CONICET | Buscador de Institutos y Recursos Humanos

Motivated by the analysis of biomedical imaging data, we shall discuss the use of dimension reduction in combination with standard learning tools. Orthogonal projections are a powerful analysis tool to emphasize specific data features and at the same time reduce the overall complexity simplifying further processing. The underlying objective in the use of random projections is the preservation of relative pairwise distances, theoretically supported by the famous Johnson-Lindenstrauss-Lemma. Principal component analysis (PCA), on the other hand, identifies an orthogonal projector that maximizes the total variance. We observe that the preservation of relative pairwise distances and the maximization of the total variance are competing objectives, in particular, in high dimensions. Therefore, the specific choice of the orthogonal projection used for subsequent analysis is critical and highly depends on the data and the learning task. Besides the specific architecture, iterative learning frameworks usually depend on a loss function to quantify residuals in intermediate steps. We introduce variational loss functions based on orthogonal projectors to integrate and emphasize data features. We then apply these variational loss functions in a medical image classification problem. The overall task is the classification of photoreceptor layers in the human retina and their disruptions. Optical coherence tomography scans with binary pixel-wise annotations by retinal specialists enable data analysis in a supervised manner with deep convolutional neural networks. Optimizing standard loss functions does not yield sufficient results concerning the classification of disruptions, whereas the use of our proposed variational loss function can improve the results for photoreceptor segmentation.

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