1. A spectral data processing apparatus comprising: an analyzer configured to perform principal component analysis of spectral data acquired for each of a plurality of regions of a sample, the analyzer obtaining an eigenvector by performing the principal component analysis of first spectral data of a first region out of the plurality of regions, and performing the principal component analysis of second spectral data of a second region different from the first region out of the plurality of regions using the obtained eigenvector; and a time comparator configured to compare a required time Te from the termination of acquisition of the second spectral data until acquisition of an eigenvector by performing the principal component analysis of the second spectral data and a required time Ti from the termination of acquisition of the second spectral data until the termination of acquisition of spectral data of a third region different from the first and second regions, wherein the analyzer performs the principal component analysis of the second spectral data by using the eigenvector obtained by performing the principal component analysis of the first spectral data in a case where Te is longer than Ti, and performs the principal component analysis of the second spectral data by using the eigenvector obtained by performing the principal component analysis of the second spectral data in a case where Te is shorter than Ti or in a case where Te and Ti are equal.