目前，我有6个在6种不同的颜色，如下图所示的曲线。 其实都是由一个同样的实验 6的试验产生的6条曲线。也就是说，理想情况下，他们应该是相同的曲线，但由于噪声和不同的试验参与者，他们只是看起来很相似，但不完全相同。

Currently, I have 6 curves shown in 6 different colors as below. The 6 curves are in fact generated by 6 trials of one same experiment. That means, ideally they should be the same curve, but due to the noise and different trial participants, they just look similar but not exactly the same.

现在我希望创建一个算法，它能够识别出6曲线基本上是相同的，并聚集在一起成一个集群。 我应该使用什么样的相似度？

Now I wish to create an algorithm that is able to identify that the 6 curves are essentially the same and cluster them together into one cluster. What similarity metrics should I use?

注意：

的 X轴确实不会在所有问题！我只是调整它们放在一起进行可视化的目的。因此，随意左/右移动的曲线，如果这样做会有所帮助。 在子曲线是可能会出现在曲线的一部分。该归属是重要的，因此需要识别为好。但同样，左/右移位是允许的。 The x-axis does NOT matter at all! I simply align them together for visual purpose. Thus, feel free to left/right shift the curves, if doing so helps. "Sub-curves" that are part of the curves may appear. The "belongingness" is important and thus needs identifying as well. But again, left/right shifting is allowed.

我已经attemped学习一些聚类算法，如DBSCAN，K均值，模糊C均值等，但我看不出其是否适宜在这种情况下，因为归属感需要被发现！

I have attemped to learn some of the clustering algorithm, such as DBSCAN, K-means, Fuzzy C-means, etc. But I don't see their appropriateness in this case, because the "belongingness" needs to be spotted!

任何建议或意见都很好欢迎。我明白，这是很难给出精确解这个问题。我只是期待一些启发性的建议，在这里。的

推荐答案

看一看时间序列相似功能，如动态时间规整。

Have a look at time series similarity functions, such as dynamic time warping.

它们可以与例如用于DBSCAN但不包括K-手段。（你不能计算出一个合理的的意思是对这些距离; K-均值是真正专为平方欧氏距离）

They can be used with e.g. DBSCAN but NOT with k-means (you cannot compute a reasonable "mean" for these distances; k-means is really designed for squared Euclidean distances).