Abstract :
[en] Introduction:
It has been shown that machine-learning methods applied to voxel-based morphometry (VBM) data allows the prediction of brain age [1]. Dimensionality reduction is a critical aspect of such brain-based prediction of phenotypical characteristics to counter the curse of dimensionality associated with voxel-wise analysis. While previous age-predictions have employed PCA based compression, non-negative matrix factorization (NNMF) has recently been suggested as a plausible factorization of high-dimensional VBM data [4]. Non-negativity and sparsity of the components obtained from NNMF facilitate relatively more optimal solution than the PCA based compression [4]. Here, we evaluate, i) whether NNMF compression allows predictions of biological age that reproduce those from previously reported analyses [2], ii) the impact of the NNMF’s granularity on the prediction accuracy, iii) the possible effect of the factorizations derived from different datasets on the prediction, and iv) whether explicit adjustment can address the model bias inherent to many brain-based predictions.
Methods:
VBM8 preprocessing (using only non-linear modulation and 8 mm FWHM smoothing [3]) was used to compute voxel-wise GM volumes for two datasets, 1) 693 healthy older adults (age: 55-75 years) scanned at a single site (“1000BRAINS) [1], 2) 1084 healthy adults (age: 18-81 years), scanned at multiple sites (“Mixed”) (Fig 1A). NNMF solutions for both groups were derived at different levels of granularity. Age prediction was performed by fitting LASSO regression models either on the coefficient matrix from the respective NNMF or by those that were derived from projecting a group’s data on the respective other groups components. Model generalization was evaluated by 10-fold cross-validation replicated 25 times. To address the known bias towards the mean, i.e., overestimation of young and underestimation of older subjects, we additionally tested models that explicitly fitted the regression-slope between the real and predicted training set and used this to adjust the expected slope of the test set to 45 degrees.
Results:
In both datasets, NNMF components resembled neurobiologically reasonable patterning of the brain (Fig 1B). Prediction accuracy based on the projection of data on the components from either group was virtually identical (Fig 2A). For both datasets, mean absolute errors (MAE) declined with higher granularity of the components and reached values well comparable to previous approaches even when using components derived from an independent sample (MAE: 3.6 years for 1000BRAINS; 6.4 years for Mixed). Plotting the prediction error relative to the biological age of the subjects revealed the bias towards the mean across both datasets (Fig 2B). Adjusting for the slope estimated in the training set allows removing this bias, though it needs to be noted that this comes at the cost of reduced precision, i.e., unbiased estimates yield a slightly higher MAE.
Conclusion:
NNMF allows the definition of co-variation patterns in VBM data. Due to the non- negativity and sparseness, NNMF enable substantially easier and higher biological interpretation than other methods for data compression such as PCA [4]. We showed that NNMF compression of VBM data over the lifespan allows predicting previously unseen subjects’ age with a precision that is comparable to earlier reports using PCA for data compression [2], while offering the potential for neurobiological interpretation. Importantly, accuracy seems to be independent of whether the components were derived from the same dataset or from a dataset that is not only independent but also different in age distribution. We note that accuracies tend to continuously decrease with higher granularity, although performance tends to plateau at about 300 components. Finally, adjusting the inherent bias of sparse regression models yields unbiased out-of-sample predictions but comes at the expense of slightly higher mean errors.
