An Ordinal Weighted EDM Model for Nonmetric Multidimensional Scaling

Qing-Na Li, Chi Zhang, Mengzhi Cao
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Abstract

Multidimensional scaling (MDS) is to recover a set of points by making use of noised pairwise Euclidean distances. In some situations, the observed Euclidean distances may contain large errors or even missing values. In such cases, the order of the distances is far more important than their magnitude. Non-metric multidimensional scaling (NMDS) is then to deal with this problem by taking use of the ordinal information. The challenge of NMDS is to tackle the large number of ordinal constraints on distances (for [Formula: see text] points, this will be of [Formula: see text]), which will slow down existing numerical algorithms. In this paper, we propose an ordinal weighted Euclidean distance matrix model for NMDS. By designing an ordinal weighted matrix, we get rid of the large number of ordinal constraints and tackle the ordinal constraints in a soft way. We then apply our model to image ranking. The key insight is to view the image ranking problem as NMDS in the kernel space. We conduct extensive numerical test on two state-of-the-art datasets: FG-NET aging dataset and MSRA-MM dataset. The results show the improvement of the proposed approach over the existing methods.
非度量多维标度的有序加权EDM模型
多维尺度(MDS)是利用带噪声的两两欧氏距离来恢复一组点。在某些情况下,观测到的欧几里得距离可能包含很大的误差甚至缺失值。在这种情况下,距离的顺序远比它们的大小重要。非度量多维尺度(NMDS)利用有序信息来解决这一问题。NMDS的挑战在于处理大量关于距离的有序约束(对于[公式:见文本]点,这将是[公式:见文本]),这将减慢现有的数值算法。本文提出了一种NMDS的有序加权欧氏距离矩阵模型。通过设计一个有序的加权矩阵,我们摆脱了大量的有序约束,并以一种软的方式处理有序约束。然后我们将我们的模型应用于图像排序。关键的洞察力是将图像排序问题视为内核空间中的NMDS。我们对两个最先进的数据集进行了广泛的数值测试:FG-NET老化数据集和MSRA-MM数据集。结果表明,该方法比现有方法有了改进。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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