标题： 函数多维标度 显示英文标题

标题： Functional Multidimensional Scaling

摘要： 本文介绍了一种用于低维平滑表示的时间变化差异的功能方法。 该方法通过使用三次B样条基函数，在多维标度和功能数据分析的平滑方法中结合了差异表示。 该模型旨在通过迭代过程达到最优表示，使得由估计表示计算出的差异几乎与低维中原对象的原始差异相同，这更容易被人们识别。 为了解决优化中的昂贵计算，我们提出了一种计算效率高的方法，即使用随机梯度下降算法针对目标函数的各个子函数采取梯度步长。 关键词: 多维标度，功能数据分析，统计建模，拟牛顿法，随机梯度下降 显示英文摘要

摘要： This article introduces a functional method for lower-dimensional smooth representations in terms of time-varying dissimilarities. The method incorporates dissimilarity representation in multidimensional scaling and smoothness approach of functional data analysis by using cubic B-spline basis functions. The model is designed to arrive at optimal representations with an iterative procedure such that dissimilarities evaluated by estimated representations are almost the same as original dissimilarities of objects in a low dimension which is easier for people to recognize. To solve expensive computation in optimization, we propose a computationally efficient method by taking gradient steps with respect to individual sub-functions of target functions using a Stochastic Gradient Descent algorithm. Keywords: Multidimensional Scaling, Functional Data Analysis, Statistical Modeling, Quasi-Newton Method, Stochastic Gradient Descent