标题： 监督分位数归一化 显示英文标题

标题： Supervised Quantile Normalisation

摘要： 分位数规范化是一种流行的归一化方法，适用于受不需要的变化影响的数据，如图像、语音或基因组数据。 它对每个样本的特征值应用单调变换，以确保归一化后，它们遵循每个样本相同的靶分布。 然而，选择“好的”靶分布仍然主要是经验性的和启发式的，并且通常是独立于归一化数据的后续分析进行的。 我们建议将分位数规范化步骤与后续分析相结合，并与其他参数一起优化靶分布。 我们在归一化数据上估计线性模型的问题上说明了这一原则，并表明它导致了一个特定的低秩矩阵回归问题，可以高效解决。 我们通过模拟数据、图像和基因组数据来说明我们的方法的潜力，我们将该方法称为SUQUAN，在这些数据中，它的表现优于标准的分位数规范化。 显示英文摘要

摘要： 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.