7 Concluding Discussion
The Exit-point framework proposed in this paper broadens the search region in order to obtain an improved solution which may potentially correspond to a better motif. In most of the profile based algorithms, EM is used to obtain the nearest local optimum from a given starting point. In our approach, we consider the boundaries of these convergence regions and find the surrounding local optimal solutions based on the theory of stability regions. We have shown on both real and synthetic data sets that beginning from the EM converged solution, the Exit-point approach is capable of searching in the neighborhood regions for another solution with an improved information content score. This will often translate into finding a pattern with less Hamming distance from the resulting alignments in each sequence. Our approach has demonstrated an improvement in the score on all datasets that it was tested on. One of the primary advantages of the Exit-point methodology is that it can be used with different global and local methods. The main contribution of our work is to demonstrate the capability of this hybrid EM algorithm in the context of the motif finding problem. Our algorithm can potentially use any global method and improve its results efficiently.
From our results, we see that motif refinement stage plays a vital role and can yield accurate results deterministically. We would like to continue our work by combining other global methods available in the literature with existing local solvers like EM or GibbsDNA that work in continuous space. By following the example of [4], we may improve the chances of finding more promising patterns by combining our algorithm with different global and local methods.