## 3 Results
### Application of SVM Classification to Implant Deformation Data  
The functional dependence ID--force applied was redefined introducing a categorical data, the implant type. In such way, the simple three-component regression problem (for three implant types) was be converted into a unique classification problem.  
SVM classification was expected to settle bounds of the data set limits depending on the implant type and to establish if a statistically significant difference existed between PLS and HEF in terms of ID--force applied data. In other words, by reconfiguring a simple problem of ID as a function of applied force as a classification problem it was possible to answer the question whether or not a statistically significant advantage of PLS over HEF existed.  
To implement an SVM classifier for the ID--applied force data set, the Python _sklearn_ library was employed. The three data sets (one for each implant type) were joined in one set consisting of \(38\times 3=114\) pairs of applied force--ID values. First 38 pairs correspond to LP type, the next 38 to PLS and the last 38 to HEF type. The categorical data--implant type was being provided as an input to the classifier as a column vector containing implant type information.  
The data science platform Anaconda3 was used with Jupyter Notebook 6.0.3 and Python Kernel 3.7.6. Jupyter Notebook is an open source web application that allows creation and sharing of live code documents. The _sklearn_ classifier regularization parameter C value was chosen 1.5 following the guidelines from [40]. Since a linear or quasi-linear separation was expected, the linear type kernel was selected. As the classifier operates best with normalized data, both \(X\) columns were scaled to the range [-1,1]. The scaled data is plotted in Figure 17 using marker color selected according to the categorical data.  
Figure 16: Box plot of ID data.  
To render each region cluster as a distinct color 2-D region, a dense mesh of points was created and the classifier previously trained with the force--ID data set was applied to the dense mesh. The results are presented in Figure 18.  
The classifier identified three distinct regions (defined in Figure 18 by three different color) and did not wrongly classify points belonging to one implant type to another region i.e., each implant device specific data set is placed in one region only. However, an obvious trend of the PLS points to approach the HEF region boundary can be observed. In fact, the PLS point corresponding to the applied force 3150 N (Figure 18, last point of the PLS data set) falls very close (or onto) the region boundary HEF--PLS. The data trend shown in Figure 18 can be interpreted as follows: As the applied force increased, the difference in terms of deformation between HEF and PLS decreased steadily, indicating that the advantage of PLS over HEF became statistically irrelevant. At the upper limit (3150 N), the classifier established that HEF and PLS performed similarly in a statistical sense, meaning that no statistically significant difference exists between HEF and PLS at this value of the applied force (3150 N).  
The key conclusion that can be drawn from this observation: the maximum load that can be expected has to be also included in the implant device selection criteria.  
Figure 17: Data set categorized by implant type.  
Figure 18: Data set and regions defined by the SVM classifier.