Generic One-to-One Association Examples

These examples demonstrate how to use the OneToOneAssociator class for three varied uses. The three examples include associating State, Track and words.

The OneToOneAssociator is used for associating objects with an appropriate BaseMeasure object. Subclasses of BaseMeasure take two objects and return a float value to assess the separation between the two objects. This is used by the OneToOneAssociator to optimally associate objects.

First some generic imports and variables are set up as they are needed for all the examples.

import datetime

from stonesoup.dataassociator.general import OneToOneAssociator
from stonesoup.measures.multi import StateSequenceMeasure, MeanMeasure
from stonesoup.measures.base import BaseMeasure, SetComparisonMeasure
from stonesoup.dataassociator.tracktotrack import OneToOneTrackAssociator
from stonesoup.measures import Euclidean
from stonesoup.plotter import Plotterly
from stonesoup.types.state import State
from stonesoup.types.track import Track

colours = ["darkgreen", "firebrick", "gold", "mediumvioletred", "dodgerblue", "black", "blue",
           "lime"]

One-to-One States Association Example

In this example the OneToOneAssociator is used to associate State objects. Consider the scenario having two conflicting sources reporting the location of objects. An associator can be used to judge where multiple sensors are observing the same object. For simplicity a standard State with no uncertainty information is used. This means the Euclidean metric is appropriate to compare the states.

Create States

We have states from source A and source B marked as states_from_a and states_from_b respectively.

states_from_a = [State([1, 5]), State([0, 5]), State([1, 0]), State([2, 2]), State([4, 3]),
                 State([8, 6])]
states_from_b = [State([0, 3]), State([1, 6]), State([2, 1]), State([3, 0]), State([3, 1]),
                 State([4, 6]), State([2, 6])]

state_names = {**{state: f"state a{idx}" for idx, state in enumerate(states_from_a)},
               **{state: f"state b{idx}" for idx, state in enumerate(states_from_b)}}

Next, use Plotly to visualise the scenario, with source A states shown in green crosses and source B states shown in red circles:

colours_iter = iter(colours)

plotter = Plotterly()
plotter.plot_tracks(tracks=[Track(state) for state in states_from_a],
                    mapping=[0, 1], track_label="Source A",
                    mode="markers", marker=dict(symbol="cross", color=next(colours_iter)))

plotter.plot_tracks(tracks=[Track(state) for state in states_from_b],
                    mapping=[0, 1], track_label="Source B",
                    mode="markers", marker=dict(symbol="circle", color=next(colours_iter)))

plotter.fig

This scenario has been designed such the optimal association between states_from_a and states_from_b is unclear to the human eye.

Create Associator & Associate States

Create Associator. Create a OneToOneAssociator which can associate State objects. The Euclidean metric is used to compare the objects.

state_associator = OneToOneAssociator(measure=Euclidean(mapping=[0, 1]),
                                      maximise_measure=False,
                                      association_threshold=3)

Associate States. The OneToOneAssociator will minimise the total measure (Euclidean distance) between the two states. The OneToOneAssociator uses SciPy’s linear_sum_assignment() function (a modified Jonker-Volgenant algorithm) to minimise the distance. For pairs of objects with a distance equal to or above the threshold, these pairs won’t be associated together.

associations, unassociated_states_a, unassociated_states_b = \
    state_associator.associate(states_from_a, states_from_b)

Results of State Association

The results are visualised below using Plotly:

colours_iter = iter(colours)
plotter = Plotterly()
for idx, assoc in enumerate(associations.associations):
    state_from_a = [state for state in assoc.objects if state in states_from_a][0]
    state_from_b = [state for state in assoc.objects if state in states_from_b][0]

    colour = next(colours_iter)
    track = Track(state_from_a, init_metadata=dict(source="a", association=idx))
    plotter.plot_tracks(track,
                        mapping=[0, 1], mode="markers",
                        track_label=f"{state_names[state_from_a]}, Association {idx}",
                        marker=dict(symbol="cross", color=colour))

    track = Track(state_from_b, init_metadata=dict(source="b", association=idx))
    plotter.plot_tracks(track, mapping=[0, 1], mode="markers",
                        track_label=f"{state_names[state_from_b]}, Association {idx}",
                        marker=dict(symbol="circle", color=colour))

    track = Track([state_from_a, state_from_b], init_metadata=dict(association=idx))
    plotter.plot_tracks(track, mapping=[0, 1], mode="lines",
                        track_label=f"Association {idx}",
                        line=dict(color=colour))

    dist_between_states = Euclidean()(state_from_a, state_from_b)
    print(f"State {list(state_from_a.state_vector)} from source A is associated to state "
          f"{list(state_from_b.state_vector)} from source B. The distance between the states is "
          f"{dist_between_states:.1f}")


for state in unassociated_states_a:
    print(f"State {list(state.state_vector)} from source A isn't associated any states from "
          f"source B.")
    colour = next(colours_iter)
    track = Track(state, init_metadata=dict(source="a", association=None))
    plotter.plot_tracks(track, mapping=[0, 1],
                        track_label=f"{state_names[state]}, No Association",
                        mode="markers", marker=dict(symbol="cross", color=colour))

for state in unassociated_states_b:
    print(f"State {list(state.state_vector)} from source B isn't associated any states from "
          f"source A.")
    colour = next(colours_iter)
    track = Track(state, init_metadata=dict(source="b", association=None))
    plotter.plot_tracks(track, mapping=[0, 1],
                        track_label=f"{state_names[state]}, No Association",
                        mode="markers", marker=dict(symbol="circle", color=colour))

