A 3D Clinical Face Phenotype Space of Genetic Syndromes Using a Triplet-Based Singular Geometric Autoencoder

Abstract

Clinical diagnosis of syndromes benefits strongly from objective facial phenotyping. This study introduces a novel approach to enhance clinical diagnosis through the development and exploration of a low-dimensional metric space referred to as the clinical face phenotypic space (CFPS). As a facial matching tool for clinical genetics, such CFPS can enhance clinical diagnosis. It helps to interpret facial dysmorphisms of a subject by placing them within the space of known dysmorphisms. In this paper, a triplet loss-based autoencoder developed by geometric deep learning (GDL) is trained using multi-task learning, which combines supervised and unsupervised learning approaches. Experiments are designed to illustrate the following properties of CFPSs that can aid clinicians in narrowing down their search space: a CFPS can 1) classify syndromes accurately, 2) generalize to novel syndromes, and 3) preserve the relatedness of genetic diseases, meaning that clusters of phenotypically similar disorders reflect functional relationships between genes. The proposed model consists of three main components: an encoder based on GDL optimizing distances between groups of individuals in the CFPS, a decoder enhancing classification by reconstructing faces, and a singular value decomposition layer maintaining orthogonality and optimal variance distribution across dimensions. This allows for the selection of an optimal number of CFPS dimensions as well as improving the classification capacity of the CFPS, which outperforms the linear metric learning baseline in both syndrome classification and generalization to novel syndromes. We further proved the usefulness of each component of the proposed framework, highlighting their individual impact. From a clinical perspective, the unique combination of these properties in a single CFPS results in a powerful tool that can be incorporated into current clinical practices to assess facial dysmorphism.

Keywords: 3D shape analysis; clinical genetics; computer-aided diagnosis; deep phenotyping; geometric deep learning; precision public health.

FIGURE 1.

The complete model consists of three main components: a triplet-based encoder, a singular value decomposition (SVD) layer, and a decoder. Projection function $P_{\mathit{\text{SGE}}}$ for geometric model (alternatively $P_{\mathit{\text{LDA}}}$ for baseline) projects a facial mesh f into a facial embedding $e$ in the CFPS. A facial mesh $f^{\prime }$ is reconstructed from the embedding e with decoding function $p_{\mathit{\text{SGD}}}$. Note that the reconstruction is not possible within the baseline and TB-GAE. Classification from the embedding space into syndrome groups is performed by a classification function g, which in this work constitutes a balanced K-nearest-neighbor classifier.

FIGURE 2.

The architecture of a singular geometric autoencoder (SGAE) with a singular value decomposition (SVD) layer. $\Lambda$ contains right singular vectors of the SVD. Once trained, the geometric encoder constitutes the projection function $P_{\mathit{\text{SGE}}}$, and the geometric decoder constitutes the decoding function $P_{\mathit{\text{SGD}}}$.

FIGURE 3.

Experiment one - Classification Performances: (a) Individual-based top-$S$ accuracy plots for TB-SGAE, TB-GAE, TB-SGE, and the baseline $(S\le 10)$; (b) Individual-based top-$S$ accuracy plot for TB-SGAE ($S\le 10$) separated by categories (A, B, C, and controls); (c) Classification metrics based on a balanced KNN classifier with $K=10$; (d) The average group-level metrics for all groups in categories A, B, and C based on TB-SGAE.

FIGURE 4.

(a) PLS regression of accuracy onto phenotypic predictors and sample size. (b) 2D UMAP visualization of the trainset (smaller dots, and test set (larger dots) into the space, colored by categories. (c) Colored 2D UMAP visualization of the four RASopathies together with the rest of the trainset (smaller dots) and test set (larger dots) colored in black.

FIGURE 5.

(a) The training error of reconstruction (left) and out-of-fold error of reconstruction (right); (b) The reconstruction of the average embedding of individuals with Achondroplasia, Wolf Hirschhorn, Apert, and Williams using the geometric decoder; (c) The comparison of the clustering improvement factor (CIF) for individuals in the six left-out groups of the generalization test (experiment 3), projected to the CFPSs obtained by TB-SGAE, PCA+LDA (baseline), and PCA. Error bars indicate the standard error of the mean over five folds.