Fig 1.
Comparison of classification results of simulated data with SNR = 1/10.
The First column (panels a, c and e) is the normalized histogram of angular distances. More accurate classification produces curve with higher peak concentrated at lower angular distance. The second column (panels b, d and f) shows the class sizes arranged in an ascend order. The most balanced classification has a horizontal line in this plot. (a) and (b) are from experiments using different clustering algorithms in MRA approach under SPARX. (c) and (d) are from experiments using different clustering algorithms in MRA/MSA approach under EMAN2. (e) and (f) are from experiments using different clustering algorithms in RFA approach under SPIDER. In all graphs, red curves present the results from the ACK-means algorithm.
Fig 2.
Convergence of K-means, EQK-means and ACK-means in MRA.
The three algorithms behave similarly as iteration increases, converging very fast at the first several iterations.
Table 1.
The running time of different algorithms in different approaches.
Fig 3.
2D class averages of GroEL using the traditional K-means (a), EQK-means (b) and ACK-means (c) in MRA approach from SPARX. Class size is shown at the left bottom of each class average. ACK-means (b) is the best by having the most number of clear classes.
Fig 4.
2D class averages of GroEL using the traditional K-means (a) and ACK-means (b) in MRA/MSA from EMAN2. Class size is shown at the left bottom of each class average. Their performance is similar, but ACK-means (b) has the more number of clear classes.
Fig 5.
2D class averages of GroEL using the traditional K-means (a) and ACK-means (b) in RFA from SPIDER. Class size is shown at the left bottom of each class average. The quality of class averages from both algorithms is comparable, but ACK-means (b) substantially improved the balance of class sizes.
Fig 6.
2D class averages of Inflammasome using the traditional K-means (a), EQK-means (b) and ACK-means (c) in MRA from SPARX. Class size is shown at the left bottom of each class average. The traditional K-means generated many blurred class averages and EQK-means produced some class averages with misaligned features.
Fig 7.
2D class averages of Inflammasome using the traditional K-means (a), and ACK-means (b) MRA/MSA from EMAN2. Class size is shown at the left bottom of each class average. ACK-means generated improved results as compared to the traditional K-means.
Fig 8.
2D class averages of inflammasome using the traditional K-means (a), and ACK-means (b) in RFA from SPIDER. Class size is shown at the left bottom of each class average. There are many classes in (a) with only one particle. Traditional K-means generated many classes with only one particle, which is avoided in the results from ACK-means.
Fig 9.
2D class averages of RP using the traditional K-means (a) and ACK-means (b) in MRA from SPARX. Class size is shown at the left bottom of each class average. There are many blurred classes in (a) generated by the traditional K-means.
Fig 10.
2D class averages of RP using the traditional K-means (a) and ACK-means (b) in MRA/MSA from EMAN2. Class size is shown at the left bottom of each class average. Classes generated by ACK-means (a) are clearer than those by the traditional K-means (a).
Fig 11.
2D class averages of RP using the traditional K-means (a) and ACK-means (b) in RFA from SPIDER. Class size is shown at the left bottom of each class average. The traditional K-means (a) generated some poor classes with only one particle. The performance of ACK-means (b) is better than the traditional K-means.