时间序列距离度量 [英] Time series distance metric

问题描述

为了聚类一组时间序列，我正在寻找一种智能的距离度量标准. 我尝试了一些众所周知的指标，但没有一个适合我的情况.

In order to clusterize a set of time series I'm looking for a smart distance metric. I've tried some well known metric but no one fits to my case.

ex:假设我的集群算法提取了这三个质心[s1，s2，s3]:

ex: Let's assume that my cluster algorithm extracts this three centroids [s1, s2, s3]:

我想将这个新示例[sx]放在最相似的集群中:

I want to put this new example [sx] in the most similar cluster:

最相似的质心是第二个质心，因此我需要找到一个距离函数d，它赋予我d(sx, s2) < d(sx, s1)和d(sx, s2) < d(sx, s3)

The most similar centroids is the second one, so I need to find a distance function d that gives me d(sx, s2) < d(sx, s1) and d(sx, s2) < d(sx, s3)

修改

在这里使用度量[余弦，欧几里得，明可夫斯基，动态类型翘曲] ]

Here the results with metrics [cosine, euclidean, minkowski, dynamic type warping] ]3

修改2

用户Pietro P建议将距离应用于时间序列的累积版本 该解决方案有效，这里是曲线图和度量标准:

User Pietro P suggested to apply the distances on the cumulated version of the time series The solution works, here the plots and the metrics:

推荐答案

很好的问题！在这些时间序列上使用R ^ n的任何标准距离(欧几里得，曼哈顿或通常的minkowski)都无法获得所需的结果，因为这些度量标准与R ^ n坐标的排列无关(而时间是严格排序的，并且是您要捕捉的现象.

nice question! using any standard distance of R^n (euclidean, manhattan or generically minkowski) over those time series cannot achieve the result you want, since those metrics are independent of the permutations of the coordinate of R^n (while time is strictly ordered and it is the phenomenon you want to capture).

一个简单的窍门，可以使用时间序列的累积版本(随时间增加的时间总和)来执行您所要求的，然后应用标准指标. 使用曼哈顿度量标准，您将获得两个时间序列之间的距离，即两个时间序列之间的累积版本之间的距离.

A simple trick, that can do what you ask is using the cumulated version of the time series (sum values over time as time increases) and then apply a standard metric. Using the Manhattan metric, you would get as a distance between two time series the area between their cumulated versions.

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