CN112783950A - Human movement predictability quantification method based on information entropy - Google Patents

Human movement predictability quantification method based on information entropy Download PDF

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CN112783950A
CN112783950A CN202110136498.4A CN202110136498A CN112783950A CN 112783950 A CN112783950 A CN 112783950A CN 202110136498 A CN202110136498 A CN 202110136498A CN 112783950 A CN112783950 A CN 112783950A
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於志文
吴奇龙
郭斌
王柱
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Abstract

The invention discloses a human movement predictability quantification method based on information entropy, which comprises the steps of firstly obtaining user movement data through sensing equipment, converting the user movement data into a position sequence on a time dimension to obtain a user movement track, then figuratively describing the predictability of the user movement track according to the magnitude of the information entropy, then calculating the conditional probability distribution of the user reaching different positions at the next moment according to the historical movement track of the user, next determining the position with the highest probability at the next moment of the user as a position point which is most probably reached by the user, and finally calculating the probability of accurately predicting the position of the user at the next moment according to the conditional probability distribution to obtain the predictability of the user track. The method can measure the upper limit of the movement track which can be accurately predicted, can be used as an evaluation method of a human movement track prediction algorithm, and evaluates the quality of the prediction algorithm according to the accuracy of the prediction algorithm and the predictability of the movement track sequence.

