Fig.4 Actomyosin complex particles and 3D map of actin and myosin.
3.2 The architecture ofcascade
Cascade part consists of three-stage cascading classifiers in which a total feature is 107. Each stage in cascade is required to have a very high detection rate, and suitable false positive rate. If an input sub-windows pass through all stages of cascade, it is classified as actomyosin particles. Otherwise it is rejected as non- actomyosin particles. In the cascade, subsequent classifiers are trained using those examples that pass all the previous the stages, therefore, the second classifier is faced more difficult task than first. The examples that make it through the first stage are hard than typical examples. The cascading classifier speeds up detection procedure because it rejects many of non-particle sub-windows.
The cascade of classifier is designed as follows. The first stage cascading classifier includes 2 layers that the number of feature per layer is 2, 5 respectively. The second stage cascading classifier includes three layers that the number of features per layer is 7, 9, 11. The third stage is 4 layers in which number of features per layer is 13, 15, 20, 25, and the features totaled up to 73. Negative sub-windows about 60-80% is rejected by first layer in cascade while detecting rate per layer is approximately 99.9% of actomyosin particles. About choosing the number of stages and features, which are chosen by a trial test. The number of features per layer is chosen by a trial in which the number of features is increased until the false positive rates are a significant reduction. More stags were added until the target detection and false positive rates are met for this stage. The rates are determined by testing on the validation set.
About training, each layer of the cascade is trained by AdaBoost. The cascading classifiers with total 107 features were trained with the 750 actomyosin and 900 non-actomyosin sub-windows using the AdaBoost. The non-actomyosin sub-windows used to train subsequent classifiers were obtained by scanning the partial cascade across large non- actomyosin images and collect false positives of the previous stage.
The second part consists of SVM classifier that is final classifier of system (see Fig. 1). The features that have been selected by AdaBoost process in the third stage cascade are used for input pattern representation of SVM classifier. For each input 48×48 sub-window, these feature values before applying SVM will be scaled to [-1, +1] to form a feature vector for SVM classifier. The final SVM classifier takes 25 features of the last layer in the third stage classifier used as feature vector and trained. In the last stage in cascade, negative examples (false positives of previous stages) are more complex and similar actomyosin particles, and classify them is more difficult. And convergence speed of cascading classifier will be very slow. If we want to classify them continuously, the number of feature and stage will be added, and computed time is also increased. Therefore, we replace subsequent stages in cascade of classifier with SVM classifier that is used as the final classifier to implement better detection performance and speed up detection process.
4 Experimental Results
In our experiments, the test set consists of 25 features, 350 sub-images of actomyosin, and 700 sub-images of non-actomyosin. The 5-fold cross-validation method is used to test and select the best available parameters to implement optimization model. C= 2.18 and γ=0.135 is selected with RBF kernel function. Experimental results show that only 1.62% hard examples are put into SVM classifier to make final decision classification. The detection rate achieved 94% with false positive rate of 2.14% leading to a total rate of 96.57% of examples that were correct classified and the area under the ROC curve (AUC) is 0.9705.
The experimental results are better than other algorithm. ROC curve is shown in Fig. 5.
5 Conclusion and Future Work
The experimental results shown good performance that detection rate and detection speed are enhanced and false positive rate is reduced. The detection rate achieved 94% and false positive rate is 2.14%.
In this paper, we emphasize simple and fast feature selection out of huge dataset, and classify actomyosin particles using SVM classifier. Also this approach represents progress that macromolecule asymmetric particles in cryo-EM image are detected automatically.
We will implement comparative performance of Ada-SVM, SVM and cascade of classification. 3D reconstruction of actin and myosin are implemented in the future.
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