At the heart of Rtrack is the processing of the raw paths to yield descriptive metrics. Some of these metrics, such as ‘path length’ and ‘time in wall zone’ are easily explained. Others are less clear, are named differently by different authors and/or depend on varying parameters.

This document describes each of the metrics calculated by calculate_metrics and the parameters used in their definition.

The metrics object

A core functionality of the Rtrack package is the calculation of metrics from the path coordinates. The rtrack_metrics object that is returned by calculate_metrics contains the results of these calculations which are used for prediction by the machine learning model. This section explains the information contained in the rtrack_metrics object and describes the individual metrics in detail.

Object metadata

This section contains information that has been passed to the calculate_metrics function and is embedded in the rtrack_metrics object for convenience.

id

This is the track id supplied either to read_path or read_experiment and should be a unique identifier for the track. This will be used to name track analysis output and to title the plots generated by plot_path or plot_density.

arena

The rtrack_arena object associated with this track. See the function read_arena for details.

Arena zones

Briefly, the Morris water maze arena is defined as a ‘pool’ that is divided into several, often overlapping, zones. The zones for this arena type are as follows:

  • The pool is defined as the circular arena in which the water maze was performed. The raw size, shape and centre point (to allow for path recording calibration) are set by the experimenter in the arena definition file/s (see the function read_arena). The fraction of time spent in this zone should be 1 (excepting only small calibration errors).
  • The wall is defined as a ring with the outer extent bounded by the pool/arena and the inner radius equal to 80 % of the arena radius (i.e. the wall zone width is 10 % of the pool/arena diameter).
  • The far wall is defined as a ring with the outer extent bounded by the wall (see above) and the inner radius bounded by the annulus (see below).
  • The annulus is defined as a ring, centred on the centre of the pool/arena, with a width such that the entire goal exactly fits inside it. In other words, the inner radius of the annulus is the minimal distance between the edge of the goal zone and the arena centre, and the outer radius is the maximal distance between the edge of the goal zone and the arena centre.
  • The goal is the target platform. This is required, even for a probe trial where the platform is not physically present. The size and position are defined by the experimenter in the arena definition file/s (see the function read_arena).
  • The old goal is the previous position the target platform was in before a reversal. This is optional and will not be present during training/acquisition or a probe trial. The size and position (if present) are defined by the experimenter in the arena definition file/s (see the function read_arena).
  • The quadrants. The north quadrant is the quarter of the arena area that is centred on the goal. The other quadrants are defined based on this. The quadrant definitions thus change when the goal is moved (such as during a reversal).

area

A list of the areas of each of the arena components. This is used in several of the metrics calculations.

path

The rtrack_path object associated with this track. See the function read_path for details.

Core metrics

This section contains all the metrics, including those calculated for all time points (such as distance from goal and heading error).

path.length

The length of the path. This is in whatever units the path was measured in (millimetres, inches, pixels).

velocity

The speed of movement at each time interval. In normalised path units per second.

total.time

The total time the subject spent in the arena. This is given in seconds.

goal.crossings

Zone crossings are the number of times the path crossed (i.e. entered and exited once) a particular zone. This is measured by calculating the intersection of the path and the zone polygon and identifying the transitions between ‘inside’ and ‘outside’ of the zone. Half of these transitions will be entries which is equivalent to the number of crossings (this value is in fact rounded up in case the track ends in a goal zone, as expected for the goal, which should be counted as a ‘crossing’).

old.goal.crossings

The same as goal.crossings for the old goal.

coverage

The fraction of the arena covered by the path. This is measured by calculating the area of the minimal polygon enclosing the path (i.e. the ‘silhouette’; actually the ‘convex hull’ in technical terms) as a fraction of the area of the arena.

angle.from.xaxis

The angle between each point in the path and the x-axis. This is also used to generate the turning and absolute.turning metrics by calculating the difference in angles between adjacent points.

outliers

The percentage of the path that is not in the not in approach corridor.

initial.path

The initial path is the section of the path from the start to a length equal to the direct distance between the start and the centre of the goal.

initial.heading.error

The angle between each point of the initial path and the direct line from start to goal.

initial.displacement.error

The distance between each point of the initial path and the corresponding point on the direct path from start to goal.

initial.trajectory.error

The distance between the last point of the initial path and the centre of the goal.

efficiency

The percentage of initial.heading.error values below 15\(^\circ\).

roaming.entropy

This is an application of the Shannon entropy measure to spatial paths. In Rtrack, it is estimated by calculating a density map with a 50 \(\times\) 50 grid (and a bandwidth of 1/50) which is clipped to the bounds of the arena. This gives a computationally fast estimate of \(p\); the likelihood of the path passing through any one of the grid cells. The entropy is then calculated using Shannon’s equation: \(-\sum(p\times log(p))\). This value is then normalised by dividing by the log of the total number of grid cells present in the arena (so that the final value ranges between 0 and 1). A roaming entropy of 1 means that the path covers the entire arena and it is impossible to predict a point on the path. A roaming entropy of 0 occurs when the entire path is within one grid cell. Lower entropy values indicate a more predictable path. The idea behind the roaming entropy measure is demonstrated at http://www.brandmaier.de/roamingentropy/.

latency.to.zone

The time at which the subject first crossed each zone. This is a list, with values computed for each of the defined zones.

time.in.zone

The fraction of the path spent in each zone. The time at which the subject first crossed the each zone. This is a list, with values computed for each of the defined zones.

