Extracting information from multiple datasets by matrix factorization and common subspace computation
(2019)
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- Abstract
- With the constantly growing capability to measure and store data, dealing with different datasets representing similar phenomena is becoming increasingly common. An example in bioinformatics is gene expression data, where the same disease can be studied in different hospitals at different times by measuring the gene expression levels of patients. It is then desirable to merge the different measures obtained, in order to improve the robustness of the subsequent analysis. In this thesis, we investigate different ways of extracting common information from multiple datasets with common features. We propose two different types of approach: removing the differences across datasets, and, keeping the common information. To remove the differences across datasets, we use a matrix factorization approach: we develop a new spatiotemporal version of independent component analysis that we apply to all concatenated datasets, and use the resulting components to model the differences to be removed. The approach is validated on gene expression datasets, and compared to other existing methods in the wider context of a classification task. In the second part of the thesis, we propose a minimax formulation to model the problem of finding a common subspace across a set of subspaces associated with the datasets. We develop multiple algorithms to solve this minimax problem,with some convergence guarantees, and compare their performances on synthetic and real data.
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Citations
Renard, E. (2019). Extracting information from multiple datasets by matrix factorization and common subspace computation. https://hdl.handle.net/2078.5/63919