A Gaussian scenario for unsupervised learning
A Gaussian scenario for unsupervised learning
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DOI：
10.1088/0305-4470/29/13/021
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发表时间：
1996-07-07
期刊：
影响因子：
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通讯作者：
Bex, GJ
中科院分区：
文献类型：
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作者：
Reimann, P;VandenBroeck, C;Bex, GJ
我们考虑N球面上的随机图案，这些图案是均匀分布的，除了一个对称破缺的方向，沿着它是高斯分布的。在大N极限下，利用复制品方法研究了不同学习规则对该方向的无监督识别。该模型足够简单，在分析上容易处理，并且足够丰富，足以显示用其他模式分布观察到的大多数现象。提出了一种基于代价函数最小化的学习算法，该算法达到了最优(贝叶斯)学习场景所规定的理论上限。给出了该算法的具体实现，并进行了数值测试。
We consider random patterns on the N-sphere which are uniformly distributed with the exception of a single symmetry-breaking orientation, along which they are Gaussian distributed. The unsupervised recognition of this orientation by different learning rules is studied in the large-N limit using the replica method. The model is simple enough to be analytically tractable and rich enough to exhibit most of the phenomena observed with other pattern distributions. A learning algorithm based on the minimization of a cost function is identified which reaches the upper theoretical limit imposed by the optimal (Bayes-) learning scenario. An implementation of this algorithm is proposed and tested numerically.