Adaptive Euclidean maps for histograms: generalized Aitchison embeddings
Adaptive Euclidean maps for histograms: generalized Aitchison embeddings
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直方图的自适应欧几里得映射：广义 Aitchison 嵌入
DOI：
10.1007/s10994-014-5446-z
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发表时间：
2015
期刊：
影响因子：
7.5
通讯作者：
Marco Cuturi
中科院分区：
文献类型：
--
作者：
Tam Le;Marco Cuturi
专门设计用来比较概率单纯形中的直方图的学习距离最近引起了机器学习界的注意。学习这样的距离很重要，因为大多数机器学习问题都涉及到大量的特征，而不是简单的向量。大量的经验证据表明，一般的欧几里德距离，特别是马氏度量学习，可能不适合于量化单纯形中点之间的距离。本文通过推广Aitchison(J R Stat Soc 44：139-177,1982)提出的嵌入族，将概率单纯形映射到合适的欧氏空间，从而提出了解决这个问题的新贡献。我们在以前关于度量学习方法的工作的基础上，提供了估计此类映射的参数的算法。我们研究的准则不是凸的，我们考虑交替优化方案和加速梯度下降方法。这些算法产生的表示比在各种上下文中比较直方图的其他方法更好。
Learning distances that are specifically designed to compare histograms in the probability simplex has recently attracted the attention of the machine learning community. Learning such distances is important because most machine learning problems involve bags of features rather than simple vectors. Ample empirical evidence suggests that the Euclidean distance in general and Mahalanobis metric learning in particular may not be suitable to quantify distances between points in the simplex. We propose in this paper a new contribution to address this problem by generalizing a family of embeddings proposed by Aitchison (J R Stat Soc 44:139–177, 1982) to map the probability simplex onto a suitable Euclidean space. We provide algorithms to estimate the parameters of such maps by building on previous work on metric learning approaches. The criterion we study is not convex, and we consider alternating optimization schemes as well as accelerated gradient descent approaches. These algorithms lead to representations that outperform alternative approaches to compare histograms in a variety of contexts.