This page contains the various definitions and formulas used in the BehaviorDEPOT pipeline.

• The following definitions are for body parts that are derived from tracked keypoints.

• If legs are tracked: mean(BetwEars + BetwLegs)
• Otherwise: mean(BetwEars + Tailbase)
• If MidBack is tracked directly as a keypoint, then it will remain unchanged

• These definitions describe the metrics calculated from the keypoint tracking info (i.e. DLC).
• These metrics are calculated in the function 'calculateMetrics' (used in the Analysis Module).

• Angles relative to the positive X axis (degrees -180 to +180)
• Equal to arctangent(Keypoint1(Y)-Keypoint2(Y), Keypoint1(X)-Keypoint2(X))
• Units: deg

• Distance between two body parts
• Equal to sqrt((Keypoint2(X)-Keypoint1(X))²+((Keypoint2(Y)-Keypoint1(Y)²)
• Units: cm

• Distance change by frame, used to calculate linear velocity and acceleration
• Equal to x(i+1) - x(i) * framerate / resolution
• Units: cm/s

• Angle change by frame, used to calculate angular velocity
• Equal to ((angle(i+1)-angle(i) + 180)/360 – 180)
• Units: deg/frame

• Linear velocity of a keypoint
• Equal to sqrt((dx/dt)²+(dy/dt)²) [Pythagorean Theorem]
• Units: cm/s

• Angular velocity of a keypoint-based angle calculation
• Equal to ((angle(i+1)-angle(i) + 180)/360 – 180)*framerate [transform range from -180->180 to 0->360]
• Units: deg/s

• Linear acceleration of a keypoint per frame
• Equal to the velocity differential divided by framerate
• Units: cm/s²

• Cumulative sum of distance per frame times resolution
• Represents total distance traveled per frame based on central point on body
• Units: cm

• A hampel correction is applied to the data to detect outliers.
• For more info see:

1. Hampel, F. R. The Influence Curve and its Role in Robust Estimation. J. Am. Stat. Assoc. 69, 383–393 (1974)
2. MATLAB 'hampel' documentation

• Raw pose-estimation data is smoothed using the 'smooth' function from the MATLAB Curve Fitting Toolbox, which offers the choice of multiple algorithms for smoothing.
• The default method of smoothing is 'LOWESS', described below.
• Smoothing methods can be changed from the GUI.
• See MATLAB 'smooth' documentation for more information on the smoothing algorithm.

• LOWESS = Local regression using weighted linear least squares and a 1st degree polynomial model.
• The algorithm fits a local regression model to smooth data across the 'span' specified in the smoothing parameters.
• This method provides high-quality smoothing but can be slow on longer videos.
• For more information see:

1. Cleveland, W. S. LOWESS: A Program for Smoothing Scatterplots by Robust Locally Weighted Regression. Am. Stat. 35, 54 (1981)

• For more info on alternative methods, see MATLAB 'smooth' method options

• A convolution algorithm is applied to raw behavior labels to remove mislabeling due to minor tracking errors.
• The algorithm applies a vector of length 'windowWidth' to raw behavior labels, scoring each frame based on the number of positive labels when the vector is centered on the frame.
• The result is a vector that scores each frame based on the density of behavior labels around it.
• This vector is then thresholded using 'countThreshold' to produce final binary labels, represented as 1 (behavior+) or 0 (behavior-).
• Typically, a good 'windowWidth' is the approximate number of frames of the smallest behavior bout you wish to capture (e.g. windowWidth = 30 for 1 sec bout @ 30fps)
• Typically, a good 'countThreshold' is approximately 1/3 of your windowWidth.
• These values can be tested using the Optimization Module.

• These definitions describe the performance calculations made when using the BehaviorDEPOT support modules.
• Performance calculations are used in the Validation, Optimization, & Inter-Rater Modules.
• The following abbreviations apply to performance formulas:

1. TP = true positive frames
2. TN = true negative frames
3. FP = false positive frames
4. FN = false negative frames

• Quantifies the positive predictive value of the classifier against the tendency to produce false positive errors.
• Equal to TP / (TP + FP)

• Quantifies the positive predictive value of the classifier against the tendency to produce false negative errors.
• Equal to TP / (TP + FN)

• Quantifies overall classifier performance.
• Equal to (2 * precision * recall) / (precision + recall)

• Quantifies the classifier's ability to accurately label true negatives; helps ensure classifier is only labeling a single behavior.
• Equal to TN / (TN + FP)