2017/06/01 by Marine Le Morvan, Morvan, Marine Le, Jean-Philippe Vert +2
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Blind Source Separation Techniques #FOS: Biological sciences #FOS: Computer and information sciences #Face and Expression Recognition #Gene expression and cancer classification #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Quantitative Methods (q-bio.QM) #cs.LG #q-bio.QM #stat.ML
paper · pdf · doi:10.48550/arxiv.1706.00244
arxiv created 2017/06/01 · openalex publication_date 2017/06/01 · arxiv updated 2017/06/02 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
Quantile normalisation is a popular normalisation method for data subject to unwanted variations such as images, speech, or genomic data. It applies a monotonic transformation to the feature values of each sample to ensure that after normalisation, they follow the same target distribution for each sample. Choosing a "good" target distribution remains however largely empirical and heuristic, and is usually done independently of the subsequent analysis of normalised data. We propose instead to couple the quantile normalisation step with the subsequent analysis, and to optimise the target distribution jointly with the other parameters in the analysis. We illustrate this principle on the problem of estimating a linear model over normalised data, and show that it leads to a particular low-rank matrix regression problem that can be solved efficiently. We illustrate the potential of our method, which we term SUQUAN, on simulated data, images and genomic data, where it outperforms standard quantile normalisation.