Variational autoencoder provides proof of concept that compressing CDT to extremely low-dimensional space retains its ability of distinguishing dementia

Abstract

The clock drawing test (CDT) is an inexpensive tool to screen for dementia. In this study, we examined if a variational autoencoder (VAE) with only two latent variables can capture and encode clock drawing anomalies from a large dataset of unannotated CDTs (n = 13,580) using self-supervised pre-training and use them to classify dementia CDTs (n = 18) from non-dementia CDTs (n = 20). The model was independently validated using a larger cohort consisting of 41 dementia and 50 non-dementia clocks. The classification model built with the parsimonious VAE latent space adequately classified dementia from non-dementia (0.78 area under receiver operating characteristics (AUROC) in the original test dataset and 0.77 AUROC in the secondary validation dataset). The VAE-identified atypical clock features were then reviewed by domain experts and compared with existing literature on clock drawing errors. This study shows that a very small number of latent variables are sufficient to encode important clock drawing anomalies that are predictive of dementia.

Trial registration: ClinicalTrials.gov NCT01986577 NCT03175302.

Conflict of interest statement

The authors declare no competing interests.

© 2022. The Author(s).

Figures

Figure 1

Distribution of reconstructed clocks in the VAE latent space. (A) Clock drawing reconstructions are represented as a function of the two VAE latent dimensions. This shows the variety of reconstructions generated by the VAE to capture the distribution of the training dataset. (B) Scatterplot showing the distribution of the latent vectors belonging to clocks in the fine-tuning dataset divided into dementia (= 1) and control (= 0) groups. The red curve represents a possible decision boundary between the two groups. Using our neural network classifier, we aim to learn such a decision boundary to classify the two groups.

Figure 2

Generative factors of clock drawing are discovered using traversals over VAE latent space. Different regions of the two-dimensional manifold constructed by the VAE map to specific artistic features/anomalies of clock drawings. Latent Dimension 1 = Z0, Latent Dimension 2 = Z1. Left side of the VAE latent space: direction of eccentricity of reconstructed clocks reverses from left to right as Z1 increases from − 4 to + 4 given Z0 =  − 4. This change is correlated with a decrease in clock size shown by darkening of the reconstructed clock. Right side of the VAE latent space: distance of intersection point of clock hands from the geometrical clock center increases as Z1 changes from − 4 to + 4 given Z0 = 4. This change is correlated with a loss of the circular clock boundary. Top half of the VAE latent space: size of the clock hands increases as Z0 changes from − 4 to + 4 given Z1 = 4. This change is correlated with the loss of clock face boundary. Bottom half of the VAE latent space: angle of eccentricity of the clock decreases as Z0 changes from − 4 to + 4 with Z1 =  − 4. This change is correlated with an increase in clock size. X-axis of the VAE latent space: size of the clock increases as Z0 changes from − 4 to + 4 with Z1 = 0.

Figure 3

Performance of the classifier on test dataset. (A) The test dataset consists of 18 dementia and 20 control subjects. This image shows the confusion matrix. (B) Area under receiver operating characteristic is 0.77. (C) Area under precision-recall curve is 0.76.

Figure 4

Increasing the interpretability and clinical utility of the VAE latent space. (A) Diagnosis of misclassified clock drawings in test dataset. The latent projections of misclassified clocks from the test dataset were compared to their original clock drawings (salmon represents dementia clocks misclassified as controls; green represents control clocks misclassified as dementia). Dementia and control clocks formed two distinct clusters in the latent space with the control clocks being projected towards the anomalous side of the latent space, thus justifying their classification. Mapping these projections to the original clock drawings revealed that our model correlated eccentricity to dementia and circularity to non-dementia. It failed to encode missingness/shortening of hands as a predictive feature variable in dementia, and our preprocessing pipeline mis-cropped certain clocks, thereby introducing eccentricity into them. (B) Operationalization of the VAE latent space using k-nearest neighbor classifier with k = 13. K-nearest neighbors of each training datapoint were labeled uniformly while simultaneously varying k to find the best decision boundary between dementia and control samples. This decision boundary physically divided the VAE latent space into two regions: Red—Dementia and Blue—Control. The control region is smaller, and it consists of normal sized clocks with circular clockfaces whose hands intersect at the geometric center of the clockface. The dementia region is larger in size and encodes the various anomalies detected by the VAE.

Figure 5

Conceptual workflow for training VAE with unlabeled dataset and constructing classifiers with latent space of VAE. (A) Clock images are passed into the VAE encoder in the form of a 1X10,000 vector. The top part of the schema represents the VAE decoder-encoder couplet which is trained to minimize the reconstruction loss of the clock drawing using an information bottleneck of a two-dimensional latent space. The lower part of the figure shows how the latent dimensions which capture a compressed representation of a clock drawing are passed into a classifier that mimics the architecture of the VAE decoder. This classifier is fine-tuned to reduce the loss in predicting dementia. (B) This image differentiates between the self-supervised pre-training of the VAE versus the usage of the pre-trained VAE encoder for downstream classification.