# How to compare two data sets sampled at different time?

I have two time series $X$ and $Y$. These two time series contain features, $x_i \in R^{n \times 1}, i = 1...n_x$ and $y_j \in R^{n \times 1}, j=1,...,n_y$ sampled from two subjects($x_i$ are extracted from subject $A$, and $y_j$ are extracted from subject $B$). These features are extracted using the same method, but at different time indices and from different subjects. For example,$X=[x_1, x_2, x_3]$, $Y=[y_1,y_2,y_3,y_4]$, $x_i,y_j\in R^{n \times 1}$ and the sampling time indices for $X$ and $Y$ are $t_x = [10,20,30]$ and $t_y = [12,24,36,48]$ respectively. I would like to calculate distance between $X$ and $Y$. If $n_x = n_y$ and $t_x=t_y$, this is simple. However, $n_x \neq n_y$ and $t_x\neq t_y$ for my data. Is there any method to solve this problem?

• Methods will depend on what relationships you postulate between $X$ and $Y$, as well as assumptions and models about the evolution of both $X$ and $Y$ over time. Since you have said nothing about any relationship, there's not much anyone could say specifically in response. Please include within edits to your post any additional information about the meaning of these data, your model, and your assumptions. – whuber May 26 '15 at 20:19
• Thank you for the edits, but the post remains really vague. Could you elaborate on what exactly you mean by "compare" and what the objective of the comparison might be? What is the nature of these "features"? If you cannot be concrete about the details, then you must be specific about your mathematical model. Without one or the other this question just won't be answerable. – whuber May 26 '15 at 20:36