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Robust Multidimensional Scaling Using a Maximum Correntropy Criterion

机译：使用最大熵准则的稳健多维缩放

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摘要

Multidimensional scaling (MDS) refers to a class of dimensionality reduction techniques, which represent entities as points in a low-dimensional space so that the interpoint distances approximate the initial pairwise dissimilarities between entities as closely as possible. The traditional methods for solving MDS are susceptible to outliers. Here, a unified framework is proposed, where the MDS is treated as maximization of a correntropy criterion, which is solved by half-quadratic optimization in either multiplicative or additive forms. By doing so, MDS can cope with an initial dissimilarity matrix contaminated with outliers because the correntropy criterion is closely related to M-estimators. Three novel algorithms are derived. Their performances are assessed experimentally against three state-of-the-art MDS techniques, namely the scaling by majorizing a complicated function, the robust Euclidean embedding, and the robust MDS under the same conditions. The experimental results indicate that the proposed algorithms perform substantially better than the aforementioned competing techniques.
机译：多维比例缩放（MDS）是指一类降维技术，它们将实体表示为低维空间中的点，以便点间距离尽可能接近实体之间的初始成对相异性。解决MDS的传统方法容易受到异常值的影响。在这里，提出了一个统一的框架，其中将MDS视为熵准则的最大化，这可以通过乘法或加法形式的半二次优化来解决。通过这样做，MDS可以处理被离群值污染的初始不相似矩阵，因为熵准则与M估计量密切相关。推导了三种新颖的算法。通过三种最先进的MDS技术对它们的性能进行了实验评估，即通过复杂化函数的缩放，鲁棒的欧几里得嵌入和相同条件下的鲁棒MDS进行缩放。实验结果表明，所提出的算法的性能明显优于上述竞争技术。

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