Abstract
Statistical learning is today playing an increasing role in many scientific fields as varied as medicine, imagery, biology, and astronomy. Scientific advances in recent years have significantly increased measurement and calculation capabilities, and it is now difficult for a human operator to process such data exhaustively in a timely manner. In particular, many medical specialties such as medical imaging, radiology, and genomics have benefited in recent decades from major technological developments. In some instances these developments have led specialists in these fields to rethink their data practice.
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Notes
- 1.
The hypersphere is the generalization used for the ordinary sphere in spaces that have more than three dimensions.
- 2.
Some learning methods have a number of parameters that increase with the size of the space, which can be problematic in high dimensions.
- 3.
Two vectors u and v are said to be collinear if there is a scalar λ such that v = λu.
- 4.
Some models assume that the covariance matrix of each class is diagonal.
- 5.
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Readers wanting more details on this type of approach should consult Bouveyron C., Brunet-Saumard C., “Model-based clustering of high-dimensional data: A review,” Computational Statistics and Data Analysis, 2014, vol. 71, pp. 52–78.
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Mattei P.-A., Bouveyron C., Latouche P., Bayesian Variable Selection for Globally Sparse Probabilistic PCA, Preprint HAL No. 01310409, Paris Descartes University, 2016.
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Some parameters of the model are then seen as random variables with their own a priori distribution.
- 12.
Orlhac F., Mattei P.-A., Bouveyron C., Ayache N., Class-specific Variable Selection in High-dimensional Discriminant Analysis through Bayesian Sparsity, Preprint HAL No. 01811514, Côte d’Azur University, 2018.
- 13.
Orlhac F., Humbert O., Pourcher T., Jing L., Guigonis J.-M., Darcourt J., Bouveyron C., Ayache N., “Statistical analysis of PET radiomic features and metabolomic data: Prediction of triple-negative breast cancer,” SNMMI 2018 Annual Meeting, Journal of Nuclear Medicine, 2018, vol. 59, p. 1755.
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Bouveyron, C. (2020). High-Dimensional Statistical Learning and Its Application to Oncological Diagnosis by Radiomics. In: Nordlinger, B., Villani, C., Rus, D. (eds) Healthcare and Artificial Intelligence. Springer, Cham. https://doi.org/10.1007/978-3-030-32161-1_17
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DOI: https://doi.org/10.1007/978-3-030-32161-1_17
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