# Complex and Hypercomplex-Valued Support Vector Machines: A Survey
## 3 Applications
### Robotics, Computer Vision
The authors argue that it was done because the hypercomplex-valued kernels \"capture the inherent data relationships in a more accurate and physically-meaningful way, while being robust to overfitting\". The real- and quaternion-valued Gaussian kernels were used in KRR to perform channel equalization. See Section 3.4. Even when an SVR was not used in the above two applications, quaternion-valued kernels were designed and proved in real applications and their advantages over real-valued kernels were demonstrated. The advantages of using quaternion-valued kernels could be extended when SVR is used instead of KRR. Another technique that can be used to teach robots human movement and motion is the one presented in [13] and revised in Section 2.2.4. Here, an octonionic SVR was applied to the biomechanical study of human locomotion, called the gait analysis. The objective for the regressor was to estimate correct measurements of key events of the endpoint foot trajectory during human treadmill walking. The task was achieved with high accuracy. All the above proposals to predict 3D transformations could be used in robotics, computer vision and computer graphics to model motion and 3D shapes, simulation of the interaction between robots and their environment, predictive control, and structure from motion, among others. The robot path-planning problem was addressed in [9]. This problem was solved using an LSTM-CSVM recurrent system and training the LSTM module with reinforcement learning (RL). A labyrinth environment was modeled as an occupation grid. Each observation of the navigator robot was described using a quaternion, where each element of the quaternion indicates if one robot sensor reads 0, and if the next cell of the grid was free or 1 if it was occupied by an obstacle. A cross-neighborhood, as regards the actual position of the robot on the grid, was used; thus, four inputs of one quaternion were used to describe an observation (forward, backward, left, and right), and two positions of a second quaternion were used for determining the 2D coordinates of the position of the robot on the plane. The four outputs were packed in a quaternion, and they represented the action that the robot has to perform in the actual state to get the maze output (go forward, backward, left, or right). In order for the path-planning system to be used, firstly, this had to be trained using some mazes, and then proven with never-before-seen mazes. Therefore, once the path is computed, the robot can follow it in real time. Here, the hypercomplex inputs and outputs were used to get a MIMO SVM that reads two quaternions and returns one. See Section 2.1. In Table 6, the applications mentioned in this subsection for solving robotics and computer vision problems are presented in a compact manner. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Ref./Year** & **Application** & **SVM Extension Used** \\ \hline
[8]/2001 & Prediction of 3D rotation and 3D transformations using computer vision data & Multivector-valued SVM and the GA framework \\ \hline
[9]/2010 & Robot path-planning & Combined recurrent system of LSTM-CSVM \\ \hline
[13]/2012 & Study of human locomotion (the gait analysis) & Complex valued SVR \\ \hline
[57]/2014 & Simulation of 3D inertial body sensor data & KRR using quaternion-valued kernels \\ \hline
[60]/2017 & Prediction of 3D transformations & DQ regression, SVR and ridge regression to approximate the error metric for the blending of unit dual quaternions \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Applications of complex and hypercomplex SVMs for robotics and computer vision problems.