Description

Human movement predictability quantification method based on information entropy
Technical Field
The invention belongs to the technical field of machine learning, and particularly relates to a human movement predictability quantification method.
Background
With the continuous development of the internet of things and the continuous popularization of sensing equipment, people can record own daily behaviors in an increasingly abundant mode, and sufficient data are provided for the research of human behaviors. The research aiming at human behavior movement has an important role in the fields of geographic area analysis, urban traffic and planning, computer science, public health and the like, and the research is used as the basic representation of human behavior and the potential social and economic activity depicting standard and reflects the movement mode of people.
Existing research on human movement behavior mainly includes characterization of movement trajectories and prediction of positions at the next moment. The position prediction method for the next moment of the human mainly comprises a regression method, a moving self-averaging method and a machine learning method, and the accuracy of human movement prediction is higher and higher due to the gradual complexity of a model and the continuous increase of movement trajectory data. However, these operations are only to improve the accuracy of the prediction of the movement trajectory on a model level, and cannot fundamentally answer how predictable the corresponding movement trajectory history sequence is, that is, how to quantify the maximum probability of accurately predicting the position at the next time given the movement history trajectory of the user.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a human movement predictability quantification method based on information entropy, which comprises the steps of firstly obtaining user movement data through sensing equipment, converting the user movement data into a position sequence on a time dimension to obtain a user movement track, then regularly describing the predictability of the user movement track according to the size of the information entropy, then calculating the conditional probability distribution of the user reaching different positions at the next moment according to the historical movement track of the user, next determining the position with the highest probability at the next moment of the user as the position point which is most probably reached by the user, and finally calculating the probability of accurately predicting the position of the user at the next moment according to the conditional probability distribution to obtain the predictability of the user track. The method can measure the upper limit of the movement track which can be accurately predicted, can be used as an evaluation method of a human movement track prediction algorithm, and evaluates the quality of the prediction algorithm according to the accuracy of the prediction algorithm and the predictability of the movement track sequence.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: using a sensing device to obtain user movement data;
step 2: converting user movement data into a position sequence on a time dimension to obtain a user movement track;
the longitude and latitude information of a user is sampled at fixed time, the longitude and latitude information is mapped to a map grid, and a position change sequence X of the user in a time dimension is obtained as { X }1,x2,…,xnIn which xiThe position of the user at the ith moment is represented, so that the discretized movement track data of the user is obtained;
and step 3: calculating the information entropy E of the user track:
Figure BDA0002926894860000021
wherein, X is a position point of a user moving track, { X } is a position change sequence set of the user moving track, and p (X) is the probability of the position point X appearing in the position change sequence set of the user moving track;
measuring the predictability of the user movement track qualitatively according to the information entropy E:
when E is 0, the user track is completely regular, and the predictability of the corresponding user movement track is 1;
when E is log2When the position change sequence of the user movement track is | { X } |, the track of the user at the next moment is a random value of the historical track, and is completely unpredictable, the predictability of the corresponding user movement track is 0, wherein | { X } | is the size of a position point set in the position change sequence of the user movement track;
when E is equal to other values, entering step 4, and calculating predictability PA of the movement track of the user;
and 4, step 4: calculating the real conditional probability of the user reaching different positions at the next moment according to the historical movement track of the userDistribution: defining the historical movement track sequence of the user at the previous n time as h (n) ═ x1,x2,…,xnWherein x appears in h (n)nThe number of times of (x) is count (x)n) From xnThe number of times of → x is count (x)n→ X), then h (n) corresponds to the true conditional probability distribution P { X ═ X | h (n), X ∈ h (n) }:
Figure BDA0002926894860000022
and 5: finding the position with the maximum probability from the true conditional probability distribution in step 4 as the position point x which is most likely to be reached by the user at the next momentml，
Figure BDA0002926894860000023
Corresponding probability of being
Figure BDA0002926894860000024
Figure BDA0002926894860000025
Step 6: calculating the probability of accurately predicting the position of the user at the next moment according to the conditional probability distribution to obtain the predictability of the user track;
step 6-1: adopting a prediction algorithm, and predicting the probability distribution of the user reaching different positions at the next moment according to the historical movement track sequence h (n) of the user at the previous moment n: ppa{X＝xt|xt∈h(n)}；
Step 6-2: according to the real conditional probability distribution P { X ═ X | h (n), X ∈ h (n) } when the user arrives at different positions at the next moment obtained in the step 4, the probability of accurately predicting the user arrival position at the next moment is obtained as follows:
Figure BDA0002926894860000026
step 6-3: according to step 5, the position x with the highest probability at the next moment of the usermlProbability of (2)
Figure BDA0002926894860000031
Figure BDA0002926894860000032
Then P istrue{ X ═ X | h (n) } satisfies:
Figure BDA0002926894860000033
step 6-4: defining predictability of a user movement track as PA; when the length of the user historical movement track sequence is n, the user historical movement track subsequence set H (n) { { x { (x) }i,xi+1,…,xj}|1≤i<j is less than or equal to n, the probability of the occurrence of the corresponding user historical movement track subsequence H (i) epsilon H (n) is p (H (i)), and the predictability PA of the user movement track is obtained:
Figure BDA0002926894860000034
preferably, the latitude and longitude information of the user is sampled at regular time in the step 2, and the regular time is 1 hour.
Preferably, the size of the map grid in step 2 is 500m × 500 m.
Preferably, the prediction algorithm in step 6-1 is a Markov model or a long-short term memory network or a recurrent neural network.
The invention has the following beneficial effects:
1. in the prior art, mainly aiming at the aspect of prediction of human movement tracks, the invention evaluates the predictability of the human movement tracks from the aspects of quantification and qualification, namely the degree of accurate prediction.
