STATISTICAL-MECHANICS OF UNSUPERVISED STRUCTURE RECOGNITION
STATISTICAL-MECHANICS OF UNSUPERVISED STRUCTURE RECOGNITION
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DOI：
10.1088/0305-4470/27/6/015
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发表时间：
1994-03-21
期刊：
影响因子：
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通讯作者：
MIETZNER, A
中科院分区：
文献类型：
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作者：
BIEHL, M;MIETZNER, A
研究了一个无监督学习模型，其中环境提供了从两个重叠的高斯云中提取的n维输入示例。我们考虑了两个不同的目标函数的优化：分别寻找数据中最大方差的方向和样本簇之间最大分离间隙（稳定性）的方向。通过统计力学分析，我们研究了从一组例子中推断出底层结构的程度。学习算法的性能主要取决于输入分布的实际形状。一个通用的结果是存在成功学习所需的临界数量的例子。将该学习策略与模型分布参数估计和信息论方法等精神不同的方法进行了比较。
A model of unsupervised learning is studied, where the environment provides N-dimensional input examples that are drawn from two overlapping Gaussian clouds. We consider the optimization of two different objective functions: the search for the direction of the largest variance in the data and the largest separating gap (stability) between clusters of examples respectively.By means of a statistical-mechanics analysis, we investigate how well the underlying structure is inferred from a set of examples. The performances of the learning algorithms depend crucially on the actual shape of the input distribution. A generic result is the existence of a critical number of examples needed for successful learning. The learning strategies are compared with methods different in spirit, such as the estimation of parameters in a model distribution and an information-theoretical approach.