Algorithm 1 Outlier Detection

1: Divide $X$ into $m$ sub-regions $D=\left\{d^1,d^2,\cdots ,d^m\right\}$ by Euclidean space distance of the points, and initialize

outlier cluster ${\widehat{c}}^O=\cancel{0}$;

2: Conduct random sampling on each sub-region and generate hypotheses $H$;

3: Calculate the residual histogram preference matrix $Q$;

4: Calculate the distance matrix $d_w$ for the residual histogram preferences of points $i$ and $j$;

5: Conduct linkage clustering with distance and obtain clusters $C=\left\{c^1,c^2,\cdots ,c^n\right\}$;

6: Calculate the outlier index $\xi =[{\xi }_{c^1},{\xi }_{c^2},\cdots ,{\xi }_{c^n}]$ for each cluster in $C$, and select the cluster with the maximum

outlier index as the outlier cluster $c^O=c^t$, $t=\arg {\max }_j{\xi }_{c^j}$, inlier clusters $C^I=C-c^O$;

7: If $c^O=={\widehat{c}}^O$, return $c^O$ as the outlier detection result; else ${\widehat{c}}^O=c^O$, $D=C^I$, and return to step 2.