2. The predictability measuring method provided by the invention can measure the upper limit of the accurate prediction of the movement track, can be used as an evaluation method of a human movement track prediction algorithm, and evaluates the quality of the prediction algorithm according to the accuracy of the prediction algorithm and the predictability of the movement track sequence.
3. The invention is not limited to human movement trajectories, and can be applied to measure the predictability of any discrete time sequence and evaluate the degree to which the sequence can be accurately predicted.
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FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
The invention provides a human movement predictability quantification method based on an information theory. The following principles are utilized: the predictability of the time series represents the degree of accurate prediction of the series, the information entropy of the time series can model the uncertainty degree of the corresponding series, and the larger the information entropy is, the more complex the time series is, the worse the prediction is, and the lower the predictability is represented. The information entropy of the sequence is corresponding to the predictability, so that the time sequence predictability quantification based on the information entropy can be realized, and the predictability of the human movement can be obtained by mapping the human movement track to a time dimension.
As shown in fig. 1, a method for quantifying the predictability of human movement based on information entropy comprises the following steps:
step 1: using a sensing device to obtain user movement data;
step 2: converting user movement data into a position sequence on a time dimension to obtain a user movement track;
the longitude and latitude information of a user is sampled at fixed time, the longitude and latitude information is mapped to a map grid, and a position change sequence X of the user in a time dimension is obtained as { X }1,x2,…,xnIn which xiThe position of the user at the ith moment is represented, so that the discretized movement track data of the user is obtained;
and step 3: calculating the information entropy E of the user track:
Figure BDA0002926894860000041
wherein, X is a position point of a user moving track, { X } is a position change sequence set of the user moving track, and p (X) is the probability of the position point X appearing in the position change sequence set of the user moving track;
measuring the predictability of the user movement track qualitatively according to the information entropy E:
when E is 0, the user track is completely regular, and the predictability of the corresponding user movement track is 1;
when E is log2When the position change sequence of the user movement track is | { X } |, the track of the user at the next moment is a random value of the historical track, and is completely unpredictable, the predictability of the corresponding user movement track is 0, wherein | { X } | is the size of a position point set in the position change sequence of the user movement track;
when E is equal to other values, entering step 4, and calculating predictability PA of the movement track of the user;
and 4, step 4: calculating the real conditional probability distribution of the user reaching different positions at the next moment according to the historical movement track of the user: defining the historical movement track sequence of the user at the previous n time as h (n) ═ x1,x2,…,xnWherein x appears in h (n)nThe number of times of (x) is count (x)n) From xnThe number of times of → x is count (x)n→ X), then h (n) corresponds to the true conditional probability distribution P { X ═ X | h (n), X ∈ h (n) }:
Figure BDA0002926894860000042
and 5: finding the position with the maximum probability from the true conditional probability distribution in step 4 as the position point x which is most likely to be reached by the user at the next momentml，
Figure BDA0002926894860000051
Corresponding probability of being
Figure BDA0002926894860000052
Figure BDA0002926894860000053
Step 6: calculating the probability of accurately predicting the position of the user at the next moment according to the conditional probability distribution to obtain the predictability of the user track;
step 6-1: adopting a prediction algorithm, and predicting the probability distribution of the user reaching different positions at the next moment according to the historical movement track sequence h (n) of the user at the previous moment n: ppa{X＝xt|xt∈h(n)}；
Step 6-2: according to the real conditional probability distribution P { X ═ X | h (n), X ∈ h (n) } when the user arrives at different positions at the next moment obtained in the step 4, the probability of accurately predicting the user arrival position at the next moment is obtained as follows:
Figure BDA0002926894860000054
step 6-3: according to step 5, the position x with the highest probability at the next moment of the usermlProbability of (2)
Figure BDA0002926894860000055
Figure BDA0002926894860000056
Then P istrue{ X ═ X | h (n) } satisfies:
Figure BDA0002926894860000057
step 6-4: defining predictability of a user movement track as PA; when the length of the user historical movement track sequence is n, the user historical movement track subsequence set H (n) { { x { (x) }i,xi+1,…,xj}|1≤i<j is less than or equal to n, the probability of the occurrence of the corresponding user historical movement track subsequence H (i) epsilon H (n) is p (H (i)), and the predictability PA of the user movement track is obtained:
Figure BDA0002926894860000058
the specific embodiment is as follows:
1. the user movement data is obtained through the sensing device, for example, longitude and latitude change information of a user movement track is obtained through a GPS device.
2. And converting the movement data of the user into a position sequence on a time dimension according to different discretization methods to obtain a user movement track. Preprocessing human movement track data, sampling longitude and latitude information of a user at fixed time (1 hour), mapping the longitude and latitude information to a map grid of 500m multiplied by 500m, and obtaining a position change sequence X of the user in a time dimension, wherein the position change sequence X is { X }1,x2,…,xn}。
3. And calculating the information entropy of the user track, and regularly depicting the predictability of the user movement track according to the size of the information entropy.
The predictability of the user movement track can be measured qualitatively according to the information entropy E, when E is 0, the user track is considered to be completely regular, and the corresponding predictability is 1; when E is log2When l { X } | is taken, the track of the user at the next moment is considered to be a random value of the historical track, and is completely unpredictable, that is, the corresponding predictability is 0, wherein l { X } | is the size of the position point set in the historical track. When E is equal to other values, calculating predictability PA of the movement track of the user;
4. and calculating the conditional probability distribution of the user reaching different positions at the next moment according to the historical movement track of the user.
5. Determining the position with the highest probability of the next moment of the user as the position point x which is most possibly reached by the userml。
6. And calculating the probability of accurately predicting the position of the user at the next moment according to the conditional probability distribution to obtain the predictability of the user track and finally obtain the predictability PA of the sequence.