An overview of some of the terms used in the metrics definitions.

Summary metrics

The summary metrics are derived from the core metrics above, but are each only a single value. Where metrics have been calculated for every timepoint, the value given here is either a sum, where appropriate, or the median together with the upper and lower quartiles.

features

This vector of (normalised) values is used for strategy calling using the machine learning model implemented in call_strategy. These are not useful for further analysis on their own.

summary

This is a selection of summary metrics that make sense for downstream analysis. These values use the same units as the raw input data. That is, the distances are in whatever units the track acquisition software used (this may be centimetres, inches or even just pixels from the video analysis—you will need to check with your acquisition software if you are unsure of what these are). Times are in the units specified in the arena description file. These will be ( must be!) the units of the timestamps in the raw acquisition data. Most of these values are medians of the metrics calculated for each point on the path1.

path.length

The total length of the path. This is just the sum of the distance between each point and the next point in the path.

total.time

The total time the subject spent in the arena. This is not necessarily the same as the maximum trial duration; e.g. in cases where the subject finds the platform early.

velocity

The median velocity. The speed of movement at each time interval. In path units per second.

distance.from.goal

The median distance of each point on the path from the centre of the goal.

distance.from.old.goal

The median distance of each point on the path from the centre of the old goal.

initial.heading.error

The median of the angles between the direct path from start to goal and each section of the initial path (see above).

initial.trajectory.error

The distance between the last point of the initial path and the centre of the goal.

initial.reversal.error

The distance between the last point of the initial path and the centre of the old goal. This is the same as initial.trajectory.error (and uses the same initial path) but records the distance to the old goal (if present). If no old goal has been defined, this value is NA.

efficiency

The search efficiency (see efficiency above).

roaming.entropy

The roaming entropy (see roaming.entropy above).

latency.to.goal

The time at which the subject first crossed the goal zone (see latency.to.zone above). This will be NA if the goal was not reached.

latency.to.old.goal

The time at which the subject first crossed the old goal zone (see latency.to.zone above). This will be NA if the old goal was not reached or if there was no old goal present.

time.in.wall.zone

Time in the wall zone (see Arena zones above for a definition of this zone).

time.in.far.wall.zone

Time in the wall zone (see Arena zones above for a definition of this zone).

time.in.annulus.zone

Time in the wall zone (see Arena zones above for a definition of this zone).

time.in.goal.zone

Time in the wall zone (see Arena zones above for a definition of this zone).

time.in.old.goal.zone

Time in the wall zone (see Arena zones above for a definition of this zone).

time.in.n.quadrant

Time in the north quadrant (centred on the goal position; see Arena zones above for a definition of this zone).

time.in.e.quadrant

Time in the east quadrant (see Arena zones above for a definition of this zone).

time.in.s.quadrant

Time in the south quadrant (see Arena zones above for a definition of this zone).

time.in.w.quadrant

Time in the west quadrant (see Arena zones above for a definition of this zone).

goal.crossings

The number of times the path crossed the goal zone (see goal.crossings above).

old.goal.crossings

The number of times the path crossed the old goal zone (see goal.crossings above).

Structure of the metrics object

Below is an overview of the hierarchy of the rtrack_metrics object together with the names and classes of each component. Where the class is not part of the R base package, it is given in square brackets after the class name.

