Automatic Adjustment Method of Weight Parameters for Distance and Similarity during Dimension Reduction

In this paper, we propose a new algorithm that adjusts the parameters of the distance function during dimensional compression according to the degree of influence of each component on the object variable. In this method, lower dimension space is divided into subspaces. And linear multiple regression to a predetermined objective variable is executed for each subspace. From result of this regression, weight parameters of the distance function are updated. By applying this method to the self-organizing maps using the manufacturing conditions of the hot rolling process of aluminum as input, it was confirmed that appropriate and clear dimensional compression results could be obtained. Furthermore, quantitative evaluation confirmed that the arrangement in the distance space after dimensional compression are separated for data with large differences in the object variables. This method is an algorithm that can be applied to kernel PCA and t-SNE that do not use distance functions, and is expected to be applicable to other general high-dimensional data.