Statistical Mechanics of Unsupervised Structure Recognition
نویسندگان
چکیده
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 diierent 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 diierent in spirit, such as the estimation of parameters in a model distribution and an information theoretical approach.
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تاریخ انتشار 2007