estimating the statistical power of the test. Several experiments were carried out using the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, the Dominantly Inherited Alzheimer Network (DIAN) dataset, and a MCI prediction dataset. We found in the permutation test that CV and RUB methods offer a false positive rate close to the significance level and an acceptable statistical power (although lower using cross-validation). A large separation between training and test accuracies using CV was observed, especially in one-condition designs. This implies a low generalization ability as the model fitted in training is not informative with respect to the test set. We propose as solution by applying RUB, whereby similar results are obtained to those of the CV test set, but considering the whole set and with a lower computational cost per iteration., Comment: 26 pages, 10 figures, 13 tables

Converging evidence shows that disease-relevant brain alterations do not appear in random brain locations, instead, its spatial pattern follows large scale brain networks. In this context, a powerful network analysis approach with a mathematical foundation is indispensable to understand the mechanism of neuropathological events spreading throughout the brain. Indeed, the topology of each brain network is governed by its native harmonic waves, which are a set of orthogonal bases derived from the Eigen-system of the underlying Laplacian matrix. To that end, we propose a novel connectome harmonic analysis framework to provide enhanced mathematical insights by detecting frequency-based alterations relevant to brain disorders. The backbone of our framework is a novel manifold algebra appropriate for inference across harmonic waves that overcomes the limitations of using classic Euclidean operations on irregular data structures. The individual harmonic difference is measured by a set of common harmonic waves learned from a population of individual Eigen systems, where each native Eigen-system is regarded as a sample drawn from the Stiefel manifold. Specifically, a manifold optimization scheme is tailored to find the common harmonic waves which reside at the center of Stiefel manifold. To that end, the common harmonic waves constitute the new neuro-biological bases to understand disease progression. Each harmonic wave exhibits a unique propagation pattern of neuro-pathological burdens spreading across brain networks. The statistical power of our novel connectome harmonic analysis approach is evaluated by identifying frequency-based alterations relevant to Alzheimer's disease, where our learning-based manifold approach discovers more significant and reproducible network dysfunction patterns compared to Euclidian methods.