# Top Position Sensitive Ordinal Relation Preserving Bitwise Weight for Image Retrieval
## 3 Experimental Results and Discussion
### Experimental Results  
In this section, we first encode floating data into 32-, 64-, and 128-bit binary codes by the hash methods (TORBW, LSH [7], AGH [8], KMH [9], Top-RSBC [25], and OCH [1]) and achieve ANN search tasks according to Hamming distances. Then, TORBW, WhRank [23], and QRank [24] assign different weight values to each binary bit and utilize the weighted Hamming distances to resort the tied ranking orders. The ANN search experimental results are shown in Tables 1-3 and Figures 2-4. We separately define the ground truth as 10 and 100 nearest neighbors in the Euclidean space. Figure 3: The _recall_ curves of the comparative experiments on the Cifar10 dataset mapped into 32-bit (**a**), 64-bit (**b**), and 128-bit (**c**) binary codes. The numbers of the true nearest neighbors in the first row and the second row are 10 and 100, respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ground Truth** & \multicolumn{3}{c}{**10**} & \multicolumn{3}{c}{**100**} \\
**Binary Bits** & **32** & **64** & **128** & **32** & **64** & **128** \\ \hline TORBW & 5.83 & 16.82 & 21.05 & 5.54 & 16.71 & 31.59 \\ OCH & 5.62 & 16.57 & 20.76 & 5.37 & 16.42 & 30.48 \\ Top-RSBC & 5.43 & 16.38 & 20.43 & 5.06 & 16.21 & 25.37 \\ KMH\_QRank & 5.05 & 16.21 & 20.06 & 4.82 & 16.07 & 18.35 \\ KMH & 4.38 & 8.89 & 10.17 & 3.98 & 8.76 & 8.92 \\ AGH\_QRank & 4.87 & 15.03 & 29.74 & 4.67 & 14.86 & 29.64 \\ AGH\_WhRank & 3.12 & 8.73 & 18.02 & 2.92 & 8.53 & 17.75 \\ AGH & 2.93 & 5.64 & 7.85 & 2.81 & 5.46 & 7.62 \\ LSH\_QRank & 3.74 & 10.22 & 25.15 & 3.48 & 10.07 & 24.89 \\ LSH\_WhRank & 2.81 & 6.14 & 15.92 & 2.67 & 5.94 & 15.71 \\ LSH & 2.24 & 5.44 & 7.47 & 2.03 & 5.17 & 7.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The _mAP_ (\(\%\)) values of the comparative experiments on the SIFT1M dataset. Figure 2: The _recall_ curves of the comparative experiments on the GIST1M dataset mapped into 32-bit (**a**), 64-bit (**b**), and 128-bit (**c**) binary codes. The numbers of the true nearest neighbors in the first row and the second row are 10 and 100, respectively. We perform ANOVA tests by matlab function \"anovan1()\" and show the experimental results in Table 4. From the experimental results, we know that the improvements made by our algorithm are significant. In LSH [7], the learning process is independent from training samples, and the ANN search performance cannot evidently improve as the number of binary bits increases [8]. Thus, to obtain a satisfying ANN search performance, LSH needs a long binary code or multiple hash tables. In contrast, data-dependent algorithms, such as TORBW, OCH [1], Top-RSBC [25], KMH [9], and AGH [8], utilize a kind of machine learning mechanism to learn hashing functions, which can minimize the ANN search performance loss on a training database. The data-dependent hashing algorithms can achieve a better ANN search performance with compact binary codes. In this paper, the maximum number of binary bits is only 128, and the data-dependent hashing algorithms are superior to LSH. AGH [8] generates centers with the k-means algorithm and learns binary codes with the spectral graph cut mechanism. However, AGH demands that the distribution of training samples should be uniform [10]. In practice, the databases used in this paper do not obey a uniform distribution. KMH [9] learns encoding centers, which can minimize both quantization loss and similarity loss. As a result, the performance of KMH is better than that of AGH. AGH and KMH aim to preserve a pointwise similarity relationship. Top-RSBC defines a pairwise similarity relationship restriction for learning hashing functions, which can further enhance the power of preserving a similarity relationship among samples. The ANN search task emphasizes preserving an ordinal relation. To fulfill this task, TORBW and OCH [1] generate binary codes, which can preserve an original ordinal relation among data points in a Hamming space. Thus, TORBW and OCH have a superior performance over AGH, KMH, and LSH.