# Which Features Are More Correlated to Illuminant Estimation: A Composite Substitute
## 4 Experimental Results
### Additional Experiments  
In the proposed method, many factors will affect the performances of illuminant estimation. Some experiments are conducted to explore these influences.  
**Clustering methods and cluster numbers**. For the proposed method, we perform KFCM clustering by default to classify the training data. For comparisons, the other two clustering algorithms, i.e., K-means and the two-step method [19], are also added to the proposed framework. The reason for selecting K-means and the two-step method is that the former is one of the most commonly used clustering methods, and the latter is an effective algorithm of color constancy based on cluster models. For each clustering algorithm, we can manually set different cluster numbers in order to obtain better results. Table 6 gives some statistical metrics using different clustering methods and cluster numbers. Comparing the results using different configurations, it can be seen that the proposed method along with KFCM seems to be more effective than using K-means and the two-step method. One of possible reason might be that KFCM can provide flexible division for the training set, which enhances the robustness and generalization of the proposed method. And we find \(K=4\) or \(5\) is the appropriate selection for our method under the KFCM clustering on the combination dataset of Gehler-Shi and Cube+. It is natural that the cluster number should increase for better modeling performance if we use another dataset with more image samples.  
**Kernel width of KFCM**. In the proposed method, kernel width will affect clustering divisions, which will result in different performances. Table 7 provides some statistical metrics on the Gehler-Shi and Cube+ datasets to show the influences of kernel width in KFCM clustering. We can find that the optimal choice of kernel width for our experiments is \(\sigma=100\)-\(180\). Commonly, the optimal values are obtained by trial and tried in various testing. It should be noticed that the optimal kernel width is varying with the training dataset. Therefore, as an option, Particle Swarm Optimization can be used to search for the optimal kernel width.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Clustering**} & \multicolumn{5}{c}{**Recovery AE**} & \multicolumn{5}{c}{**Reproduction AE**} \\ \hline
**Method** & **Number** & **Mean** & **Med.** & **Tri.** & **B25\%** & **W25\%** & **Max** & **Mean** & **Med.** & **Tri.** & **B25\%** & **W25\%** & **Max** \\ \hline K-means & 2 & 2.12 & 1.53 & 1.68 & 0.48 & 4.76 & 18.32 & 2.80 & 1.99 & 2.21 & 0.59 & 6.35 & 23.79 \\ KFCM & 2 & **2.10** & 1.52 & 1.67 & 0.47 & **4.70** & 15.71 & **2.76** & 1.98 & 2.19 & 0.58 & **6.25** & 18.18 \\ K-means & 3 & 2.12 & 1.51 & 1.65 & 0.46 & 4.84 & 15.15 & 2.77 & 1.95 & 2.16 & 0.57 & 6.37 & 20.10 \\ KFCM & 3 & 2.13 & 1.53 & 1.67 & 0.46 & 4.83 & 18.87 & 2.79 & 1.97 & 2.18 & 0.56 & 6.43 & 27.39 \\ twoStep & 2 \(\times\) 2 & 5.98 & 4.05 & 5.29 & 2.49 & 10.35 & **10.98** & 8.55 & 4.16 & 6.81 & 3.47 & 15.36 & **15.68** \\ K-means & 4 & 2.15 & 1.46 & 1.61 & 0.45 & 5.06 & 51.86 & 2.84 & 1.86 & 2.10 & 0.57 & 6.77 & 91.14 \\ KFCM & 4 & 2.14 & 1.54 & 1.69 & 0.48 & 4.80 & 14.83 & 2.82 & 2.06 & 2.23 & 0.58 & 6.41 & 18.86 \\ K-means & 5 & 2.11 & **1.40** & **1.56** & 0.43 & 4.99 & 31.64 & 2.78 & **1.79** & **2.04** & **0.53** & 6.64 & 52.73 \\ KFCM & 5 & 2.17 & 1.50 & 1.69 & 0.47 & 4.95 & 14.77 & 2.85 & 1.95 & 2.18 & 0.58 & 6.61 & 18.81 \\ twoStep & 2 \(\times\) 3 & 6.29 & 5.30 & 5.00 & 2.37 & 12.02 & 17.75 & 8.58 & 6.42 & 7.04 & 3.16 & 16.24 & 25.69 \\ K-means & 6 & 2.27 & 1.44 & 1.60 & **0.44** & 5.57 & 108.90 & 3.08 & 1.81 & 2.06 & 0.55 & 7.74 & 119.54 \\ KFCM & 6 & 2.22 & 1.53 & 1.70 & 0.45 & 5.16 & 21.96 & 2.91 & 1.97 & 2.20 & 0.55 & 6.86 & 28.93 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Statistical metrics on the combination dataset of Gehler-Shi and Cube+ with different clustering methods and cluster numbers.