# Machine Learning Powered Microalgae Classification by Use of Polarized Light Scattering Data
## 4 Discussion  
The four polarization parameters of each record are [_I_, \(q\), \(u\), _v_], and they are derived from the Stokes vectors of scattered light, which are basically related to the incident SOP. To find the best incident SOP and reduce the detection complexity, the performance of different incident SOP and different combinations of features are discussed and the averaged classification accuracy of all categories in Table 1 based on non-linear SVM and OVO is used to evaluate the performances. The results shown in Figure 3 collect the accuracy among all the incident SOP and different combinations of polarization parameters. When the input was [_I_, \(q\), \(u\), _v_], all the SOPs achieved an accuracy of about 0.85, while the 150\({}^{\circ}\) linear SOP was slightly better than other SOPs, and the 120\({}^{\circ}\) linear SOP was the worst. Compared with the classification accuracy derived from \(I\), it is notable that the original classification accuracy was greatly improved with the addition of the polarization features. However, the relative contribution of the polarization parameters \(u\) and \(v\) was not same. For the SOP of E, L, and R, the addition of the parameter \(v\) resulted in a higher accuracy than \(u\). However, for the other linear SOPs, the parameter \(u\) brought more effective information than the parameter \(v\). The Mueller matrix is a 4\(\times\)4 matrix, \(M\), describes the polarization property of the particle, and combines the incident SOP, _S_\({}_{i}\), and the scattered SOP, _S_\({}_{s}\), that is, _S_\({}_{s}=\textbf{M}\times S_{i}\) \begin{table}
\begin{tabular}{c c c} \hline \hline
**Accuracy Threshold** & **Categories of Microalgae** & \(n\) \\ \hline \multirow{2}{*}{0.95} & _Chattonella marina; Isochrysis; Chateocros deblitis_ & 4 \\  & _Cleve; Porphyridaceae_ & \\ \hline \multirow{4}{*}{0.90} & _Skeletonema costatum; Chattonella marina; Isochrysis; Dunaliella_ & \\  & _bardawil; Isochrysis zhangjiangensis; Isochrysis CCMP3180;_ & 8 \\  & _Scripysiella trochioda; Crystomonas_ & \\ \hline \multirow{4}{*}{0.85} & _Skeletonema costatum; Chattonella marina; Thalassiosina weissflogii;_ & \\  & _Isochrysis; Chateocros curstiets; Dunaliella hardavil; Isochrysis_ & \\  & _zhangjiangensis; Isochrysis CCMP3180; Porphyridaceae;_ & 11 \\  & _Letpcylodnatus;_ & _Cryomonas_ & \\ \hline \multirow{4}{*}{0.80} & _Skeletonema costatum; Chattonella marina; Isochrysis galhana;_ & \\  & _Isochrysis; Chateocros curstiets; Cyclotella meneghitinaa;_ & \\ \cline{1-1}  & _Isochrysis zhangjiangensis; Isochrysis CCMP3180; Karenia_ & 15 \\ \cline{1-1}  & _mikimotoi; Porphyridaceae; Leptocylindrus; Zozanthella; Scripysiella_ & \\ \cline{1-1}  & _trochoidea; Crystomonas; Platymonas helgolandica tsingtaoensis_ & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Classification results using SVM by one versus one (OVO). Figure 3: The performance comparison of different incident SOPs and different combinations of features. The 16 elements of \(\mathbf{M}\) contain different aspects of physical information of particles. Usually, we have to change \(S_{i}\) 4 times and measure the respective \(S_{s}\) to calculate \(\mathbf{M}\). We can always simultaneously get the Stoke vector in a single shot but it is hard to get \(\mathbf{M}\) in that way, especially for the suspended particles. Therefore, in the dataset, we can only provide the \(S_{s}\) of the individual microalgae in a given \(S_{i}\), as the data used in the classifications in Figure 2, and at most we can obtain the statistical \(\mathbf{M}\) but not the individual \(\mathbf{M}\) of the microalgal cells [26]. Considering that different \(S_{i}\) will bring different information regarding the elements of the \(\mathbf{M}\), it is important to discuss the contribution of the elements based on the dataset.