# The Lowess smoothing method

Lowess stays for Locally weighted scatter plot smoothing. This method fits a curve to the dataset, using a least square regression modified as follows:

▪The Lowess method uses a moving time window (or half size window) that contains a subset of sample points.

▪The Lowess method uses a 2-degree (non-linear) polynomial fit. This fit is applied to the center-point. If you use center-point, nose-point and tail-base detection, the fit is also applied to the angle between center-point and nose-point and between the center-point and tail-base. (see Notes below).

▪The Lowess method is weighted; sample points nearest to the point being fitted have a larger influence on the fit than sample points further away.

The Lowess method has been successfully applied on track data from EthoVision.

To apply Lowess smoothing

1.Choose Acquisition > Track Smoothing Profile > Open.

2.Select the Smoothing (Lowess) check box and click the Edit button.

3.Change the number of sample points in the Half window size list.

The default value is 10 which is the recommended value. Selecting a larger half window size results in a smoother path. Selecting a smaller half window size results in a path that more resembles the original path. With a lower sample rate, you should use a larger half window size to get the same smoothing as with a higher sample rate.

Notes

▪Smoothing is applied after data acquisition and after data editing, but before the Minimal Distance Moved method. The smoothed data, not the original data, are used for analysis and for export. Applying Smoothing does not change the original data.

▪Smoothing and body points. Smoothing is applied to the center-point, and subsequently, if you also tracked the nose-point and the tail-base, to the angle formed by the three body points.

▪Smoothing and missing samples. When up to 200 consecutive samples are missing, they are interpolated (see Interpolate points). Next, their x,y coordinates are re-calculated based on the Lowess method. The Subject area for missing samples is interpolated linearly, but is not smoothed.

If the subject is missing for more than 200 samples (this corresponds to 8 seconds for a sample rate of 25), that track segment stays missing, and is not smoothed.

▪Smoothing of Live Mouse Tracker data. When you apply Lowess smoothing to Live Mouse Tracker data, EthoVision XT takes the 3D coordinates of the body points (x-, y- and z-coordinates). The 3D position of the nose-point and the tail-base point are represented with spherical coordinates bound to the center-point.

▪For example, the coordinates of the nose point are based on the length r and angles q and j of the segment joining the center-point and the nose-point. The z-coordinate of the nose- (or tail-base) point includes the angle q formed between the x-y plane and the segment joining that body point and the center-point.

▪Smoothing of Live Mouse Tracker data is done as described in How the nose-point and tail-base point are interpolated, with the difference that the vectors and the angles are drawn in 3D instead of 2D like in typical EthoVision XT nose-tail data.

▪Smoothing and hidden zones. Samples assigned to a hidden zone are smoothed too. For this reason, after smoothing with the Lowess method, part of the samples in the hidden zone are “moved” outward, producing the effect shown below. Those samples add up to the total distance moved in your results. How many samples are moved depends on the original trajectory.

Below: An example of the effect of Lowess smoothing on the location of samples originally assigned to a hidden zone. After smoothing, part of the samples assigned to the hidden zone center are moved toward the adjacent samples outside the zone. A similar effect can be seen when the animal exits the hidden zone.

See also

▪For more information on the Lowess method, see http://en.wikipedia.org/wiki/Lowess.

▪For more information on the application of the Lowess method on EthoVision tracks, see:

▪Drai and Golani, 2001. SEE: a tool for the visualization and analysis of rodent exploratory behavior, Neurosci. & Biobehav. Rev. 25(5): 409-426.

▪Hen, I. et al. 2004. The Dynamics of Spatial Behavior: How can robust smoothing techniques help? J. Neurosci. Methods 133(1-2): 161-172.

▪Kafkafi, N. et al., 2005. Genotype-environment interactions in mouse behavior: a way out of the problem, Proc. Natl. Acad. Sci. USA, 102(12): 4619-4624.

Acknowledgments

We gratefully acknowledge the ongoing collaboration with Prof. Ilan Golani, Prof. Yoav Benjamini and their colleagues at Tel Aviv University. Their pioneering work on the detailed analysis of animal movement has been a source of inspiration for the developers of EthoVision and for many of its users around the world.