In this case, without the constraint of S, the matrix factorization may generate incorrect class alignment, thus lead to almost random classification results (around 50% accuracy), as shown in Figure 1, and further make unreasonable the following evaluation of queries.
when a query q j is a word, P (q j = k) is otherwise, Computational Improvement: It can be computationally intensive if the reconstruction error is computed for all unknown documents and words.