Spherical data validation of rock discontinuities orientation from Drone-derived 3D Point Clouds

This work presents a methodology for the statistical validation of discontinuity surfaces obtained from point clouds using digital photogrammetry from drones. Our methodology allows you to review the quality of the data obtained with photogrammetry and decide whether these measurements are representative of the discontinuity surfaces that they analyze. It consists of three steps, the first one being a shape analysis that allows defining which statistical model should be used: Fisher for circularly symmetric clusters or Bingham fits better for axially symmetric clusters. This step also makes the most significant difference to other works since our methodology starts from the premise that not all discontinuity surfaces are flat. Therefore, Fisher parameters do not allow validating data that do not correspond to a plane. In the second step of the methodology, we calculate the consistency parameters that depend on the statistical model defined in step 1. The parameters are similar for both models; both estimate κ which indicates how much the sample is concentrated around the mean orientation and validates the existence of this and which is the value of the generating angle of a cone with a 95 % confidence limit that it contains within the mean orientation. Finally, step 3 is used when there are control measurements to compare the point cloud data and define if both samples characterize the same discontinuity surface in the rock mass. The results obtained on a rock outcrop allowed us to observe that the measurements obtained from the drone faithfully represent the discontinuity surface analyzed when these were compared with the measurements made manually with the compass. Furthermore, the dispersion parameters (

Estimation of the number of clusters on d-dimensional sphere

Spherical data is distributed on the sphere. The data appears in various fields such as meteorology, biology, and natural language processing. However, a method for analysis of spherical data does not develop enough yet. One of the important issues is an estimation of the number of clusters in spherical data. To address the issue, I propose a new method called the Spherical X-means (SX-means) that can estimate the number of clusters on d-dimensional sphere. The SX-means is the model-based method assuming that the data is generated from a mixture of von Mises-Fisher distributions. The present paper explains the proposed method and shows its performance of estimation of the number of clusters.

Collaborative filtering with q-divergence-based fuzzy clustering for spherical data

Although recommendation systems are the most powerful tool to help people choose items, a higher recommendation accuracy is required to satisfy the needs of the people. Motivated by this requirement, this study proposes a novel collaborative filtering (CF) algorithm, which is the underlying technology of a recommendation system. It filters items for a target user based on the reactions of similar users. Cluster analysis helps detect similar users by grouping a set of users such that users in the same group are more similar to each other than to those in other groups. However, in most representative CF algorithms such as GroupLens algorithm, users are considered as spherical data, and as categorical multivariate data in the clustering phase of a previous study. This study overcomes this logic gap by proposing a novel CF method using fuzzy clustering for spherical data based on q-divergence as both the clustering phase and the GroupLens algorithm consistently deal with users as spherical data. Experiments were conducted on six real datasets—BookCrossing, Epinions, Jester, LibimSeTi, MovieLens, and SUSHI, to compare the performance of the proposed method with GroupLens and the method using fuzzy clustering for categorical multivariate data based on q-divergence, which are conventional methods, where the performance is measured by the area under the receiver operating curve. The results of the experiments indicate that the proposed algorithm outperforms the others in terms of recommendation accuracy.