## 1 Introduction
Semi-supervised learning combines supervised learning with unsupervised learning together, and it can train classifiers with few labeled samples. Typical semi-supervised learning algorithms, for example, self-training [21], hybrid models [22], graph-based ones [23] and SVM-based [24] ones can be applied to wall crack detection [25], pavement crack detection [26] and steel structure surface defect detection [27]. During the training, classifiers are trained by a small amount of labeled data and then are employed to classify a great amount of unlabeled data. Subsequently, the mislabeled samples are picked out and corrected manually and are reused as the training data in the next round. In these methods, a large amount of anomaly (crack) data is the key to obtaining a high-performance classifier. In practical engineering, it is generally difficult to obtain abnormal crack data mainly due to the low frequency of abnormal events, high artificial manufacturing cost and the difficulty of obtaining a large number of open labeled abnormal data sets. To address this issue, normal data instead of anomaly data are paid attention to and collected to train anomaly classifiers. Such a technique is called semi-supervised anomaly detection. With normal data as a training set, a classifier with a specific threshold is obtained and then employed to determine whether the testing images are abnormal. Currently, this technology has been already widely used in cancer detection [28], ultrasound detection [29], disease detection of industrial products [30; 31; 32] and infrastructure diseases [33; 34]. Although anomaly detection technology can meet practical needs to some extent, there is very limited research on how to explain it. To further investigate the working principles of anomaly detection, an anomaly detection method named deep support vector data description (DSVDD) has been exploited to learn the neural network transformation from input space to output space [35]. In this way, most of the normal data (red dots) are mapped into a hypersphere characterized by the center \(c\) and the radius \(R\) of minimum volume, and anomalies (blue dots) fall outside, as shown in Figure 1. The boundary between normal and anomaly samples is defined as the classification threshold. To visualize the neural network, a fully convolutional data description (FCDD) has been developed [36], in which the abnormal images are displayed in the form of a thermal map. In such a way, it provides a more intuitive explanation of the working principles of anomaly detection. Inspired by the transfer learning and semi-supervised anomaly detection methods, the transfer learning model based on the VGG-16 is employed to conduct semi-supervised anomaly detection. In this study, cracks on the infrastructure image are seen as abnormal, whereas images without cracks are considered normal. With a part of normal images as the training set, the classifiers are trained and employed to classify other images. In this way, the classifiers can achieve high accuracy and testing speeds and describe the working principles of the neural network. The rest of this paper is organized as follows. In Section 2, the methodology, the experimental flow and the performance evaluation indicators of the network model are briefly introduced. In Section 3, the effects of crack images in the training set on network model performance are compared. In Section 4, the effectiveness of the proposed method in different data sets is validated in terms of experiments. Finally, conclusions are made in Section 5.