# What Is the Difference Between PCA and Karhunen Loeve (KL Transform)?

I have been reading about Karhunen-Loeve or also known as KL transform and I see that when it is used to reduce dimension the procedure is identical to PCA, that is, for both methods the covariance matrix of the data is constructed and then the eigenvectors are calculated . I would like to know if there is any difference in this aspect that is being overlooked?

• This is well known. Recall that PCA is a spectral decomposition of the covariance matrix. In the continuous data case, KL transform is a spectral decomposition of the covariance function. PCA is sometimes called the discrete KL transform. – Atul Ingle May 16 '18 at 3:16
• very interesting question! – Jonas Schwarz Aug 4 '19 at 8:33