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I-Ping Tu

2012-04-13
15:00:00 - 16:40:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

In the last decade, cryo-electron microscopy (cryo-EM) has been emerging as a powerful tool for obtaining high resolution three-dimension (3-D) structures of biological macro-molecules. A Cryo-EM data set usually contains at least thousands of low signal-to-noise ratio images with random rotations and orientations. Clustering analysis is a necessary step to group the images with the same orientation after all possible rotations. In this talk, we will focus on the clustering step of a complex data analysis process. In the cryo-EM community, the common approach is to apply k- means for clustering. It is well known that k-means could be highly biased due to its random initials especially when the number of classes is large. The self-updating-procedure (SUP) avoids the randomness by starting with all data points as initials. For this application, we implement a minimum gamma-divergence estimation of q-Gaussian mixture for SUP. The use of q-Gaussian mixture model sets a hard influence range for each mixture component and rejects data influence from outside this range, and hence it leads to a robust procedure for learning each of the local components. The minimum gamma-divergence performs a soft rejection by down weighting deviant points from cluster centers and thus enhances the robustness. Furthermore, the SUP shrinks the mixture model parameter estimates toward cluster centers in each iteration, which leads an efficient estimation for a mixture model. Our simulation study shows that MPCA can reduce the dimension more efficiently and SUP can do the clustering with higher accuracy, compared to the conventional approach, for the cryo-EM images.