## 4 Experiment and Result Analysis
### Unsupervised Feature Selection
#### 4.1.4 Experimental Results  
Firstly, we compared our UFS-ID method with three popular types of missing data values, i.e., completely at random, at random (conditioned on values in another randomly chosen column, being in a random interval) or not at random (conditioned on values to be \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Instance** & **Feature** & **Class** \\ \hline CANE & 1080 & 856 & 9 \\ cifar & 60,000 & 3072 & 10 \\ connect-4 & 67,557 & 126 & 3 \\ vehicle & 78,823 & 126 & 3 \\ USPSt & 2007 & 256 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summarization of used data sets. missed). In these experiments, we used the CANE data set to evaluate the effectiveness of different types of data values missed. In Figure 2 the relative ACC is shown in a given condition. From the figure, we can obviously see that our method worked well in respect to the three popular types of data values missed, even in the difficult missing-not-at-random condition. Furthermore, our UFS-ID method with the non-random-type dataachieved better performance compared to other two types. For convenience, completely random-type data were adopted for use in the subsequent experiments. Secondly, we selected features with different incomplete instances ratios (i.e., 0, 10%, 30%, 50%, 70%, 90%) to perform clustering tasks, and the clustering results were obtained, as shown in Table 3. The best results are denoted in bold in the table. Based on the results shown in Table 3, we concluded that our UFS-ID approach achieved the best clustering performance compared to other competing UFS methods on incomplete data. In addition, the clustering results of our UFS-ID approach were statistically significantly better than those of all comparison methods in term of ACC and NMI. In particular, it can easily be verified from the table that the performance of the UFS-ID approach represented a great improvement in the large and small incomplete data set. Through further analysis of the experiment results, we can draw the following conclusions. 1. As the incomplete instance ratio increased, the performance of all schemes dropped sharply. For instance, on the cifar data set, the ACC of all schemes dropped by 1.31% on average at a ratio of 0.1, compared with a ratio of 0.9. In addition, on the vehicle data set, the ACC of all schemes dropped by 5.41% on average at a ratio of 0.1, compared with a ratio of 0.9. It also can be verified that most of the schemes achieved the best performance with small ratios, showing that the number of complete instances played an important role in those feature selection schemes. 2. The performance of our UFS-ID approach was similar to that of imputation and HQ-UFS approaches. It achieves better performance compared with other traditional feature selection approaches on the OSs of incomplete data sets. For example, on the USPSt data set, the UFS-ID approach achieved around 3.0% and 5.5% improvements at the ratios of 0.1 and 0.9, compared with RFS. This indicates that the more information is employed for the imputation, the more similar is the performance of HQ-UFS and UFS-ID. 3. The performance of GSR_knn, GSR_mean, GSR_missForest, GSR_DGM, GSR_MIWAE, and HQ-UFS was worse than that of our UFS-ID method. The reason for this is that UFS-ID utilizes neighbor data reconstruction information to improve the incomplete data structure for the selection of discriminative features, whereas other approaches do not add the information derived from neighbor data. Figure 2: Comparison of ACC performance across the CANE data set with three varying types of missing data values.