Divergence-Based Vector Quantization
Divergence-Based Vector Quantization
复制标题
基于散度的矢量量化
作者：
T. Villmann;S. Haase
用于分类和聚类的有监督和无监督矢量量化方法传统上使用相异性，通常被认为是欧几里得距离。在这篇文章中，我们调查分歧的适用性，而不是专注于在线学习。我们推导出其利用基于梯度的在线矢量量化算法的数学基础。它与泛函分析中称为Frchet导数的发散的广义导数有关，Frchet导数以自然的方式将有限维问题简化为偏导数。我们展示了这种方法的应用广泛应用的监督和无监督的在线矢量量化方案，包括自组织映射，神经气体，学习矢量量化。此外，超参数优化和相关学习的监督矢量量化的情况下，参数化的分歧的原则，以实现更高的分类精度。
Supervised and unsupervised vector quantization methods for classification and clustering traditionally use dissimilarities, frequently taken as Euclidean distances. In this article, we investigate the applicability of divergences instead, focusing on online learning. We deduce the mathematical fundamentals for its utilization in gradient-based online vector quantization algorithms. It bears on the generalized derivatives of the divergences known as Frchet derivatives in functional analysis, which reduces in finite-dimensional problems to partial derivatives in a natural way. We demonstrate the application of this methodology for widely applied supervised and unsupervised online vector quantization schemes, including self-organizing maps, neural gas, and learning vector quantization. Additionally, principles for hyperparameter optimization and relevance learning for parameterized divergences in the case of supervised vector quantization are given to achieve improved classification accuracy.
影响因子：
6
作者：
X. Zhu;A. Gisbrecht;F.-M. Schleif;B. Hammer
通讯作者：
B. Hammer