No Albert
Department of Electronic and Electrical Engineering, Hongik University, Seoul 04066, Korea.
Entropy (Basel). 2019 Jun 10;21(6):580. doi: 10.3390/e21060580.
We established a universality of logarithmic loss over a finite alphabet as a distortion criterion in fixed-length lossy compression. For any fixed-length lossy-compression problem under an arbitrary distortion criterion, we show that there is an equivalent lossy-compression problem under logarithmic loss. The equivalence is in the strong sense that we show that finding good schemes in corresponding lossy compression under logarithmic loss is essentially equivalent to finding good schemes in the original problem. This equivalence relation also provides an algebraic structure in the reconstruction alphabet, which allows us to use known techniques in the clustering literature. Furthermore, our result naturally suggests a new clustering algorithm in the categorical data-clustering problem.
我们建立了有限字母表上对数损失的通用性，将其作为固定长度有损压缩中的失真准则。对于任意失真准则下的任何固定长度有损压缩问题，我们证明在对数损失下存在一个等效的有损压缩问题。这种等效性是在强意义上的，即我们表明在对数损失下相应的有损压缩中找到好的方案本质上等同于在原始问题中找到好的方案。这种等价关系还在重构字母表中提供了一种代数结构，这使我们能够使用聚类文献中的已知技术。此外，我们的结果自然地提出了一种在分类数据聚类问题中的新聚类算法。
