# Machine learning on data with only time stamps

I'm working on trying to predict physical traffic volume over a network of intersections.

The data I have is sorted per intersection and consists of the time (in sec after epoch) they passed and the direction someone came from. A mock sample here (I have months worth of data for 60 intersections):

   Intersection 1:{
(1456140051, 1),
(1456140066, 2),
(1456140070, 2),
(1456140073, 3),
(1456140078, 1),
(1456140091, 1)}
Intersection 2:{
(1456140051, 1),
(1456140058, 4),
(1456140060, 3),
(1456140063, 2),
(1456140067, 2),
(1456140071, 4)}


(Note: the data is not for the complete network, there are many smaller intersections for which no data is gathered)

So far I've done some fourier analysis which gives me strong weekly and daily periodicity (obviously) and thus calculated daily/weekly averages/noise etc. for each intersection, and I've looked for some correlations between some neighbouring intersections. The next step for me is to use the data from all the intersections to estimate the traffic volume at one intersection, and then do the same for the traffic volume 10 minutes in the future.

I have found various machine learning methods that should work well with time series with constant time intervals and differing values (e.g. 1 data point of varying value every minute), and I can aggregate my data so I get a value of traffic volume each minute or so (typical traffic is between 5 and 100 /minute /intersection). However, I feel I would lose a lot of information that way.

So what I'm looking for it a method that can work with the data I have (or some derivative of that without much information loss) as input. Can anyone recommend some articles or point me in the right direction?

• If you think that making your time series regular (fixed time intervals) will make things easier, maybe a solution would be to discretize time (e.g., number of passes in an intersection during a 1 minut window). Then you'll be able to create a new time series with a sample every second. Now you can start experimenting different methods such as ARIMA and such. Another option is some sort of a dynamic bayesian network where neighbors traffic at time $t-1$ affect a specific intersection at time $t$ – Omri374 Feb 22 '16 at 18:44
• You mean moving my 1 min summation by 1 second steps? I guess that'd preserve most of the information and work with ARIMA. I don't really get the DBN option yet, but I'll look into that further. Thanks – Swier Feb 23 '16 at 11:14
• The moving average approach works quite well during busy periods, which is when it's most relevant. For the quiet periods the time since the last time someone passed the intersection seems to work adequately (but has a strong bias towards long times between passes, some log scale could help) – Swier Mar 9 '16 at 11:04