Claims (4)

1. A human movement predictability quantification method based on information entropy is characterized by comprising the following steps:
step 1: using a sensing device to obtain user movement data;
step 2: converting user movement data into a position sequence on a time dimension to obtain a user movement track;
the longitude and latitude information of a user is sampled at fixed time, the longitude and latitude information is mapped to a map grid, and a position change sequence X of the user in a time dimension is obtained as { X }1，x2，...，xnIn which xiThe position of the user at the ith moment is represented, so that the discretized movement track data of the user is obtained;
and step 3: calculating the information entropy E of the user track:
Figure FDA0002926894850000011
wherein, X is a position point of a user moving track, { X } is a position change sequence set of the user moving track, and p (X) is the probability of the position point X appearing in the position change sequence set of the user moving track;
measuring the predictability of the user movement track qualitatively according to the information entropy E:
when E is 0, the user track is completely regular, and the predictability of the corresponding user movement track is 1;
when E is log2When the position change sequence of the user movement track is | { X } |, the track of the user at the next moment is a random value of the historical track, and is completely unpredictable, the predictability of the corresponding user movement track is 0, wherein | { X } | is the size of a position point set in the position change sequence of the user movement track;
when the month is equal to other values, entering a step 4, and calculating the predictability PA of the movement track of the user;
and 4, step 4: calculating the real conditional probability distribution of the user reaching different positions at the next moment according to the historical movement track of the user: defining the historical movement track sequence of the user at the previous n time as h (n) ═ x1，x2，...，xnWherein x appears in h (n)nThe number of times of (x) is count (x)n) From xnThe number of times of → x is count (x)n→ X), then h (n) corresponds to the true conditional probability distribution P { X ═ X | h (n), X ∈ h (n) }:
Figure FDA0002926894850000012
and 5: finding the position with the maximum probability from the true conditional probability distribution in step 4 as the position point x which is most likely to be reached by the user at the next momentml，
Figure FDA0002926894850000013
Corresponding probability of being
Figure FDA0002926894850000014
Figure FDA0002926894850000015
Step 6: calculating the probability of accurately predicting the position of the user at the next moment according to the conditional probability distribution to obtain the predictability of the user track;
step 6-1: adopting a prediction algorithm, and predicting the probability distribution of the user reaching different positions at the next moment according to the historical movement track sequence h (n) of the user at the previous moment n: ppa{X＝xt|xt∈h(n)}；
Step 6-2: according to the real conditional probability distribution P { X ═ X | h (n), X ∈ h (n) } when the user arrives at different positions at the next moment obtained in the step 4, the probability of accurately predicting the user arrival position at the next moment is obtained as follows:
Figure FDA0002926894850000021
step 6-3: according to step 5, the position x with the highest probability at the next moment of the usermlProbability of (2)
Figure FDA0002926894850000022
Figure FDA0002926894850000023
Then P istrue{ X ═ X | h (n) } satisfies：
Figure FDA0002926894850000024
Step 6-4: defining predictability of a user movement track as PA; when the length of the user historical movement track sequence is n, the user historical movement track subsequence set H (n) { { x { (x) }i，xi+1，...，xjAnd j is more than or equal to i and less than or equal to n, the probability of the corresponding user historical movement track subsequence H (i) epsilon H (n) is p (H (i)), and the predictability PA of the user movement track is obtained:
Figure FDA0002926894850000025
2. a method for quantifying predictability of human movement based on information entropy as claimed in claim 1, wherein in step 2, longitude and latitude information of the user is sampled periodically with a timing time of 1 hour.
3. A method for quantifying predictability of human movement based on information entropy as claimed in claim 1, wherein the size of the map grid in step 2 is 500m x 500 m.
4. A method for quantifying human movement predictability based on information entropy according to claim 1, wherein the prediction algorithm in step 6-1 is markov model or long-short term memory network or recurrent neural network.
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