Transfer Fuzzy C-Means Clustering Based on Maximum Mean Discrepancy
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摘要: 该文针对迁移聚类问题，提出一种基于最大平均差异的迁移模糊C均值(TFCM-MMD)聚类算法。TFCM-MMD解决了迁移模糊C均值聚类算法在源域与目标域数据分布差异大的情况下迁移学习效果减弱的问题。 该算法基于最大平均差异准则度量域间差异，通过学习源域和目标域的投影矩阵，以减小源域和目标域数据在公共子空间分布的差异，进而提升迁移学习的效果。最后，通过基于合成数据集和医学图像分割数据集的实验，进一步验证了TFCM-MMD算法在解决域间差异大的迁移聚类问题上的有效性。Abstract: In this paper, a Transfer Fuzzy C-Means clustering algorithm based on Maximum Mean Discrepancy (TFCM-MMD) is proposed. TFCM-MMD solves the problem that the transfer learning effect of the transfer fuzzy C-means clustering algorithm is weakened when the data distribution between source domain and target domain is very different. The algorithm measures inter-domain differences based on the maximum mean discrepancy criterion, and reduces the differences of data distribution between source domain and target domain in the common subspace by learning the projection matrix of source domain and target domain, so as to improve the effect of transfer learning. Finally, experiments based on synthetic datasets and medical image segmentation datasets verify further the effectiveness of TFCM-MMD algorithm in solving transfer clustering problems with large inter-domain differences.
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Key words:
- Transfer learning /
- Fuzzy clustering /
- Maximum Mean Discrepancy(MMD)
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算法1 TFCM-MMD 输入：源域数据${{\boldsymbol{X}}_{\text{s} } }$, 目标域数据${{\boldsymbol{X}}_{\text{t} } }$，源域聚类数$ {C_{\text{s}}} $, 目标域聚类数$ {C_{\text{t}}} $，模糊加权系数$ {m_1} $, $ {m_2} $，迁移率λ，学习率η, 最大迭代次数nmax，
终止阈值$ \varepsilon $输出：目标域模糊隶属度矩阵${\boldsymbol{U}}$ (1) 根据源域聚类数$ {C_{\text{s}}} $, 利用FCM对源域数据${{\boldsymbol{X}}_{\text{s} } }$进行聚类, 获得源域的聚类中心${\tilde {\boldsymbol{V}}_k}$; (2) 根据目标域聚类数$ {C_{\text{t}}} $初始化模糊隶属度矩阵${\boldsymbol{U}}(0)$，聚类中心相关性矩阵${\boldsymbol{R}}(0)$，根据投影后矩阵的维数r初始化投影矩阵${\boldsymbol{H}}(0)$，迭代次
数t=0;(3) 重复; (4) t=t+1; (5) 利用式(7)计算聚类中心${\boldsymbol{V}}(t)$; (6) 利用式(8)计算模糊隶属度矩阵${\boldsymbol{U}}(t)$; (7) 利用式(9)计算聚类中心相关性矩阵${\boldsymbol{R}}(t)$; (8) 利用式(15)计算投影矩阵${\boldsymbol{H}}(t)$; (9) 直到$ |{J_{{\text{TFCM - MMD}}}}(t) - {J_{{\text{TFCM - MMD}}}}(t - 1)| < \varepsilon $或者 t>nmax 
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表 1 不同噪声水平下TFCM与TFCM-MMD抗负迁移性能比较(以AC为例)(%)
目标域数据 TFCM最差聚类结果 TFCM-MMD最差聚类结果 聚类性能提升 T2-1 69.86 70.36 0.5 T2-2 67.64 71.67 4.0 T2-3 61.21 67.40 6.2
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表 2 FCM-MMD与TFCM-MMD聚类性能对比(AC)
S1_1-T1_1 S1_2-T1_2 S2-T2_1 S2-T2_2 S2-T2_3 FCM-MMD 0.633 0.330 0.767 0.700 0.624 TFCM-MMD 0.767 0.767 0.747 0.744 0.739 CI* [0.6157, 0.9183] [0.6157, 0.9183] [0.7605, 0.7735] [0.7373, 0.7507] [0.7323, 0.7457] *最后一行是最佳方法的95%置信区间
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表 3 FCM-MMD与TFCM-MMD聚类性能对比(RI)
S1_1-T1_1 S1_2-T1_2 S2-T2_1 S2-T2_2 S2-T2_3 FCM-MMD 0.639 0.310 0.694 0.660 0.611 TFCM-MMD 0.733 0.736 0.691 0.688 0.684 CI [0.5747, 0.8913] [0.5783, 0.8937] [0.6869, 0.7011] [0.6809, 0.6951] [0.6769, 0.6911]
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表 4 FCM-MMD与TFCM-MMD聚类性能对比(DB)
S1_1-T1_1 S1_2-T1_2 S2-T2_1 S2-T2_2 S2-T2_3 FCM-MMD 0.923 \ 0.473 0.530 0.558 TFCM-MMD 0.797 0.797 0.552 0.550 0.556 CI [0.6531, 0.9409] [0.6531, 0.9409] [0.4654, 0.4806] [0.5224, 0.5376] [0.5484, 0.5636]
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