State [np.int64(1), np.int64(0)] from source A is associated to state [np.int64(3), np.int64(0)] from source B. The distance between the states is 2.0
State [np.int64(0), np.int64(5)] from source A is associated to state [np.int64(1), np.int64(6)] from source B. The distance between the states is 1.4
State [np.int64(1), np.int64(5)] from source A is associated to state [np.int64(2), np.int64(6)] from source B. The distance between the states is 1.4
State [np.int64(4), np.int64(3)] from source A is associated to state [np.int64(3), np.int64(1)] from source B. The distance between the states is 2.2
State [np.int64(2), np.int64(2)] from source A is associated to state [np.int64(2), np.int64(1)] from source B. The distance between the states is 1.0
State [np.int64(8), np.int64(6)] from source A isn't associated any states from source B.
State [np.int64(0), np.int64(3)] from source B isn't associated any states from source A.
State [np.int64(4), np.int64(6)] from source B isn't associated any states from source A.

The plot below shows the states. Source A states are shown with crosses and source B states are shown with circles. Associations are shown by matching colours and lines between the states.

plotter.fig

Summary

• Five states from source A have been associated to five states from source B

• Three states aren’t associated to another state

• State a5 and b5 would be associated but the distance between them is above the threshold

• State b0 isn’t associated to a state due to there being better combinations of other states

Track to Track Association Example

This example demonstrates the ability of the OneToOneTrackAssociator to associate tracks together. This can be used in Track to Track Fusion.

Create Tracks

Six tracks are created that represent three tracks from each source ‘A’ and ‘B’. These tracks represent a varied scenario for a track association algorithm.

start_time = datetime.datetime(2023, 1, 1, 0, 0, 0)

track_a1 = Track(states=[State(state_vector=[[i], [i]],
                               timestamp=start_time + datetime.timedelta(seconds=i))
                         for i in range(10)],
                 id="Track a1")

track_b1 = Track(states=[State(state_vector=[[i + 0], [i + 1]],
                               timestamp=start_time + datetime.timedelta(seconds=i))
                         for i in range(1, 7)], id="Track b1")

track_a2 = Track(states=[State(state_vector=[[10-i], [i]],
                               timestamp=start_time + datetime.timedelta(seconds=i))
                         for i in range(10)],
                 id="Track a2")

track_b2 = Track(states=[State(state_vector=[[6 - i/6], [i]],
                               timestamp=start_time + datetime.timedelta(seconds=i))
                         for i in range(10)],
                 id="Track b2")

track_b3 = Track(states=[State(state_vector=[[i+0.5], [i]],
                               timestamp=start_time + datetime.timedelta(seconds=i + 20))
                         for i in range(10)],
                 id="Track b3")

track_a3 = Track(states=[State(state_vector=[[i + 5], [15]],
                               timestamp=start_time + datetime.timedelta(seconds=i))
                         for i in range(10)],
                 id="Track a3")

tracks_a = {track_a1, track_a2, track_a3}
tracks_b = {track_b1, track_b2, track_b3}

The tracks are plotted. As before, we use different colours to separate tracks_a from tracks_b.

colours_iter = iter(colours)

plotter = Plotterly()

colour = next(colours_iter)
for track in tracks_a:
    plotter.plot_tracks(track, mapping=[0, 1], track_label=track.id, marker=dict(color=colour))

colour = next(colours_iter)
for track in tracks_b:
    plotter.plot_tracks(track, mapping=[0, 1], track_label=track.id, marker=dict(color=colour))

plotter.fig

Track a1 and Track b1 are close to each other. They should be associated to each other unless the tolerance for association is very high.

Track a2 and Track b2 are close to each other. Depending on the association threshold they may or may not be associated to each other.

Track a3 is too far away to associated with any of the other tracks.

Track b3 appears to be closer to Track a1 than Track b1 is. However, Track b3 takes place 20 seconds after Track a1 and Track b1, therefore there are no overlapping time periods for association.

Create Associator & Associate Tracks

The full_state_sequence_measure (StateSequenceMeasure) measure will apply the Euclidean state measure to each state in the tracks, with the same time. This produces a multiple measures for each state.

full_state_sequence_measure = StateSequenceMeasure(state_measure=Euclidean(mapping=[0, 1]))

track_measure (MeanMeasure) will take the multiple measures from full_state_sequence_measure and condense it down into one single measure by taking the mean.

track_measure = MeanMeasure(measure=full_state_sequence_measure)

The OneToOneTrackAssociator is a subclass of OneToOneAssociator and TwoTrackToTrackAssociator.

associator = OneToOneTrackAssociator(measure=track_measure,
                                     association_threshold=5,  # Any pairs >= 5 will be discarded
                                     maximise_measure=False  # The minimum measure is needed
                                     )

associations, unassociated_a, unassociated_b = associator.associate(tracks_a, tracks_b)

/home/docs/checkouts/readthedocs.org/user_builds/stonesoup/checkouts/v1.4/stonesoup/measures/multi.py:63: UserWarning:

No measures are calculated as there are not any times that match between the two state sequences.

