利用区域映射模型研究样本集的空间分布

Analysis of sample set's spatial distribution using region mapping model

针对样本集在神经网络中所起到的重要作用,用大量的仿真试验研究了区域映射模型输出与输入空间的拓扑相似性。结果表明,区域映射模型可实现从高维空间到二维空间具有拓扑相似性的映射,因此,可以作为研究样本集空间分布的新的可视化工具,同时为样本集的组织和筛选提供了新的手段。仿真试验也直观地揭示了隐层单元数和权值在神经网络中所起的作用,即隐层单元数用来调节投影的角度,权值则用来调整样本空间的输出图像在输出空间中的位置。

The topological similarities between the output distribution and the input distribution of the region mapping model are investigated through a lot of computer simulations. Different sample sets with different shapes are input into the region mapping model, and the network outputs are observed. The simulation results show that the output distribution of the region mapping model can reflect the shape, convexity, concavity of the sample set in the input space and the relative position relationship between different regions in the sample set. So the region mapping model can realize the map with topological similarity from the high dimensional space to two-dimensional space, and it provides a new visualization tool for analyzing the spatial distribution of the sample set. The simulations reveal the roles of the number of hidden neurons and network weights in neural networks: the number of hidden neurons adjusts the mapping angle; the weights adjust the position of the output data distribution in the output space. The region mapping model is applied to rearrange the sample set to improve the learning speed of neural network and to delete some undesired samples.