## 4 Experiment  
### Dataset  
We qualitatively and quantitatively evaluated our method on the Architectural Cultural Heritage (ArCH) dataset [17]. In the state of the art, the most used datasets to train unsupervised learning are: ModelNet40 [13] with more than 100 k CAD models of objects from 40 different categories (e.g., table, chair, lamp, etc.) for classification tasks and ShapeNetPart [58] dataset with 31,693 meshes classified into 16 common object classes (e.g., plane, table, chair, etc.); each object has two to five parts for part-segmentation tasks. However, none of them can be used for the segmentation of buildings' point-cloud. Other outdoor datasets used in this task, such as Semantic3D [59] and Oakland [60], feature LoD1 or LoD2 for the architectural elements. To date, there are no published datasets focusing on point clouds of urban buildings with a sufficient level of details, such as LoD3.  
A building in LoD3 has detailed surface structures such as walls, roof and openings (doors and windows). The components of architectural heritage including detailed roof, facade structures, openings and some specific structures such as vaults, columns and front porches are similar to but more involved than in standard modern buildings. Networks trained on these kinds of datasets are easy to generalize to other building scenes. Therefore, we chose an immovable CH asset dataset with fine per-point labels, named ArCH dataset, to evaluate our method. For data acquisition techniques, it is acquired by static terrestrial laser scanners, namely a FARO Focus 3D X 120 and 130, and a Riegl VZ-400, and by applying structure-from-motion photogrammetry [61; 62] based on images collected by Nikon D880E, D3100 and D3X cameras, and a DJI Phantom UAV platform equipped with a SONY ILCE 5100L camera.  
The ArCH dataset consists of 17 indoor and outdoor labeled scenes, 15 for training and 2 for testing purposes, respectively. It includes different types of scenes such as rooms, churches, chapels, cloisters, pavilions, squares and porticoes. Many of these scenes are part of (or candidate to be listed in) the UNESCO World Heritage List (WHL- whc.unesco.org/ en/list. Accessed on 24 September 2021). These scenes represent various historical periods and architectural styles of historical built heritage. As a consequence, the use of this kind of dataset as training data may improve the generalization ability of our network among various types of buildings.  
Our primary motivation to study unsupervised classification problems was that the number of training data is limited. To test the performance when the number of unlabeled and labeled data is small, as shown in Figure 3, we select three small outdoor scenes (namely, \"SMV_1\", \"SMV_24\", \"SMV_28\") from the 15 labeled scenes as the training data in both unsupervised AE training and supervised segmentation training stages. The training data in our experiment are only 10% of total number of points with respect to the standard of the state of the art [5], where all scenes are used as training data. Then we follow the settings adopted by [5] that removed the \"others\" category. Since validation data is used in deep learning to tune parameters, to choose features, and so on, the availability of validation data has no effect on our ability to evaluate the model's performance. As a result, unlike [5], where \"Scene A\" and \"Scene B\" are used as validation and test sets, we use two unseen scenes (\"A_SMG_portico\" as \"Scene_A\" and \"B_SMV_chapel_27 to35\" as \"Scene_B\") as our test data (see Figure 3). It is worth mentioning that our training data include only the type of the outdoor chapel, but our test data include both indoor and outdoor and different types of architectural elements (\"portico\" and \"chapel\"), which is more challenging than the supervised methods including different types of scenes in their training data.