Incomplete data are often represented as vectors with filled missing attributes joined with flag vectors indicating missing components. In this paper, we generalize this approach and represent incomplete data as pointed affine subspaces. This allows to perform various affine transformations of data, such as whitening or dimensionality reduction. Moreover, this representation preserves the information, which coordinates were missing. To use our representation in practical classification tasks, we embed such generalized missing data into a vector space and define the scalar product of embedding space. Our representation is easy to implement, and can be used together with typical kernel methods. Performed experiments show that the application of SVM classifier on the proposed subspace approach obtains highly accurate results.