## 2 Basics of CAD systems
### Classification process  
In the classification process for CAD systems, the feature vector of each lesion candidate provided by a feature extractor is used for assigning the candidate to one of the possible categories (_e.g._ lesion or normal tissue) according to the output of a classifier. Prior to the practical test, the classifier should be designed by inputting feature values from training cases, and teaching the classifier true category labels (_e.g._, one or zero). This learning method is called, \"supervised learning.\" In general, the unsupervised learning method, which does not need training data, has not been adopted so often in the CAD research fields, because the practical CAD systems should be \"educated\" or trained based on the clinical truth or evidence.  
In order to improve generalization and robustness of a CAD system, the CAD system should be designed using a sufficient number of training cases. However, if a CAD system is trained by a small number of cases, the system may allow perfect classification of the training cases, but it is not likely to  
Figure 8: Relationships between the distance between centroids of each candidate and a brain and circularity for (a) true positive regions and (b) false positive regions [30,31]. The dotted lines indicate a threshold value of 0.6 for dividing all MS candidate regions into two groups with higher and lower circularities.  
correctly classify unknown cases. This situation is known as overtraining. According to [PERSON]'s report [56], the generalization accuracy (higher than 80%) of a CAD system saturated from 150 test cases using a leave-one-out test method. Moreover, we should consider the curse of dimensionality, which causes the problem that classification performances of the CAD systems could deteriorate if the ratio of the number of training cases to that of features used for the classifier is relatively small [57]. A ratio of more than 5 or 10 would be better for avoiding the curse of dimensionality [57].  
Major machine learning classifiers, which have been used for CAD systems, are linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), artificial neural network (ANN), support vector machine (SVM), Bayesian-based classifier, _etc._ In a CAD system for Alzheimer's disease (AD) from [PERSON] _et al._[27], AD cases were identified by using an SVM classifier, which was trained by atrophic image features (_e.g._, cortical thickness and cerebrospinal fluid (CSF) volume) of AD and non-AD cases, and then an unknown case was classified into either AD or non-AD category based on an SVM model. The reasons why we employed the SVM as a classifier were high generalization ability, avoiding local minimum traps, and overcoming the curse of dimensionality [58, 59].  
In the CAD system for classification of cerebral tumors, the ANN was designed to differentiate among 4 categories of tumors (high-grade gliomas, low-grade gliomas, metastases, and malignant lymphomas) with use of 2 clinical parameters (age and history of malignant tumor) and 13 radiologic findings (_e.g._, location, signal intensity on T2-weighted images) in MR images [60]. Figure 9 shows an ANN classifier for differentiating cerebral tumors into 4 categories, which was composed of 15 input units and 4 output units.  
Figure 9: An ANN classifier for differentiating cerebral tumors into 4 categories, which was composed of 15 input units and 4 output units [60].  
In many CAD systems, at first, simple rule-based methods have been used for reducing \"obvious false positive outliers\", and then the subsequent machine learning classifier for removing various kinds of many false positives including \"fake positives\", _i.e.,_ lesion-like false positives. The rules for removing false positive outliers are based on some simple threshold values, such as the minimum and maximum threshold values determined by a mean value \(\pm\) a few times standard deviation of the feature values of all true positive regions [30,31].