# Passing Time Series Data to an Unsupervised model

I have a particular segment of temporal data for 3 days. It looks like this:

Day_1_Hour_14 = [d1x1,d1x2,...,d1xn] and [d1y1,d1y2,...,d1yn]
Day_2_Hour_14 = [d2x1,d2x2,...,d2xn] and [d2y1,d2y2,...,d2yn]
Day_3_Hour_14 = [d3x1,d3x2,...,d3xn] and [d3y1,d3y2,...,d3yn]


When I use these 3 days 1 hour each worth of data on an unsupervised algorithm like DBSCAN, is it better to give the x_axis as an increasing order of index with their respective y_value?

Meaning,

x_axis_total = [1,2,3,4.,...,n] from d1x1 to d3xn
y_axis_total = [d1y1,d1y2,,.d1yn,d2y1,d2y2,...,d3y1,d3y2,..,d3yn]


And then I pass x_axis_total and y_axis_total to DBSCAN

I am quite confused about how to pass the data to the algorithm. Or is it better to include the actual timestamp of each observation as the x_value? When I use the timestamp the data points are aligned in a straight line from 1 - n in 4 rows in the graph and DBSCAN does not work good when applied like this.

Any suggestions will be appreciated

If I make the x_axis in an increasing order I get this result [Day 1 - 3 of Hour 14]:

If I use the timestamp as x_axis I get this result [Day 1 - 3 of Hour 14]:

My aim is to detect Outliers in my data and the data is vehicular traffic data - It is contextual. That is the reason I am selecting 4 similar days of the same hour for this example.

My main question is am I losing any information if I do it the first way I mentioned? That is, the x_axis in increasing order from 1-n because using timestamp gives me bizzart results.

Is there a better way to do it?

• Do you wish to detect outlier datapoints or outlier time-series? It seems to me that you are right now clustering the datapoints and not the time-series. – Nikolas Rieble Mar 7 '18 at 16:26
• By the way: You would always want to standardize all features before passing them to DBSCAN. Otherwise the feature with the highest variance dominates the clustering result. – Nikolas Rieble Mar 7 '18 at 16:36
• @NikolasRieble - I am looking to cluster the data points. I currently have only two features. The x_index and the speed which is the y_axis. Does this seem correct? – RPT Mar 7 '18 at 16:40
• Alright, this clears up a lot. You want to detect irregular behavior within a time-series. This is not equal to time-series clustering. I would recommend you to use a sliding window approach instead of considering only a single datapoint. Thereby you can consider the previous points as well and detect things such as a sudden increase of speed. I would neglect the time stamp for all further processing since you are not so much interested in when a behaviour occurs rather than if a deviant behaviour occured. – Nikolas Rieble Mar 7 '18 at 19:14
• Thanks for the reply, Nikolas. Could you explain briefly how I could use a sliding window approach here? Or refer me to some useful paper? Thanks a lot. Also I could easily get back the time at which the deviant behaviour has occurred, once clustered and anomalies have been detected – RPT Mar 7 '18 at 19:24

Your question would benefit from more explanation regarding the data as well as the target. I am not certain whether I fully understand your question, but i will summarize my thoughts to your problem.

It seems you wish to work on the task of time-series clustering.

1) Using DBSCAN:

• You did not specify the dissimilarity measure that you are using. The quality of the clustering results strongly depends on the measure you choose to compare the time-series. A standard measure to use would be Euclidean Distance, yet the are quite a few reasons why not to use Euclidean Distance on time-series best explained here by Eamon Keogh (This is a link to one of his tutorials on time-series analysis).
• Although DBSCAN is quiet a wonderful algorithm, it is highly sensitive to its parameters. Therefore I would suggest to firstly use simpler algorithms. You can find alternatives here.

2) Time-series clustering: You can cluster time-series either directly on the time-series data using dissimilarity measures such as Dynamic Time Warping (DTW) or you can transform your time-series into a feature space (such as mean, max, min, kurtosis, skewness per dimension) and use Euclidean Distance in the feature space. The choice of relevant/appropriate features depends on the nature of the data - which you did not specify.

If you wish to get more specific answers, please plot some time-series, explain what sort of clusters you expect and describe the origin of your data.

• Thanks for your reply. I have edited my question. Regarding the DBSCAN - I am aware of the parameters selection process. I am mainly confused on how to pass the data to the algorithm. – RPT Mar 7 '18 at 16:15