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摘要: 针对自适应聚类集成选择方法（Adaptive cluster ensemble selection，ACES）存在聚类集体稳定性判定方法不客观和聚类成员选择方法不够合理的问题，提出了一种改进的自适应聚类集成选择方法（Improved ACES，IACES）.IACES依据聚类集体的整体平均归一化互信息值判定聚类集体稳定性，若稳定则选择具有较高质量和适中差异性的聚类成员，否则选择质量较高的聚类成员.在多组基准数据集上的实验结果验证了IACES方法的有效性：1）IACES能够准确判定聚类集体的稳定性，而ACES会将某些不稳定的聚类集体误判为稳定；2）与其他聚类成员选择方法相比，根据IACES选择聚类成员进行集成在绝大部分情况下都获得了更佳的聚类结果，在所有数据集上都获得了更优的平均聚类结果.Abstract: Adaptive cluster ensemble selection (ACES) is not only non-objective in judging the stability of cluster ensemble but also unreasonable in selecting cluster members. To overcome such drawbacks, an improved adaptive cluster ensemble selection (IACES) approach is proposed. First, IACES judges the stablity of cluster ensemble according to its total average normalized mutual information. Second, if cluster ensemble is stable, then cluster members with high quality and moderate diversity are selected, else, cluster members with high quality are selected. We evaluate the proposed method on several benchmark datasets and the results show that IACES can judge the stability of cluster ensemble correctedly while ACES misjudges some unstable cluster ensemble as stable. Besides, ensembling the cluster members selected by IACES produces better final solutions than other cluster member selection methods in almost all cases, and is superior average results in all cases.
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Key words:
- Machine learning /
- cluster analysis /
- cluster ensemble /
- cluster ensemble selection
1) 本文责任编委 赵铁军 -
图 2 采用聚类集体P1时获得的聚类结果(NMI值和F值)
Fig. 2 Clustering results obtained when using cluster ensemble P1 (NMI scores and F measures)
图 3 采用聚类集体P2时获得的聚类结果(NMI值和F值)
Fig. 3 Clustering results obtained when using cluster ensemble P2 (NMI scores and F measures)
图 4 当采用聚类集体P1时获得的聚类结果(平均NMI值和平均F值)
Fig. 4 Clustering results obtained by combining cluster members selected by ACES and IACES via CSPA, AL, SC and KM++ when using cluster ensemble P1 (Total average NMI scores and total average F measures)
图 5 当采用聚类集体P1时获得的聚类结果(平均NMI值和平均F值)
Fig. 5 Clustering results obtained by combining cluster members selected by ACES and IACES via CSPA, AL, SC and KM++ when using cluster ensemble P1 (Total average NMI scores and total average F measures)
表 1 实验数据集描述
Table 1 Description of datasets
Dataset $n_{d}$ $n_{w}$ $k$$^{\ast }$ $n_{c}$ Balance tr11 414 6 429 9 46 0.046 tr23 204 5 832 6 34 0.066 tr41 878 7 454 10 88 0.037 tr45 690 8 261 10 69 0.088 la1 3 204 31 472 6 534 0.290 la2 3 075 31 472 6 543 0.274 la12 6 279 31 472 6 1 047 0.282 hitech 2 301 10 080 6 384 0.192 reviews 4 069 18 483 5 914 0.098 sports 8 580 14 870 7 1 226 0.036 classic 7 094 41 681 4 1 774 0.323 k1b 2 340 21 839 6 390 0.043 ng3 2 998 15 810 3 999 0.998 
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表 2 分别根据ACES和IACES判定的聚类集体稳定性结果
Table 2 Stability results of cluster ensemble according to ACES and IACES
聚类集体$P_{1}$ 聚类集体$P_{2}$ ACES IACES ACES IACES Dataset MNMI Number Stability TANMI Proportion Stability MNMI Number Stability TANMI Proportion Stability tr11 0.655 989 S 0.539 0.7498 S 0.682 940 S 0.574 0.8384 S tr23 0.663 991 S 0.607 0.9361 S 0.712 904 S 0.649 0.8736 S tr41 0.731 999 S 0.642 0.9939 S 0.732 959 S 0.649 0.8922 S tr45 0.718 1 000 S 0.640 0.9917 S 0.705 922 S 0.616 0.8121 S la1 0.597 863 S 0.514 0.5553 S 0.592 894 S 0.541 0.6879 S la2 0.593 934 S 0.524 0.6296 S 0.539 735 S 0.489 0.4374 NS la12 0.634 973 S 0.558 0.7586 S 0.570 838 S 0.493 0.4938 NS hitech 0.551 727 S 0.475 0.3251 NS 0.537 654 S 0.458 0.2602 NS reviews 0.683 940 S 0.610 0.8480 S 0.672 958 S 0.608 0.7622 S sports 0.736 998 S 0.652 0.9637 S 0.651 958 S 0.585 0.7443 S classic 0.801 966 S 0.692 0.8375 S 0.709 945 S 0.594 0.7500 S k1b 0.673 994 S 0.585 0.8992 S 0.654 969 S 0.555 0.7811 S ng3 0.541 664 S 0.451 0.3791 NS 0.525 648 S 0.467 0.4441 NS
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