metrics : rtrack_metrics [Rtrack]
    id : character
    arena : rtrack_arena [Rtrack]
        id : character
        type : character
        description : data.frame
            type : character
            time.units : character
            arena.bounds : character
            goal : character
            (old.goal : character) **this component is optional and may be missing**
        correction : list
            t : numeric
            x : numeric
            y : numeric
            r : numeric
        pool : list
            shape : character
            x : numeric
            y : numeric
            radius : numeric
        goal : list
            shape : character
            x : numeric
            y : numeric
            radius : numeric
        old.goal : list 
            shape : character
            x : numeric
            y : numeric
            radius : numeric
        zones : list
            pool : PackedSpatVector [terra]
            wall : PackedSpatVector [terra]
            far.wall : PackedSpatVector [terra]
            annulus : PackedSpatVector [terra]
            goal : PackedSpatVector [terra]
            old.goal : PackedSpatVector [terra]
            n.quadrant : PackedSpatVector [terra]
            e.quadrant : PackedSpatVector [terra]
            s.quadrant : PackedSpatVector [terra]
            w.quadrant : PackedSpatVector [terra]
            goal.corridor : PackedSpatVector [terra]
    area : list
        pool : numeric
        wall : numeric
        far.wall : numeric
        annulus : numeric
        goal : numeric
        old.goal : numeric
        n.quadrant : numeric
        e.quadrant : numeric
        s.quadrant : numeric
        w.quadrant : numeric
    path : rtrack_path
        id : character
        raw.t : numeric
        raw.x : numeric
        raw.y : numeric
        t : numeric
        x : numeric
        y : numeric
    path.length : numeric
    velocity : numeric
    total.time : numeric
    goal.crossings : numeric
    old.goal.crossings : numeric
    coverage : numeric
    angle.from.xaxis : numeric
    outliers : numeric
    initial.path : numeric
    initial.heading.error : numeric
    initial.displacement.error : numeric
    initial.trajectory.error : numeric
    efficiency : numeric
    roaming.entropy : numeric
    alpha : numeric
    heading.error : numeric
    velocity.in.zone : numeric
    latency.to.zone : numeric
    time.in.zone : numeric
    features : numeric
        path.length : numeric
        lower.velocity : numeric
        median.velocity : numeric
        upper.velocity : numeric
        total.time : numeric
        coverage : numeric
        turning : numeric
        absolute.turning : numeric
        lower.angle : numeric
        median.angle : numeric
        upper.angle : numeric
        lower.d.centroid : numeric
        median.d.centroid : numeric
        upper.d.centroid : numeric
        lower.d.goal : numeric
        median.d.goal : numeric
        upper.d.goal : numeric
        lower.d.old.goal : numeric
        median.d.old.goal : numeric
        upper.d.old.goal : numeric
        lower.d.origin : numeric
        median.d.origin : numeric
        upper.d.origin : numeric
        centroid.goal.displacement : numeric
        centroid.old.goal.displacement : numeric
        median.initial.heading.error : numeric
        initial.trajectory.error : numeric
        initial.reversal.error : numeric
        efficiency : numeric
        roaming.entropy : numeric
        velocity.in.wall.zone : numeric
        velocity.in.far.wall.zone : numeric
        velocity.in.annulus.zone : numeric
        velocity.in.goal.zone : numeric
        velocity.in.old.goal.zone : numeric
        velocity.in.n.quadrant : numeric
        velocity.in.e.quadrant : numeric
        velocity.in.s.quadrant : numeric
        velocity.in.w.quadrant : numeric
        latency.to.wall.zone : numeric
        latency.to.far.wall.zone : numeric
        latency.to.annulus.zone : numeric
        latency.to.goal.zone : numeric
        latency.to.old.goal.zone : numeric
        latency.to.n.quadrant : numeric
        latency.to.e.quadrant : numeric
        latency.to.s.quadrant : numeric
        latency.to.w.quadrant : numeric
        time.in.wall.zone : numeric
        time.in.far.wall.zone : numeric
        time.in.annulus.zone : numeric
        time.in.goal.zone : numeric
        time.in.old.goal.zone : numeric
        time.in.n.quadrant : numeric
        time.in.e.quadrant : numeric
        time.in.s.quadrant : numeric
        time.in.w.quadrant : numeric
        wall.zone.crossings : numeric
        far.wall.zone.crossings : numeric
        annulus.zone.crossings : numeric
        goal.zone.crossings : numeric
        old.goal.zone.crossings : numeric
        n.quadrant.crossings : numeric
        e.quadrant.crossings : numeric
        s.quadrant.crossings : numeric
        w.quadrant.crossings : numeric
    summary : numeric
        path.length : numeric
        total.time : numeric
        velocity : numeric
        distance.from.goal : numeric
        distance.from.old.goal : numeric
        initial.heading.error : numeric
        initial.trajectory.error : numeric
        initial.reversal.error : numeric
        efficiency : numeric
        roaming.entropy : numeric
        latency.to.goal : numeric
        latency.to.old.goal : numeric
        time.in.wall.zone : numeric
        time.in.far.wall.zone : numeric
        time.in.annulus.zone : numeric
        time.in.goal.zone : numeric
        time.in.old.goal.zone : numeric
        time.in.n.quadrant : numeric
        time.in.e.quadrant : numeric
        time.in.s.quadrant : numeric
        time.in.w.quadrant : numeric
        goal.crossings
        old.goal.crossings

  1. Most of the metrics are not normally distributed and therefore so-called parametric statistics may not be appropriate. For this reason, Rtrack defaults to using non-parametric descriptive statistics such as median and the upper/lower quartiles.↩︎