Maximum Mean Discrepancy Kerenels

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A relevant yet difficult area in Computational Pathology (CPath) is using routine histology Whole Slide Images (WSIs) for various diagnostic and prognostic tasks often approached via deep learning methods. However, due to the memory requirements associated with multi-gigapixel WSIs pathologists must first divide images into smaller patches meaning these methods can only generate patch level prediction scores. This comes at the price of losing information distributed over scales greater than the patch size. To get WSI-level predictions we make use of common aggregation techniques on these scores such as max-pooling. In this research, we propose that we approach the aggregation problem from a different perspective - the use of Maximum Mean Discrepancy (MMD) as a measure of (dis)similarity between entire WSIs. We hypothesize that (dis)similarity between two WSIs can be captured by their MMD by simply representing each WSI as a set of features of its constituent patches. Such a metric allows for the generation of WSI-level kernels that condense the relationships of an entire dataset into a single matrix which can fit into memory. These kernels allow us to use widely researched kernel methods in order to perform a multitude of tasks such as predictive modelling, clustering and out of bag prediction. To the best of our knowledge, this is the first report of WSI level kernels in this domain and, as such, this work has the potential to pave the way for a new branch of CPath. We have presented a proof of feasibility in our recent paper where we used MMD kernels to achieve state-of-the-art results for TP53 mutation prediction and survival analysis of breast cancer patients from The Cancer Genome Atlas Program (TCGA). However, this work has to be extended in a more comprehensive study. On top of this similarity metrics between WSIs on the slide level has not been studied extensively. Thus, the development of this metric has a lot of potential in various existing yet challenging domains of CPath. For example, the metric can be used for similar WSI lookup in a database which is often utilised to train new pathologists to recognise cancer types. Furthermore, other extensions include working with different cancer types, measuring domain shift in CPath, regression tasks and survival analysis.