## 1 Introduction  
An important task in machine learning and artificial intelligence is to build a classifier for prediction and classification given available training samples or other prior information [1]. Statistical Learning Theory (SLT) plays an important role in prediction estimation and machine learning in that it provides a unified framework for solving finite-sample learning problems [2; 3; 4]. In the past few decades, Support Vector Machine (SVM), a method based on SLT, has been widely applied for the construction of a classifier when limited samples are available [5; 6; 7]. Unlike other classifiers, which assume that the number of samples can tend to infinity, SVM offers the best generalization and prediction capability after it is trained using limited samples. SVM is one among many classification methods capable of handling large or small samples, nonlinear, or those with high dimensional issues [8]. A vital question, however, in using SVM is still unresolved, namely, how many samples are necessary for a certain standard of prediction accuracy. To address this question, we devise here a new idea that not only pays attention to the performance of the model on the training set, but also puts additional focus on the model's prediction accuracy of unknown new data. Typically, a model overfits when it is trained so well on the training data that it fails to generalize. Accordingly, the ability of the model to adapt to new data decreases. It is generally accepted that the primary factor in generalization performance is sample size. However, very little study has focused on studying the quantitative relationship between sample size and generalization. In this paper, we use the medical diagnosis of lung cancer based on computed tomography (CT) images as an example to solve the relationship problem; wherein, it is difficult to obtain large-scale samples in practice.  
The construction of any classifier must include training and testing processes according to available samples. In this context, training error refers to the learning ability whereas testing error reflects the prediction and generalization ability [9]. In SLT, a learning error is called an empirical risk (EMP) while a generalization error is called an expected risk (EXP) [10]. Minimizing EMP is a necessary condition for building a classifier with generalization ability or an EXP, but it is not a sufficient condition [11]. In fact, a low EMP may lead to a high EXP, wherein the prediction and generalization ability involves both the number of samples and choice of the classifier type. Under the same EMP, a classifier with simple structure can often lead to a high generalization ability [12]. Nevertheless, SLT can act as the theoretical basis that connects EMP and EXP [13].  
Recently, a number of methods have been proposed to diagnose lung cancer using CT images [14; 15]. Invasive adenocarcinoma (IA) is a primary type of lung cancer and often presents as ground glass nodules (GGNs) in patient's CT images [16]. Accurately discriminating IA from non-IA based on GGNs has critical implications for providing an effective treatment plan. Existing studies on classifying IA and non-IA have mostly focused on how minimizing EMP can improve classification accuracy and with very little consideration given to EXP. Moreover, the generalization and prediction ability of the classifier is not guaranteed in practice. To date, little is known about the interrelation between EXP and EMP, and more specifically, it remains unclear as to how many samples are necessary under a certain requirement of prediction accuracy. In this paper, the effect of different sample sizes on EXP is explored, and the minimum sample size is estimated to achieve the desired generalization requirements.