## 6 Dimensionality Reduction
### AFS with Acquisition Cost  
In designing an intelligent sensor system, the objective function of the AFS in the optimization tool (ADIMSS) is often associated with certain cost. The aim of the AFS with acquisiton Cost (AFSC) is to discard the unnecessary and expensive features. The accumulative expression of the objective function is:  
\[\textit{fitness}=w_{1}\ q+w_{2}\Bigg{(}1-\frac{C_{s}}{C_{t}}\Bigg{)}+w_{3} \Bigg{(}1-\frac{f_{s}}{f_{t}}\Bigg{)} \tag{29}\]  
where \(q\) can be the quality of overlap measurement given in subsection 3.5 and/or the classification rate depending on the user selection, \(w_{i}\) are weighting factor with \(\sum_{i=1}^{3}w_{i}=1\). \(C_{s}\) denotes the sum of costs from selected features, \(C_{t}\) denotes the sum of total cost from all features, \(f_{s}\) is the number of selected features, and \(f_{t}\) is the number of whole features. Table 6 shows one example of defining the cost value by designer for each mathematical operation used to extract features in feature computation methods.  
Figure 21: Process of intelligent multi-sensor system design focused on the structure optimization by elimination of redundant feature computation and sensors.  
Table 7 gives the details of the parameter settings of PSO and GA with regard to the automated design activities based on automatic feature selection with acquisition cost and the cost assignment of eye image dataset. Again, these parameter settings of PSO and GA are heuristically set based on the knowledge base. The cost assignment for the three feature computation operators is determined with regard to the number of multiplication and addition operations. In these experiments, the assuming multiplication has the cost of 10 additions. Therefore, the cost of each feature for Gabor filter, ELAC, and LOC is determined as shown in Table 7. From the experimental results shown in Table 8, the AFSC employing PSO or GA can select low cost and less number of features (_i.e._, six of 58 features).  
\begin{table}
\begin{tabular}{l l c} \hline
**No.** & **Operation** & **Cost** \\ \hline
1 & Addition (+) & 1 \\
2 & Substraction (-) & 1 \\
3 & Multiplication (*) & 4 \\
4 & Substraction (/) & 4 \\
5 & Comparison (\(>\),\(\geq\), \(<\), \(=\), \(\
eq\)) & 2 \\
6 & Root square & 6 \\
7 & Exponential (e\({}^{*}\)) & 8 \\
8 & logarithm & 8 \\ \hline \end{tabular}
\end{table}
Table 6: The cost values for basic operations mostly used to evaluate the computational effort of methods of feature computation.  
\begin{table}
\begin{tabular}{l l l l} \hline
**AFS - GA** & **AFS - PSO** & **Eye image data** \\ \hline Population = _20_ & Population = _20_ & Gabor filter = 12 features \\ Selection = _Roulette Wheel_ & \(w_{start}=0.9\); \(w_{end}=0.4\) & ELAC = 13 features \\ Recombination = _discrete_; P\({}_{c}\) = _0.8_ & \(c_{1}\) = _2; \(c_{2}\) = 2_ & LOC = 33 features \\ Mutation = _uniform_; P\({}_{m}\) = _0.01_ & Update fcn = _binary_ & Cost: \\ Elitism = _10\%_ & Maximum generation = _100_ & Gabor filter = 6358 per feature \\ Maximum generation = _100_ & Assessment fcn = _NPOM_ (\(k\) = 5) & ELAC = 3179 per feature \\ Assessment fcn = _NPOM_ (\(k\) = 5) & & LOC = 1445 per feature \\ \hline \end{tabular}
\end{table}
Table 7: Parameter settings of GA and PSO, as well as the acquisition cost  
\begin{table}
\begin{tabular}{l c c c c c} \hline
**Method** & **Cost** & **Feature** & **9-NN (\%)** & **RNN (\%)** & **NNs (\%)** \\ \hline without AFS & 165308 & 58 & 96.72 & 80.33 & 97.87 \\ AFS-GA & 53176 & 16 & 98.36 & 95.08 & 96.81 \\ AFSC-GA & 13872 & 6 & 96.72 & 95.08 & 96.81 \\ AFS-PSO & 45951 & 18 & 100 & 95.08 & 98.94 \\ AFSC-PSO & 10404 & 6 & 96.72 & 98.36 & 98.94 \\ \hline \end{tabular}
\end{table}
Table 8: The AFS and AFSC results for eye-image data [19].