zeromean

Zeromean, often written as zero-mean or demeaning, refers to data, signals, or random variables whose average value is zero. In practice, a zero-mean version of a dataset is obtained by subtracting its mean: x′i = xi − μ, where μ is the mean (sample or population). This operation is commonly called demeaning or centering and is a standard preprocessing step in statistics, signal processing, and machine learning.

In statistics and machine learning, zero-mean data helps remove bias related to the dataset’s location and can improve numerical stability and the interpretability of models. Centering features or targets is standard before applying methods such as principal component analysis, ridge regression, or algorithms that assume zero-mean inputs. While it does not change the relationships among variables if the model includes an intercept, it can affect coefficient estimates when the intercept is omitted.

In signal processing, removing the DC offset to create a zero-mean signal is important for accurate spectral analysis and filtering. Zero-mean assumptions are also common for random processes; a variable with mean zero satisfies E[X] = 0, and zero-mean processes are often used in whitening and decorrelation tasks.

Implementation considerations include using a running mean for online data or applying per-feature centering to multivariate data. Caution is advised: centering removes information about the absolute level, which may be important in certain contexts, so the use of zeromean should align with the analysis goals.