algorithm to compare timeseries

newuser55

New member
Joined
May 8, 2018
Messages
1
hi,

first of all, im not really sure where to put this question. please move it appropriately, thanks.

Found a paper [1] about a algorithm to compare timeseries, its a extension to FastDTW, and i cant wrap my head around the formula on page: 4.
This is it, with a little example (i hope they are bigger in the final post):

2018-05-08 12_26_37-paper.dvi - pods05-ftw.pdf.jpg2018-05-08 12_27_16-paper.dvi - pods05-ftw.pdf.png

How do they calculate P^R and P^T ?




[1] : http://www.cs.cmu.edu/~christos/PUBLICATIONS/pods05-ftw.pdf
 
I do not see that \(\displaystyle P^T\) is defined.

i suggest that you ask one of the authors.
 
I think there is actually enough information here to reconstruct their \(\displaystyle p_i^R \) values. It's annoying, and I have no idea what any of it actually means, but you can do it from the stated definitions. So, the time interval \(\displaystyle p_i^T \) is not actually calculated by them, it's simply given as \(\displaystyle p_i^T = 3 \) for \(\displaystyle i = \{1, ... , 6\} \)

For \(\displaystyle i = 1 \):

We have that \(\displaystyle x = 1\) and \(\displaystyle y = \sum_{j=1}^1 3 = 3 \). Therefore the lower time series value is \(\displaystyle p_1^L = \min\{p_1, p_2, p_3\} = \min\{3, 2, 3\} = 2 \). The upper time series value is \(\displaystyle p_1^U = \max\{p_1, p_2, p_3\} = \max\{3, 2, 3\} = 3 \). So it follows that \(\displaystyle p_1^R = \{p_1^L, p_1^U\} = \{2,3\} \)

So far it looks to me like you're trying to find an \(\displaystyle i^\mathrm{th}\) segment of time series \(\displaystyle P\) consisting of two values that are separated by the time interval \(\displaystyle p_i^T\), and then you are ordering those two values ascending. As to why, I do not know. Let's try it again:

For \(\displaystyle i = 4 \):

We have that \(\displaystyle x = 1 + \sum_{j=1}^3 3 = 1 + 3 + 3 + 3 = 1 + 9 = 10\). Meanwhile \(\displaystyle y = \sum_{j=1}^4 3 = 3 + 3 + 3 + 3 = 12 \). Therefore the lower time series value is \(\displaystyle p_4^L = \min\{p_{10}, p_{11}, p_{12}\} = \min\{10, 12, 11\} = 10 \). The upper time series value is \(\displaystyle p_4^U = \max\{p_{10}, p_{11}, p_{12}\} = \max\{10, 11, 12\} = 12 \). So it follows that \(\displaystyle p_4^R = \{p_4^L, p_4^U\} = \{10,12\} \).

Et cetera...
 
Top