# Image Retrieval Method Based on Image Feature Fusion and Discrete Cosine Transform
## 4 Experimental Results and Analyses
### Influence of Variable Factors on the Experiment
#### 4.3.4 Feature Dimensionality Reduction  
Dimension reduction is transforming data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data. AvgPool-DCT  
Here, we conduct comparative experiments on the dataset by applying DCT transform to deep features of the AvgPool layer. Table 6 lists the APs and ARs by this structure. The NR is 20, and the Canberra metric is used for the similarity measure. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Performance**} & \multicolumn{5}{c}{**Network Architecture, Feature Dimension**} \\ \cline{3-6}  & & **AlexNet, 1000** & **GoogleNet, 1000** & **ResNet50, 1000** & **GooglePlaces, 365** & **ResPlaces, 434** \\ \hline \multirow{3}{*}{Corel-1k} & AP (\%) & 89.72 & 93.71 & **94.09** & 92.75 & 93.59 \\  & AR (\%) & 17.95 & 18.74 & **18.82** & 18.55 & 18.72 \\ \cline{1-1}  & AP (\%) & 35.86 & 39.24 & **42.3** & 36.74 & 41.74 \\ \cline{1-1}  & AR (\%) & 7.17 & 7.85 & **8.46** & 7.35 & 8.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: APs and ARs results using deep features extracted from different networks, Top NR = 20. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Performance**} & \multicolumn{5}{c}{**Network Architecture, Layer, Dimension**} \\ \cline{3-6}  & & **GoogleNet, FC,** & **GoogleNet,** & **ResNet50, Fc, 1000** & **ResNet50, AvgPool, 2048** \\ \hline \multirow{3}{*}{Corel-1k} & AP (\%) & 93.71 & 94.97 (\(\uparrow\)1.26) & 94.09 & 94.67 (\(\uparrow\)0.58) \\  & AR (\%) & 18.74 & 18.99 (\(\uparrow\)0.25) & 18.82 & 18.93 (\(\uparrow\)0.11) \\ \cline{1-1}  & AP (\%) & 39.24 & 41.12 (\(\uparrow\)1.88) & 42.3 & 46.48 (\(\uparrow\)4.18) \\ \cline{1-1}  & AR (\%) & 7.85 & 8.22 (\(\uparrow\)0.37) & 8.46 & 9.30 (\(\uparrow\)0.84) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: APs and ARs results by using deep features extracted from different layers, Top NR = 20. The experimental results show that adding DCT does not significantly reduce image retrieval performance, and in some cases, even enhances it. Therefore, DCT can be used for feature dimensionality reduction. Then, we conduct comparative experiments on the dataset by reducing deep feature dimensions. The DCT has a substantial \"energy compaction\" property, capable of achieving high quality at high data compression ratios. Table 7 lists the APs and ARs by using DCT methods. The NR is 20, and the Canberra metric is used for the similarity measure. When the feature dimension is reduced by 75%, the maximum drop does not exceed 1%, and when it is reduced by 87%, the drop does not exceed 2%. Therefore, DCT can be used to reduce the dimensionality of features. AvgPool-PCA  
PCA [73] is a statistical procedure that orthogonally transforms the original n numeric dimensions into a new set of n dimensions called principal components. Keeping remains of only the first m < n principal components reduces data dimensionality while retaining most of the data information, i.e., variation in the data. The PCA transformation is sensitive to the relative scaling of the original columns, and therefore we use L2 normalization before applying PCA. The results are listed in Table 8.  
It can be seen that the use of PCA does not significantly reduce the performance of the feature while reducing its dimension and even optimizes the feature to be more suitable for image retrieval.