A 'No Panacea Theorem' for multiple classifier combination

We introduce the 'No Panacea Theorem' for classifier combination in the two-classifier two-class case. It states that if the combination function is continuous and diverse, there exists a situation in which the combination algorithm will always give very bad performance. Thus, there is no optimal algorithm, suitable in all situations. From this theorem, we see that the probability density functions (pdf's) play an important role in the performance of combination algorithms, so studying the pdf's becomes the first step in finding a good algorithm.