Results of Track Association

The results will be visualised and printed.

plotter = Plotterly()
colours_iter = iter(colours)

for assoc in associations.associations:
    print('Associated together', [track.id for track in assoc.objects])
    colour = next(colours_iter)
    for track in assoc.objects:
        plotter.plot_tracks(track, mapping=[0, 1], track_label=track.id,
                            marker=dict(color=colour))

print("Not Associated in A: ", [track.id for track in unassociated_a])
print("Not Associated in B: ", [track.id for track in unassociated_b])

for track in [*unassociated_a, *unassociated_b]:
    colour = next(colours_iter)
    plotter.plot_tracks(track, mapping=[0, 1], track_label=track.id, marker=dict(color=colour))

plotter.fig

Associated together ['Track b1', 'Track a1']
Associated together ['Track a2', 'Track b2']
Not Associated in A:  ['Track a3']
Not Associated in B:  ['Track b3']

Word Association Example

The association algorithm can be used to associate many things. In this example we’ll associate words to demonstrate the versatility of the algorithm.

In the example scenario an application can only accept standard colour names. However, the user interface also accepts CCS colours. The association algorithm must try to match the user’s input to a ‘standard’ colour. The ‘standard’ colours the application can use are:

standard_colours = ["White", "Black", "Yellow", "Red", "Blue", "Green", "Orange", "Purple",
                    "Grey"]

Measure 1 - Example 1

WordMeasure is a crude measure to compare how similar words are. It calculates the number of letters that both words have in common and divides by the total number of unique letters.

class WordMeasure(BaseMeasure):
    def __call__(self, word_1: str, word_2: str) -> float:
        return SetComparisonMeasure()(set(word_1.lower()), set(word_2.lower()))

The colours that are inputted by a user:

received_colours_scheme = ["FloralWhite", "LightGreen", "Magenta"]

The association process:

associator = OneToOneAssociator(measure=WordMeasure(),
                                maximise_measure=True,
                                association_threshold=0.3)

association_dict = associator.association_dict(standard_colours, received_colours_scheme)

Print association results

print("Received Colour:\tAssociated Standard Colour")
for received_colour in received_colours_scheme:
    standard_colour = association_dict[received_colour]
    print(received_colour, "matched with: \t", standard_colour)

Received Colour:        Associated Standard Colour
FloralWhite matched with:        White
LightGreen matched with:         Green
Magenta matched with:    Orange

Magenta shouldn’t be match with Orange. We need a better measure.

Measure 2 - Example 1

MatchingWordMeasure looks for words that are identical or is a word/phrase is contained within another word/phrase.

class MatchingWordMeasure(BaseMeasure):
    PERFECT_MATCH = 1.0
    PARTIAL_MATCH = 0.5
    NO_MATCH = 0.0

    def __call__(self, word_1: str, word_2: str) -> float:
        word_1 = word_1.lower()
        word_2 = word_2.lower()

        if word_1 == word_2:
            return self.PERFECT_MATCH
        elif word_1 in word_2 or word_2 in word_1:
            return self.PARTIAL_MATCH
        else:
            return self.NO_MATCH

The association process:

associator = OneToOneAssociator(measure=MatchingWordMeasure(),
                                maximise_measure=True,
                                association_threshold=0.3  # Just below PARTIAL_MATCH
                                )

association_dict = associator.association_dict(standard_colours, received_colours_scheme)

Print association results:

print("Received Colour:\tAssociated Standard Colour")
for received_colour in received_colours_scheme:
    standard_colour = association_dict[received_colour]
    print(received_colour, "matched with: \t", standard_colour)

Received Colour:        Associated Standard Colour
FloralWhite matched with:        White
LightGreen matched with:         Green
Magenta matched with:    None

Measure 2 - Example 2

received_colours_scheme = ["LightSeaGreen", "OrangeRed", "MediumVioletRed"]

association_dict = associator.association_dict(standard_colours, received_colours_scheme)

Print association results:

print("Received Colour:\tAssociated Standard Colour")
for received_colour in received_colours_scheme:
    standard_colour = association_dict[received_colour]
    print(received_colour, "matched with: \t", standard_colour)

Received Colour:        Associated Standard Colour
LightSeaGreen matched with:      Green
OrangeRed matched with:          Orange
MediumVioletRed matched with:    Red

Summary

The OneToOneAssociator can be used for multiple varied purposes. It was created originally for track association but can be used to associate anything. The examples above show its use in associating StateMutualSequence, State and str. It’s a flexible association class that can be tailored for many use cases.