Stability Analysis for Clustering

本课题提出并分析了一种基于信息论的新的模型验证原理。根据目标函数从噪声数据中推断出像聚类或图切割中的数据划分这样的离散结构。由于测量(数据)中的噪声，学习算法必须返回一组被认为是统计上不可区分的近似划分。数据中的不确定性导致分区空间的量化，从而定义了编码方案。对该代码的信息论分析得出了由目标函数表示的基础模型的近似能力。该选择准则在信息量和稳定性之间进行权衡，并通过逼近精度来控制模型的复杂性。近似解通过有限温度下的Gibbs抽样进行抽样。这种新的信息论模型选择原则将被应用于蛋白质相互作用数据聚类中的相关性聚类。此外，我们将应用这一原则学习系统生物学中的动态系统，并在信息安全应用程序中推断用户角色。

A new model validation principle based on information theory is developed and analyzed in this project. Discrete structures like data partitions in clustering or graph cuts are infered from noisy data according to an objective function. Due to the noise in the measurements (data), learning algorithms have to return a set of approximate partitionings which are considered to be statistically indistinguishible. The uncertainty in the data induce a quantization of the space of partitionings and, thereby, defines a coding scheme. An information theoretic analysis of this code yields an approximation capacity of the underlying model represented by an objective function. This selection criterion trades informativeness against stability and controls the model complexity by the approximation precision. Approximate solutions are sampled by Gibbs sampling at a finite temperature. This novel information theoretic model selection principle will be applied to correlation clustering in the context of clustering protein interaction data. Furthermore, we will apply this principle for learning dynamical systems in systems biology and for infering user roles in information security applications.