# Rainfall Similarity Search Based on Deep Learning by Using Precipitation Images
## 4 Experiment and Result Analysis
### Comparative Analysis  
To further verify the applicability and robustness of NDCG-IPSO, this experiment compared the image search results of our method with color histogram (CH) [28; 29], BORDA [30], principal component analysis (PCA) [31], and the NDCG-PSO under the same conditions. Table 3 shows the image search results of the five methods on the same dataset.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Images** & **Accuracy** & **NDCG@5** & **NDCG@10** \\ \hline Training sample & 0.984 & 0.978 \\ Test sample & 0.978 & 0.964 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Optimal weights of the three feature distances for precipitation image.  
Figure 7: Image search results of NDCG-IPSO.  
A color histogram is widely used in many image retrieval systems, which search similar images by extracting color histograms in images and calculating the distance between the histograms. Considering that precipitation images mainly adopt color features to represent different precipitation information, the color histogram is perhaps the most suitable method for precipitation image similarity searches. The global CH [28] and the block CH [29] with 3 \(\times\) 3 blocks are used to search similar precipitation images. The results shown in Table 3 indicate that though global CH it can well characterize the color features of precipitation images, it ignores the spatial information of color features and results in low accuracy of similarity retrieval. The block CH considers part of the spatial information, and its searching accuracy is better than that of the global CH. However, block CH does not consider the physical meaning of the different colors on the precipitation image, which leads to worse searching accuracy than that of NDCG-IPSO.  
The PCA and BORDA are two commonly used multi-index comprehensive evaluation methods, which are also widely used in the mining of multivariate hydrological similarity. The PCA conducts principal component analysis on all three feature distances and takes the feature with cumulative variance contribution rates greater than 85% as the principal component, and then weighs the features according to their variance contribution rates to obtain the search results after sorting. The BORDA sorts the feature distance once and synthesizes the similarity search results of those feature distances by BORDA to obtain the final query result. Although PCA, BORDA and NDCG-IPSO extract precipitation spatial distribution, precipitation center, and regional precipitation and comprehensively consider three distances to search similar images, NDCG-IPSO uses machine learning algorithms to optimize ensemble weighing method parameters and thus achieves better results than that of PCA and BORDA.  
The only difference between NDCG-PSO and NDCG-IPSO is that the latter adopts the inertia weight and two learning factors in the PSO algorithm with an increase in the number of iterations. This adaptive adjustment improves the search performance and accuracy of the NDCG-IPSO. Figure 8 shows the fitness function value, namely _NDCG@5_, varying with the number of iterations in the NDCG-PSO and NDCG-IPSO. It can be seen from Figure 8 that NDCG-IPSO obtains the optimal particle fitness of 0.984 after 18 iterations; while NDCG-PSO gets stuck in a local optimum of 0.959 after 27 iterations. This indicates that IPSO can improve the search accuracy and optimization speed of image similar search and thus provides support for improving similar precipitation image retrieval.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Accuracy** & **NDCG@5** & **NDCG@10** \\ \hline NDCG-IPSO & 0.978 & 0.964 \\ Global CH [28] & 0.721 & 0.662 \\ Block CH [29] & 0.834 & 0.803 \\ BORDA [30] & 0.836 & 0.796 \\ PCA [31] & 0.702 & 0.623 \\ NDCG-PSO & 0.959 & 0.923 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparative analysis of image search results based on different methods.