Schneider Petra, Biehl Michael, Hammer Barbara
Institute of Mathematics and Computing Science, University of Groningen, 9700 AK Groningen, The Netherlands.
Neural Comput. 2009 Oct;21(10):2942-69. doi: 10.1162/neco.2009.10-08-892.
Discriminative vector quantization schemes such as learning vector quantization (LVQ) and extensions thereof offer efficient and intuitive classifiers based on the representation of classes by prototypes. The original methods, however, rely on the Euclidean distance corresponding to the assumption that the data can be represented by isotropic clusters. For this reason, extensions of the methods to more general metric structures have been proposed, such as relevance adaptation in generalized LVQ (GLVQ) and matrix learning in GLVQ. In these approaches, metric parameters are learned based on the given classification task such that a data-driven distance measure is found. In this letter, we consider full matrix adaptation in advanced LVQ schemes. In particular, we introduce matrix learning to a recent statistical formalization of LVQ, robust soft LVQ, and we compare the results on several artificial and real-life data sets to matrix learning in GLVQ, a derivation of LVQ-like learning based on a (heuristic) cost function. In all cases, matrix adaptation allows a significant improvement of the classification accuracy. Interestingly, however, the principled behavior of the models with respect to prototype locations and extracted matrix dimensions shows several characteristic differences depending on the data sets.
诸如学习矢量量化（LVQ）及其扩展等判别式矢量量化方案，基于通过原型对类别进行表示，提供了高效且直观的分类器。然而，原始方法依赖于欧几里得距离，这对应于数据可以由各向同性聚类表示的假设。因此，已经提出了将这些方法扩展到更一般的度量结构，例如广义LVQ（GLVQ）中的相关性自适应和GLVQ中的矩阵学习。在这些方法中，基于给定的分类任务学习度量参数，从而找到一种数据驱动的距离度量。在这封信中，我们考虑在先进的LVQ方案中进行全矩阵自适应。特别是，我们将矩阵学习引入到LVQ的一种最新统计形式化方法——鲁棒软LVQ中，并将在几个人工和真实数据集上的结果与GLVQ中的矩阵学习进行比较，GLVQ是基于（启发式）代价函数推导的类似LVQ的学习方法。在所有情况下，矩阵自适应都能显著提高分类准确率。然而，有趣的是，模型在原型位置和提取的矩阵维度方面的原理性行为，根据数据集的不同显示出几个特征差异。
