Pearson Distance is not a Distance
Pearson Distance is not a Distance
复制标题
皮尔逊距离不是距离
DOI：
--
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
V. Solo
中科院分区：
文献类型：
--
作者：
V. Solo
一对具有相关性的随机变量X，Y之间的皮尔逊距离
ho_{xy}$，即1-$
HO_{xy}$已经在诸如基因表达分析、脑成像和网络安全的领域中获得了广泛的使用，特别是用于聚类。在所有这些应用中，隐含地假设/要求距离度量是度量，从而满足三角不等式。然而，我们表明，皮尔逊距离不是一个度量。我们继续表明，这可以通过回顾结果来修复，（在其他文献中众所周知），$sqrt{1-
ho_{xy}}$是一个度量。我们同样表明，一个相关的利益衡量标准，1美元-|
联系我们|$，它对$的符号是不变的
ho_{xy}$不是度量，但$sqrt{1-
ho_{xy}^2}$是。我们也给出了这些结果的推广。
The Pearson distance between a pair of random variables $X,Y$ with correlation $
ho_{xy}$, namely, 1-$
ho_{xy}$, has gained widespread use, particularly for clustering, in areas such as gene expression analysis, brain imaging and cyber security. In all these applications it is implicitly assumed/required that the distance measures be metrics, thus satisfying the triangle inequality. We show however, that Pearson distance is not a metric. We go on to show that this can be repaired by recalling the result, (well known in other literature) that $sqrt{1-
ho_{xy}}$ is a metric. We similarly show that a related measure of interest, $1-|
ho_{xy}|$, which is invariant to the sign of $
ho_{xy}$, is not a metric but that $sqrt{1-
ho_{xy}^2}$ is. We also give generalizations of these results.