OCL: Ordinal Contrastive Learning for Imputating Features with Progressive Labels

TL;DR

This work tackles the challenge of missing multi-modal imaging in Alzheimer's disease studies by introducing ordinal contrastive learning within a modality-agnostic embedding space. The proposed two-network framework comprises an encoder $E$ and a modality-conditioned decoder $D$, optimized with losses $\mathcal{L}_{DA}$, $\mathcal{L}_{OC}$, and $\mathcal{L}_{MC}$ to align progression and modalities. A modality-conditioned reconstruction objective enables translating existing measurements to unobserved modalities, enabling holistic imputation across subjects. Experimental validation on the ADNI dataset shows improved imputation quality and downstream classification accuracy, with the ordinal loss enhancing the alignment with disease severity and the modality-coherence loss personalizing embeddings across modalities. Overall, the method enables robust use of incomplete imaging data for AD analysis and can extend to other neuroimaging missing-data scenarios.

Abstract

Accurately discriminating progressive stages of Alzheimer's Disease (AD) is crucial for early diagnosis and prevention. It often involves multiple imaging modalities to understand the complex pathology of AD, however, acquiring a complete set of images is challenging due to high cost and burden for subjects. In the end, missing data become inevitable which lead to limited sample-size and decrease in precision in downstream analyses. To tackle this challenge, we introduce a holistic imaging feature imputation method that enables to leverage diverse imaging features while retaining all subjects. The proposed method comprises two networks: 1) An encoder to extract modality-independent embeddings and 2) A decoder to reconstruct the original measures conditioned on their imaging modalities. The encoder includes a novel {\em ordinal contrastive loss}, which aligns samples in the embedding space according to the progression of AD. We also maximize modality-wise coherence of embeddings within each subject, in conjunction with domain adversarial training algorithms, to further enhance alignment between different imaging modalities. The proposed method promotes our holistic imaging feature imputation across various modalities in the shared embedding space. In the experiments, we show that our networks deliver favorable results for statistical analysis and classification against imputation baselines with Alzheimer's Disease Neuroimaging Initiative (ADNI) study.

Figures (4)

• Figure 1: Illustration of our framework. (a) An encoder $E$ is trained to extract disease progression information across various input modalities through $\mathcal{L}_{DA}$ and $\mathcal{L}_{OC}$. Additionally, $E$ is guided to maximize the similarity of embeddings from the same subject using $\mathcal{L}_{MC}$. (b) A decoder $D$ is trained to reconstruct the embedding of a fixed $E$ to its original input under its original modality condition, utilizing $\mathcal{L}_{D}$. (c) The trained $E$ and $D$ facilitate the translation of an input to the target modality when the corresponding condition is provided, while preserving disease progression information.
• Figure 2: Comparison of supervised (left) and ordinal (right) contrastive learning: Both approaches contrast the set of all samples from the same class as positives against the negatives from the rest of the batch. While supervised contrastive learning repels each negative without differentiation on labels denoted as $(a)\approx(b)\approx(c)$, ordinal contrastive learning assigns the penalizing strength based on the label distance.
• Figure 3: Visualizations of embeddings under each loss by t-SNE tsne. Each individual encoder is trained with three distinct losses including Cross-Entropy $\mathcal{L}_{CE}$ (left), Supervised Contrastive Loss $\mathcal{L}_{SC}$ (center) and our Ordinal Contrastive Loss $\mathcal{L}_{OC}$ (right) along with domain adversarial loss $\mathcal{L}_{DA}$. (a) and (b) correspond to training and testing data respectively. (Color: AD-stage labels, Shape: imaging scan types.)
• Figure 4: $p$-values from group comparisons with Bonferroni correction at $\alpha=0.01$: (a) before imputation, (b) after imputation from our model. Top: Resutant $p$-value maps on a brain surface (left hemisphere) brainpainter in a $-log_{10}$ from CN and EMCI comparison with cortical thickness, and (b) shows higher sensitivity. Bottom: Number of significant ROIs. Number of common ROIs before-and-after imputation are in ().