The dynamics of spatial behavior: how can robust smoothing techniques help?
Introduction
In the neurosciences, data on locomotor behavior, spatial orientation, navigation, spatial memory, and even social behavior often consist of a time series of coordinates representing the organism’s location. Common experimental setups collecting such data include the Open Field Test, the Photobeam Cage, the Morris Swim Task, the Elevated Plus Maze, the Holeboard, and a variety of other spatial mazes. Most of the studies performed in these setups focus on the animal’s location, ignoring velocity and acceleration (see, however, Kafkafi et al., 2001, Pierce-Shimomura et al., 1999, Tchernichovski and Golani, 1995; Tchernichovski et al., 1998, Wallace et al., 2002, Whishaw et al., 2001).
The benefits of moment-to-moment record of velocity and acceleration cannot, however, be overestimated. Within a dynamic framework, the acceleration and velocity of the animal are the outcome of all the concurrent endogenous and exogenous “forces” acting upon it. Conversely, the attraction or repulsion exerted by a wall, a cliff, a familiar place, a partner or a chemical gradient is revealed by the momentary values of these parameters. In rodent open field studies, for example, the forces exerted by the animal’s home base (Eilam and Golani, 1989), or any other familiar place (Tchernichovski et al., 1996), are reflected in the animal’s velocity and acceleration. The momentary velocity of an animal can tell us whether it “thinks” it is running away or toward its home base, or how familiar the immediate environment is (Tchernichovski and Golani, 1995, Tchernichovski et al., 1998), or what method of navigation it uses (Wallace et al., 2002, Whishaw et al., 2001).
One ethologically-relevant point regarding velocities is that involving zero or close-to-zero velocities, i.e., stops. An organism’s locomotor behavior often consists of an alternation between progression and stopping, be it a nematode (Pierce-Shimomura et al., 1999), an insect (Collins et al., 1994, Collins et al., 1995, Miller, 1979), a fish (Nilsson et al., 1993, O’Brien et al., 1989, Winberg et al., 1993), a lizard (Pietruska, 1986), a bird (Pienkowski, 1983), or a mammal (Golani et al., 1993, Kenagy, 1974). The movements it performs during a stop, be it foraging movements, scanning or movements related to any other form of information gathering, are reflected indirectly in the spatiotemporal properties of the stop, (e.g., Drai et al., 2000). Mouse inbred strains, for example, may differ substantially in the rate, type, rhythm, and number of scans they perform during a stop. These differences in the manner and intensity of information gathering are indirectly reflected in the duration, spatial spread, and average velocity of movement during stopping behavior (Drai and Golani, 2001). Characterizing the stop-and-go behavior should therefore be both ethologically meaningful and results-wise fruitful.
As elaborated in this study, however, the data acquired by the above listed mazes and setups suffer from noise and artifact problems, which are inherent to all tracking systems and critically affect the results. Even a straightforward measure such as the overall distance traveled by the animal is highly sensitive to these problems, but they have a particularly devastating effect on the derivation of velocities and accelerations. Smoothing the raw data is required to obtain a smooth path, correct computation of velocities when the animal is moving, and an isolation of arrests (zero velocity) when stopping. As we show, however, the sometimes-erratic nature of animal movement requires the correct application of the appropriate smoothing methods. Furthermore, those methods appropriate when the animal is on the go become inappropriate when it stops. Therefore, a combination of methods must be used. An automated high-throughput analysis of moment-to-moment velocities becomes proper only after the data have been carefully smoothed by such combination of methods.
Section snippets
Methods of testing
As a test case for investigation of the noise sources and of performances of smoothing methods we used the Open Field test (Hall, 1934) with mice of several common inbred strains, tracked with Noldus EthoVision® video tracking system (Noldus et al., 2001, Spink et al., 2001) at a rate of 25 records (frames) per second. The diameter of the arena was 250 cm and the spatial resolution about 1.3 cm per video pixel (for detailed description of methods and analysis see Kafkafi et al., 2003a). In the
Sources of noise in tracking spatial behavior
Most current tracking systems (either photobeam, photo-cell or video systems) are constrained by the resolution of a recording system using pixels or “tiles”. The recorded location is therefore of discrete nature—two records cannot be closer than the resolution level unless they are at exactly the same location. Furthermore, since the typical pixel length is smaller than the animal, the system actually records the location of the animal’s “center of gravity”.
Whatever the noise level of the
Common smoothing techniques and their properties
Most current photobeam and photo-cell systems and some video tracking systems do not employ any form of smoothing, and are therefore exposed to the noise sources described in Section 3. We are not aware of any serious attempt to evaluate the results of such systems against the actual behavior. Some video systems try to cope with the problem by reducing the sampling rate (also known as down sampling), for example, by using only every other recorded location. The purpose of down-sampling is to
LOWESS: a robust smoothing technique
In order to solve both the precision noise and outliers problems we have incorporated the method of Locally Weighted Scatter Plot Smoothing (LOWESS, see Cleveland, 1977) into our smoothing algorithm. This is an iterative procedure combining the ideas of LP smoothing with robustness to outliers (see Appendix A for the detailed algorithm and choice of parameters). As in the weighted LP, the first iteration of LOWESS fits a polynomial to the data in a time-window centered at t. The resulting
Identifying arrests with Repeated Running Median
The simplest robust smoother is the Running Median (RM, see Tukey, 1977). The RM procedure is similar to the MA, but instead of replacing an observation with the average of its neighboring observations, one uses their median. This seemingly small change has enormous effect on the performance, as the median is a robust function of the data. In simple words, in any window containing more than two observations a single outlier, however wild, will have no effect on the median. Generally speaking,
SEE Path Smoother: a combined smoothing algorithm
The smoothing algorithm we constructed combines the advantages of LOWESS for robust smoothing and velocity estimation during progression with the advantages of RRM for robust identification of arrests. The algorithm smooths the raw data with both methods in parallel. For locations the LOWESS-smoothed results are used during movement, but during arrests (as identified by the RRM) the locations are set to a linear interpolation between the (LOWESS-smoothed) start coordinate and end coordinate of
Examples and experimental evaluation
In this section, we evaluate the previously described smoothing methods side-by-side, using typical examples and samples out of the behavior of mice from several inbred strains.
Fig. 2 displays 6 s (150 frames) from the movement of a DBA/2 mouse. For the sake of simplicity we consider only the movement along the X dimension (the same analysis is also performed in the Y dimension). It is not hard to identify from the raw data (or from watching the video) that during this period the mouse stopped
Potential applications
As demonstrated in the previous sections, a combination of the appropriate smoothing methods must be employed for correct analysis of spatial behavior. This is true even for simple measures such as the distance traveled, but is especially critical for dynamic analysis involving higher derivatives of locations and the identification of stops. Automatic high-throughput recording of undistorted velocities and accelerations has wide implications for ethology and the various branches of behavioral
Acknowledgements
This study is part of the project “Phenotyping mouse exploratory behavior” supported by NIH 1 R01 NS40234-03. We thank two anonymous reviewers for substantial comments that helped improve this paper considerably. We thank Noldus Information Technology for the use of their EthoVision® system in Tel-Aviv University. SEE Path Smoother and other SEE related programs can be downloaded at http://www.tau.ac.il/∼ilan99/see/help.
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These authors contributed equally to the paper.