Manga (Japanese comic) is a globally popular content. In recent years, sales of e-comics that converted to electronic data from paper-based manga are increasing because of the widespread use of electronic terminals. Against this background, it has been proposed to improve the accessibility of e-comics by tagging manga images with metadata. In order to allocate metadata more efficiently, technology that automatically extracts elements such as character and speech is required. One way to classify characters is to get image features from the character's faces and cluster them. Previous research has shown that using the intermediate output of CNN which fine-tuned with character face images is effective for character face recognition. We proposed a clustering method using Density-Based Spatial Clustering of Applications with Noise (DBSCAN) to classify character face images without specifying the number of clusters. However, DBSCAN is greatly affected by the hyperparameter. The purpose of this study is to automatically classify character face images without complicated hyperparameter setting. We examine the application of Ordering Points to Identify the Clustering Structure (OPTICS) and Hierarchical DBSCAN (HDBSCAN), which are density-based clustering algorithms that extend DBSCAN. OPTICS is an algorithm for finding clusters in spatial data, and HDBSCAN is an algorithm extracts flat partition from hierarchical cluster data. We also verify the effective CNN model as the feature extractor of face images. Experimental results showed that HDBSCAN is effective for character face image clustering.