The Blog of Ian Mercer.

Collinearity test for sensor data compression

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In my home automation system time series data is recorded at irregular intervals. Some values are sent when they change by more than a certain data, values may also be sent periodically even if unchanged in order to provide a 'keep-alive' signal.

This complicates any calculations but provides substantial data volume reduction. For example to calculate the difference between two sequences we need to iterate over each time value present from either series and interpolate the value in the series that doesn't have a value at that precise time.

My time series code has also always removed unchanged values. When the new value comes in, if it's the same as the previous value I simply update the timesstamp of the last value in the series and save it back to the database.

But now I've gone one step further and for each incoming value I calculate whether it is collinear with the two previous points. If so, I can remove the middle point and record only the new end point. I do this within a certain tolerance after normalizing the X and the Y values to a 0-1 range. This has the effect of removing any redundant points that don't change the shape of the curve.

    var deviation = ((y2 − y1)(x3 − x2) - (y3 − y2)(x2 − x1)) 
      / (max(y1, y2, y3) - min(y1, y2, y3))
      / (x3 - x1)

I'm expecting this change to reduce the overall data volume quite a bit since many analog values look like a straight line for considerable periods of time during the day.

Not collinear example

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