Knowledge Base

The Lowess Smoothing Method

Lowess stands 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.
• 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 to 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. 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 θ and ϕ of the segment joining the center-point and the nose-point. The z-coordinate of the nose- (or tail-base) point includes the angle θ 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 with vectors and angles drawn in 3D instead of 2D as 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. Those samples add up to the total distance moved in your results. How many samples are moved depends on the original trajectory.

References

• Drai and Golani, 2001. SEE: a tool for the visualization and analysis of rodent exploratory behavior. Neuroscience & Biobehavioral Reviews 25(5): 409–426.
• Hen, I. et al., 2004. The dynamics of spatial behavior: How can robust smoothing techniques help? Journal of Neuroscience Methods 133(1-2): 161–172.
• Kafkafi, N. et al., 2005. Genotype-environment interactions in mouse behavior: a way out of the problem. Proceedings of the National Academy of Sciences 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.

The Minimal Distance Moved Smoothing Method

Aim

To filter out small movements of the subject's center point that are caused by random noise, not by the subject's spatial displacement.

Working Principle

With the Minimal Distance Moved method, you can pick out the data when the subject moved a minimal distance from one sample to the next.

• When the distance moved between the current and the previous sample is above (or equal to) the threshold for Minimal Distance Moved, the current sample is used for analysis.
• If the distance moved between the current and the previous sample does not exceed the threshold, the current sample is "moved back" to the previous sample.

The result of this filter is that small movements of the body points, supposedly due to noise, are removed, and the trajectory of the subject becomes simpler.

Procedure

1. Choose Acquisition > Track Smoothing Profile > Open.
2. Select the Minimal Distance Moved check box and click the Edit button.
3. Under Select, enter the Minimal Distance Moved threshold.
4. Choose one of the two options:
   • Direct (A > MDM). To select samples on the basis of the shortest distance (beeline distance) between samples. Select Direct to exclude movements such as breathing when the animal is sitting still.
   • Along the Path (B + C + D > MDM). To select samples on the basis of the actual path between samples. Select Along the Path whenever you want to filter samples according to the distance moved along the path.
5. Click OK.

Notes

• Minimal Distance Moved is only applied to the center-point.
• Under some circumstances, using the Minimal Distance Moved filter might affect dependent variables other than Distance Moved and Velocity. To apply Minimal Distance Moved to some dependent variables but not others, create two Track Smoothing profiles: one with Minimal Distance Moved selected, the other without Minimal Distance Moved selected. Run batch calculations using both smoothing profiles.

Direct vs. Along the Path Minimal Distance Moved

As shown by the case of Distance Moved, calculation of the dependent variables is affected by which Minimal Distance Moved option you choose.