# Spectra-Based Selective Searching for Hyperspectral Anomaly Detection
## 4 Discussion
### Parameter Setting of Triple-S  
We investigate and demonstrate the influence of parameter settings on the results of initial oversegmentation and region merging in the proposed spectra-based selective search  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dataset** & **GRX** & **FFE** & **FEBPAD** & **LSAD-CR-IDW** & **LRSRD** & **Triple-S** \\ \hline
**AVIRIS San** & 0.9139 & 0.9873 & 0.9951 & 0.9974 & 0.9873 & **0.9997** \\
**Diego Airport** & 0.9745 & 0.9979 & 0.9981 & 0.9986 & 0.9883 & **0.9998** \\ \hline \hline \end{tabular}
\end{table}
Table 1: AUC scores of different methods.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Dataset** & **GRX** & **FFE** & **FEBPAD** & **LSAD-CR-IDW** & **LRSRD** & **Triple-S** & **Unit** \\ \hline
**AVIRIS San** & 0.11 & 30.98 & 3.671 & 2236.68 & 73.19 & 15.91 & second \\
**HYDICE Urban** & 0.09 & 12.61 & 2.696 & 15.6138 & 65.27 & 13.92 & second \\ \hline \hline \end{tabular}
\end{table}
Table 2: Computing time of different methods.  
Figure 8: Receiver operating characteristic (ROC) curves for HYDICE Urban dataset.  
method. The proposed spectra-based selective searching algorithm has two important parameters, namely \(K\) and \(T\).  
First, we randomly selected \(K\) to be 0.02, 0.2, 2, 20, 200, and 2000 for the two hyperspectral datasets, and the corresponding results of oversegmentation are shown in Figure 9a-I. As shown in Figure 9a,g, if the value of \(K\) is too small, such as \(K=0.02\), the oversegmentation results are too trivial to identify the category information of the features in the image. When \(K\) is set in an appropriate range, the hyperspectral image can be divided into different regions with a data-driven shape and size according to the shape and category of the surface features. When \(K\) gradually increases and is greater than the appropriate range, such as \(K=20\), most of the pixels in the hyperspectral image are classified as background. However, the background pixels around the anomaly regions are regarded as anomalies, and some anomaly pixels will be regarded as background. As \(K\) becomes larger, most of the anomaly pixels are submerged into the background. It is difficult to distinguish abnormal targets from the background in this case. For a better initial oversegmentation effect, the constant parameter \(K\) was set to 2 for the AVIRIS San Diego airport dataset and \(1\) for the HYDICE urban dataset in our experiment.  
Next, we get threshold \(T\) of region merging through the spectral similarity of a series of adjacent regions obtained by the step of oversegmentation. The value range of the parameter \(T\) is dependent on the similarity matrix of each pair of adjacent regions. The minimum value of the similarity matrix is the lower limit of the threshold \(T\), while the maximum value of the similarity matrix is the upper limit of the threshold \(T\). We traversed  
Figure 9: Different oversegmentation results for the two real-world HSIs with \(K=0.02\), 0.2, 2, 20, 200, and 2000; (**a–f**) correspond to the AVIRIS San Diego airport data and (**g-l**) correspond to the HYDICE urban data.  
the value of \(T\) within this range in steps of 0.05. Choosing 0.05 as the step not only ensures that a reasonable threshold \(T\) can be obtained, but also reduces the complexity of the traversal process. The optimal thresholds \(T\) are determined by the best detection result and the highest AUC value. The best detection performance of the proposed Triple-S anomaly detector could be achieved when \(T=1.15\) for the AVIRIS San Diego airport dataset and \(T=1.4\) for the HYDICE urban dataset.