The full-dimensional (metric, Euclidean, least squares) multidimensional scaling stress loss function is combined with a quadratic external penalty function term. The trajectory of minimizers of stress for increasing values of the penalty parameter is then used to find (tentative) global minima for low-dimensional multidimensional scaling. This is illustrated with several one-dimensional and two-dimensional examples.

翻译：本文将全维（度量、欧几里得、最小二乘）多维缩放应力损失函数与一个二次外部惩罚函数项相结合。通过追踪惩罚参数递增时应力最小化点的轨迹，该方法被用于寻找低维多维缩放问题的（试探性）全局最小值。文中通过若干一维与二维示例对此进行了说明。