We have applied the concept of combinatorial fusion to improve accuracy in protein structure prediction. In particular, we have successfully improved the overall predictive accuracy rate of 87% for the four classes and 69.6% for the 27 folding patterns. We improve previous results by Huang et al. [9] (65.5% for folding structures) and Ding and Dubchak [8] (56.5% for folding structures) by incorporating the method of combinatorial fusion with the RBFN neural network using the hierarchical learning architecture. These rates are higher than previous results and it demonstrates that data fusion is a viable method for feature selection and combination in the prediction and classification of protein structures. Work has been performed to improve those results which used other machine learning technique such as kernel method, SVM and genetic algorithm. For example, Yu et al. [43] has obtained good accuracy rate using SVM with
n-peptide coding schemes and jury voting. Future work can be performed to improve these
results using our combinatorial fusion approach.Also, we present a structural variant of the mountain clustering method that is suitable for data like 3-D structures of protein fragments. We have analyzed the SMCM and TSCA and have demonstrated that since TSCA does not take into account the geometry of the data, it may extract poorer building blocks than the SMCM. The utility of this algorithm is demonstrated on the same dataset used by Unger et al. In fact, the superiority of this algorithm is demonstrated on two versions of datasets (the original one and the newly updated one on the same set of proteins). To visually compare the quality of reconstructions we also proposed two alternative ways revealing that the performance of SMCM building blocks is usually better than TSCA building blocks both in terms of the local-fit RMS histogram and in terms of the average RMS deviation for individual protein. Our experiments demonstrate that the SMCM can find useful building blocks to successfully reconstruct the 3-D protein structures for the first 60 residues (as done by Unger et al.) of all test proteins with global-fit RMS error within 7.19Ao . It can also
obtain good local-fit RMS errors indicating that these building blocks can model the nearby fragments within tolerable errors.
Both SMCM and TSCA are computationally expensive when the size of training dataset is large. Hence we proposed an incremental version of the SMCM. The same concept is also used to obtain an incremental version of the TSCA. We have made extensive experimentation with these two algorithms using two versions of the dataset used by Unger et al. as well as another dataset used by other researchers. The incremental SMCM is also found to be quite effective and it is found to exhibit the properties expected from an incremental algorithm. More specifically, as the number of proteins increases in the training set, the increase in the number of building blocks decreases and consequently the rate of decrease in the global reconstruction error both on the training and test data falls down. Moreover, the incremental SMCM is found to be more effective than the incremental TSCA. Although, the SMCM usually finds more building blocks than those found by the TSCA, we have demonstrated that the improved performance for SMCM comes from the quality of the building blocks which are placed at the center of areas dense in training data.
None of the algorithms discussed here can take into account fragments of variable length.
To extend the algorithms for fragments of variable length, we need measures of similarity between fragments of different lengths. For example, if we have two fragments both are helix, but of different length, the structural similarity between the two should be very high; on a [0-1]
scale, it should be 1. We plan to investigate this in near future.
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