be interpreted in the same ways that the originals were. They are linear interpretations of the original variables. Also, if PCA is not performed properly, there is a high likelihood of information loss. PCA relies on a linear model. If a dataset has a pattern hidden inside it that is nonlinear, then PCA can actually steer the analysis in the complete opposite direction of progress. Researchers at Kansas State University discovered that the sampling error in their experiments impacted the bias of PCA results. "If the number of subjects or blocks is smaller than 30, and/or the researcher is interested in PC's beyond the first, it may be better to first correct for the serial correlation, before PCA is conducted". The researchers at Kansas State also found that PCA could be "seriously biased if the autocorrelation structure of the data is not correctly handled". PCA and information theory Dimensionality reduction results in a loss of information, in general. PCA-based dimensionality reduction tends to minimize that information loss, under certain signal and noise models. Under the assumption that that is, that the data vector is the sum of the desired information-bearing signal and a noise signal one can show that PCA can be optimal for dimensionality reduction, from an information-theoretic point-of-view. In particular, Linsker showed that if is Gaussian and is Gaussian noise with a covariance matrix proportional to the identity matrix, the PCA maximizes the mutual information between the desired information and the dimensionality-reduced output . If the noise is still Gaussian and has a covariance matrix proportional to the identity matrix (that is, the components of the vector are iid), but the information-bearing signal is non-Gaussian (which is a common scenario), PCA at least minimizes an upper bound on the information loss, which is defined as The optimality of PCA is also preserved if the noise is iid and at least more Gaussian (in terms of the Kullback–Leibler divergence) than the information-bearing signal . In general, even if the above signal model holds, PCA loses its information-theoretic optimality as soon as the noise becomes dependent. Computing PCA using the covariance method The following is a detailed description of PCA using the covariance method (see also here) as opposed to the correlation method. The goal is to transform a given data set X of dimension p to an alternative data set Y of smaller dimension L. Equivalently, we are seeking