Dimensionality reduction of multivariate time series

Question

Background

I have vehicle dynamics data collected over time. For example, my data set contains speed, steering angle, accelerator pedal position, etc. (more than 100 variables) for 50 different drivers who drove on the same road segment. I consider these as multivariate time series because of the sequential nature and multiple variables in the data set.

Objectives

My main goal for the analysis is to find similarity between time series of different drivers. I am assuming that driving styles of 2 drivers are similar if their time series are "similar". I want to use Dynamic Time Warping (DTW) to find similarity but I want to first find out which variables are more important; and reduce the space for DTW algorithm. Upon searching I found that Discrete Fourier Transform (DFT) could be used for dimensionality reduction. I now understand the basic concept of DFT.

Problem

I have searched a lot but can't find any example where a data set with few time series is taken to reduce dimensionality and find similarity among time series. MY questions are:

1. Can I use DFT on my data set?

2. Can DFT rank the variables (speed/steering angle, etc.) in terms of their importance? If no, is there any other technique for this purpose?

3. Could you please provide me with any step by step example to apply DFT and DTW on multivariate time series data? (I use R)

Answer 1

There is a very nice tutorial on DTW here http://www.cs.unm.edu/~mueen/DTW.pdf

“Can DFT rank the variables (speed/steering angle, etc.) in terms of their importance?” You have to understand that “importance” is subjective, YOU must define it.

“and reduce the space for DTW algorithm.” Carefully done (lower bounding search, warping constraints etc, see the tutorial), DTW will be fast enough on the raw data. You cannot do DTW on DFT, but you can do it on DWT. Anyway, that is a distraction, work with the raw data.