In this paper, we study the ensemble clustering problem, where the input is in the form of multiple clustering solutions. The goal of ensemble clustering algorithms is to aggregate the solutions into one solution that maximizes the agreement in the input ensemble. We obtain several new results for this problem. Specifically, we show that the notion of agreement under such circumstances can be better captured using a 2D string encoding rather than a voting strategy, which is common among existing approaches. Our optimization proceeds by first constructing a non-linear objective function which is then transformed into a 0-1 Semidefinite program (SDP) using novel convexification techniques. This model can be subsequently relaxed to a polynomial time solvable SDP. In addition to the theoretical contributions, our experimental results on standard machine learning and synthetic datasets show that this approach leads to improvements not only in terms of the proposed agreement measure but also the existing agreement measures based on voting strategies. In addition, we identify several new application scenarios for this problem. These include combining multiple image segmentations and generating tissue maps from multiple-channel Diffusion Tensor brain images to identify the underlying structure of the brain.

中文翻译：

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使用半定规划的集成聚类与应用程序

在本文中，我们研究了集成聚类问题，其中输入是多个聚类解决方案的形式。集成聚类算法的目标是将解决方案聚合成一个解决方案，使输入集成中的一致性最大化。对于这个问题，我们获得了几个新的结果。具体来说，我们表明，在这种情况下，使用 2D 字符串编码而不是投票策略可以更好地捕获这种情况下的一致性概念，这在现有方法中很常见。我们的优化首先构建一个非线性目标函数，然后使用新颖的凸化技术将其转换为 0-1 半定规划 (SDP)。该模型随后可以放松为多项式时间可解 SDP。除了理论贡献，我们在标准机器学习和合成数据集上的实验结果表明，这种方法不仅可以改进提议的一致性措施，还可以改进基于投票策略的现有协议措施。此外，我们针对这个问题确定了几个新的应用场景。这些包括组合多个图像分割和从多通道扩散张量大脑图像生成组织图，以识别大脑的底层结构。