meancentered

Mean-centered, or mean-centering, is a data preprocessing technique in statistics and data analysis. It involves subtracting the mean value of a data feature from each observation so that the feature’s mean becomes zero. This can be done per feature (column) in a data matrix, though centering can also be applied across rows in other contexts.

The typical procedure for a data matrix X with n observations and p variables is to compute the mean of each variable across observations, then subtract these means from the corresponding entries. The resulting matrix has column means of zero. Mean-centering is often a preparatory step for multivariate methods such as principal component analysis (PCA), factor analysis, and canonical correlation, where centering ensures that analyses reflect variation around the mean rather than absolute values. It is also used in linear regression to simplify interpretation and, in some cases, to reduce multicollinearity when all variables are included without an intercept.

Mean-centering differs from standardization, which scales features to have unit variance in addition to zero mean. It can also be applied to whole data sets or to specific subsets, and in some contexts, centering is done across observations rather than features. Practical considerations include handling missing values, which must be addressed before centering, and recognizing that centering can alter interpretability of intercepts and predictions in certain models. Double centering and other variants may be used in specialized matrix normalization tasks.