## 2 Multi-Classification LS-SVM Survey
### Proposed WP-SVM
#### Iii-B2 Dynamic Processing for Chunk Data  
For incremental chunk processing, the data are still acquired incrementally, but they are stored in a buffer awaiting batch processing. To update the model after capturing \(k\) sequences, the recently acquired data are processed and the model is updated as described in Eq. (18). Alternatively, we can use the Sherman-Morrison-Woodbury (SMW) [30] generalization formula to account for the perturbation introduced by matrices \(M\) and \(L\) such that \(\left({I+M^{T}A^{\scalebox{0.7}{$-$}1}L}\right)^{\scalebox{0.7}{$-$}1}\) exists. In this case, the SMW generalization formula is  
\[\left({A+LM^{T}}\right)^{\scalebox{0.7}{$-$}1}={A^{\scalebox{0.7}{$-$}1}}-{A^{ \scalebox{0.7}{$-$}1}}L(I+M^{T}A^{\scalebox{0.7}{$-$}1}L)^{\scalebox{0.7}{$-$}1}M ^{T}A^{\scalebox{0.7}{$-$}1} \tag{20}\]  
where  
\[M=\psi\left[{ \begin{array}{*{20}{c}}{{x_{{\scalebox{0.7}{$N+$}1}}}}\\ {{\left({I_{c}-I_{i}}\right)}}\end{array} }\right];\;L=\psi\left[{ \begin{array} []{*{20}{c}}{{x_{{\scalebox{0.7}{$N+$}1}}}}\\ {I}\end{array} }\right]^{T}\]  
Using Eqs. (17) and (20), the new model can represent the incrementally acquired sequences as follows:  
\[\left[{ \begin{array}{*{20}{c}}W\\ B\end{array} }\right]_{\text{new}}=\left[{ \begin{array}{*{20}{c}}W\\ B\end{array} }\right]_{\text{old}}+\left[{ \begin{array}{*{20}{c}}\Delta E\\ \Delta U\end{array} }\right]+\left[{ \begin{array}{*{20}{c}}\Delta E\\ \Delta U\end{array} }\right]-\left[{ \begin{array}{*{20}{c}}W\\ B\end{array} }\right]_{\text{old}}\left[{I-A^{\scalebox{0.7}{$-$}1}M\left(I+M^{T}A^ {\scalebox{0.7}{$-$}1}L\right)^{\scalebox{0.7}{$-$}1}M^{T}A^{\scalebox{0.7}{$-$}1 }}\right] \tag{21}\]  
Eq. (21) shows the influence of the incremental data on calculating the new separating hyper-plane slopes and intercept values for the \(c\) different classes. The proposed _WP-SVM_ meets all the main requirements for online learning and uses the learned knowledge towards incorporating new 'experiences' in a computationally efficient manner. The leftmost sub-figure 2.a represents the plane orientation before the acquisition of \(\text{x}_{\text{N+1}}\), whereas the rightmost sub-figure 2.b shows the effect of \(\text{x}_{\text{N+1}}\) on shifting the planes orientation whenever an update is necessary. Figure 2: Effect of \(\text{x}_{\text{N+1}}\) on plane orientation when model is updated. Table 2 depicts the workflow of the _WP-SVM_ classifier. **Table 2._WP-SVM_ Algorithm Flow. \begin{tabular}{l l} \hline \hline Step \# & Algorithm \\ \hline \end{tabular}   
_Step 1_ & Train initial model using _TrainSet_ which consists of \(N\) patient data each having \(f\) features. \\  & \( \begin{bmatrix}W\\ B\end{bmatrix} =\Delta^{-1}L\) ; \(A= \begin{bmatrix}(C-G)&(D-H)\\ (D-H)^{T}&(R-Q)\end{bmatrix} \) ; \(L= \begin{bmatrix}E\\ U\end{bmatrix} \) \\ \end{tabular}  
Store only \(W\) and \(B\) as _Initial_Model_. Discard _TrainSet_  
_Step 2_ & Acquire incremental data _IncSet_. _Step 3_ & Validate the generalization performance using decision function of _Initial_Model_ with the independant _TestSet_  
\[f(x)=\arg\max_{m}((w_{-}^{T}x)+b_{m}),m=1...c\]  
Case 1: If _Mis_\(Err<\) Acceptable Rate \\  & _-Initial_Model_ still valid. \\  & _-Store the incrementally acquired images in a buffer so that they are included in future updates._ \\  & _Storing these sequences will help ensure vital learning for the classifier even after several no model update steps._ \\  & _- Increment counter_Count _by 1 to keep track of the consecutive instances _Initial_Model_ not updated. \\  & _- If Mis_\(Err\) _is statistically increasing and or_Count_\(=\)_Limit, initiate a model retrain to insure learning and delete the incrementally acquired video sequence stored in the buffer. New Model=_Retrain_Model_ - Go to Step 2._ \\ \hline \end{tabular}  
_Case 2: If _Mis_\(Err>\) Acceptable Rate, apply _WP-SVM_, _Inc_Model_ becomes:_  
1- For dynamic sequential processing :  
\[ \begin{bmatrix}W\\ B\end{bmatrix} _{new}=(A+\Delta d)^{-1}(L+\Delta L) \Delta A=