Machine learning holds tremendous promise for transforming the fundamental practice of scientific discovery by virtue of its data-driven nature. With the ever-increasing stream of research data collection, it would be appealing to autonomously explore patterns and insights from observational data for discovering novel classes of phenotypes and concepts. However, in the biomedical domain, there are several challenges inherently presented in the cumulated data which hamper the progress of novel class discovery. The non-i.i.d. data distribution accompanied by the severe imbalance among different groups of classes essentially leads to ambiguous and biased semantic representations. In this work, we present a geometry-constrained probabilistic modeling treatment to resolve the identified issues. First, we propose to parameterize the approximated posterior of instance embedding as a marginal von MisesFisher distribution to account for the interference of distributional latent bias. Then, we incorporate a suite of critical geometric properties to impose proper constraints on the layout of constructed embedding space, which in turn minimizes the uncontrollable risk for unknown class learning and structuring. Furthermore, a spectral graph-theoretic method is devised to estimate the number of potential novel classes. It inherits two intriguing merits compared to existent approaches, namely high computational efficiency and flexibility for taxonomy-adaptive estimation. Extensive experiments across various biomedical scenarios substantiate the effectiveness and general applicability of our method.

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