Method for determining a similarity between a pair of traveled paths

Abstract

The present invention relates to a method for determining a similarity using a Fréchet distance (DF) between two paths (TRAi, TRAj), in which a Fréchet distance model (MOD) is constructed by machine learning (APP) implementing a Siamese architecture of a one-dimensional convolutional neural network. Figure 1 to be published

Description

Title of the invention: Method for determining a similarity between a pair of journeys traveled Technical field

[0001] The present invention relates to the field of determining a distance between two paths, in this case the Fréchet distance.

[0002] The field of transport is an essential aspect of daily life on which the global economy depends heavily. However, it also plays a major role in the degradation of air quality and the increase in CO2 emissions, particularly in urban areas. According to the World Health Organization (WHO), transport is one of the main sources of air pollution, and it is directly linked to multiple respiratory and cardiovascular diseases. In addition, global transport is responsible for approximately 24% of direct CO2 emissions from fuel combustion, of which almost three-quarters correspond to cars, trucks, buses and motorcycles, further aggravating the phenomenon of global warming. Other types of harmful emissions include nitrogen oxides (NOx), ground-level ozone (O3) and particulate matter (PM), which generally exceed the recommended limits.The importance of transport's role in air quality is also reflected in the growing number of policy actions taken in Europe in recent years, making it a central issue. Strategies to address this issue include: vehicle efficiency and low-carbon fuel standards, the development and incentives of low-emission vehicles, fiscal policies and tax regimes.

[0003] New mobility data (Floating Car Data, data from GPS-type geolocation sensors on mobile phones, telephone boundary data, etc.) present a potential that is still underexploited in the modeling of mobility behaviors in a territory. In order to use these data correctly, it is necessary to process them (noise filtering, removal of outliers, etc.) and above all to contextualize them temporally (sequences of data samples belonging to the same trip) and geographically in relation to an underlying mobility network. Indeed, once the data sequences (or trajectories) belonging to the same trip have been reconstructed, it is necessary to calculate a "distance" between trajectories (to determine the similarity of two trajectories) or between a trajectory and a cartographic reference (to geographically contextualize the trajectory).This task is essential for many applications, for example: determining a mode of transport, “map matching” (which can be translated as cartos- . pondance) which consists of projecting trajectories onto a cartographic reference to determine the road axes taken by users, the control of autonomous vehicles, etc.

[0004] Measuring the similarity between a pair of paths is of utmost importance in a growing number of applications; the notions of distances between trajectories are notably at the heart of problems such as clustering, classification of trajectories. Typical choices of similarity measures, for which multiple variants exist, include methods based on Fréchet distances, dynamic time warp (DTW), Hausdorff and Euclidean distances, as well as the so-called longest common sequence (LCSS). However, the first two measures tend to be a more appropriate choice for the study of vehicle trajectories given their continuous and ordered nature.

[0005] In general, comparing the shapes of two geometric objects (in two-dimensional or three-dimensional space) involves calculating a distance metric to evaluate the similarity between the curves constituting these objects. For example, the so-called Fréchet distance offers an effective compromise between generality and specificity. Indeed, it is invariant with respect to the trajectory speed, but strongly depends on the continuous flow of the trajectory. Its main advantage over other distances in the literature (e.g. Hausdorff) lies in its ability to evaluate the similarity by considering both all the points constituting the curves as well as the morphology of the paths. The Fréchet distance between trajectory A and B can be informally described as the length of the shortest leash allowing a person on path A to walk a dog on path B (without reversing).

[0006] In its continuous version, the Fréchet distance can be given by the formula: F(J S 5)= Ùlf 3(^(0))

[0007] where A and B are curves on a metric space (distance d), and where a and [3 represent different parameterizations of curves.

[0008] In the discrete case, the two paths are represented by two sequences P and Q of n points in 2 dimensions and the movement on the sequences is done by jumping from one point to another.

[0009] However, this calculation is very time-consuming, requires computing resources (processors and memory), is very dependent on the size of the trajectories and is not suitable for processing large volumes of data (e.g. hundreds of thousands, or even millions of trajectories). Prior art

[0010] The algorithm handling the continuous case of the Fréchet distance has a computational time complexity of O(n2lQgn), while the discrete Fréchet distance algorithm allows to obtain a solution in quadratic time O(n2) using a dynamic programming approach. The discrete Fréchet distance is an approximate solution allowing to examine only the positions of the vertices instead of scanning all the points of the polygonal curves. Although it is faster than in the continuous case, it still remains very expensive in computational time and in computing requirements (processor and memory).

[0011] Even though there are several avenues for optimizing the calculation of the Fréchet distance, it is highly unlikely to find sub-quadratic algorithms for the Fréchet distance. Patent applications CN115296288 A, CN107798346 A, and CN101770516 A propose methods for compressing / segmenting / filtering curves to reduce the calculation time. Despite the advances made, all of the methods either propose a reduction in the resolution of the trajectories, or suggest approaches that are difficult to interpret and less generic.

[0012] The paper: "Janit Anjaria, Hong Wei, Hao Li, Shlok Mishra, and Hanan Samet. 2021. TrajDistLearn: leaming to compute distance between trajectories. In Proceedings of the 14th ACM SIGSPATIAL International Workshop on Computational Transportation Science (IWCTS '21). Association for Computing Machinery, New York, NY, USA, Article 4, 1-9" proposes a new Deep Learning approach to estimate similarity distance metrics such as the Fréchet distance. In this paper, trajectories are represented as raster images and map images. The approach is based on a two-dimensional (image) "Siamese" neural network architecture. Although this approach can significantly reduce computational time, the two-dimensional (image-based) approach is limited by image resolution and computing resources (memory and processor).Indeed, learning this approach can be costly in terms of computational time and use of computer resources. In addition, images have a size, and this size defines the resolution of the trajectories. To achieve better resolution, large images must be favored, but this is constrained by memory footprint and computational time. Using low-resolution images then risks introducing noise, making learning less effective. Summary of the invention

[0013] The aim of the invention is to determine the similarity between two paths, in a precise and rapid manner, without requiring significant computer resources or complex learning. For this purpose, the invention relates to a method for determining a similarity using a Fréchet distance between two paths, in which a Fréchet distance model is constructed by machine learning implementing a Siamese architecture of a one-dimensional convolutional neural network. The use of a single dimension in machine learning and in the use of the Fréchet distance model allows for rapid implementation, by limiting the computing resources used. The invention notably allows for a calculation acceleration factor of an order of magnitude of 100.

[0014] The invention further relates to a method for determining a mode of transport and a mapping method implementing such a method for determining a Fréchet distance.

[0015] The invention relates to a method for determining a similarity between at least one pair of traveled paths, the method being implemented from a plurality of learning paths defined by positioning data. For this method, the following steps are implemented: a. Analytically determining learning Fréchet distances for each pair of learning paths using said positioning data of said learning paths; b. The said positioning data of the said learning paths are discretized; c. A learning base is constructed which includes said discretized positioning data of said learning paths and said determined learning Fréchet distances; d. A Fréchet distance model is constructed using a learning method trained on said learning base, said Fréchet distance model associating a Fréchet distance with positioning data of a pair of paths, said learning method implementing a Siamese architecture of a one-dimensional convolutional neural network; e. Positioning data of at least two journeys traveled are acquired; f. The said positioning data acquired for the said at least two journeys traveled are discretized; and g. A similarity is determined between at least one pair of said traveled paths using said Fréchet distance model and said positioning data of said traveled paths, said similarity being said Fréchet distance determined by said Fréchet distance model.

[0016] According to one embodiment, said learning Fréchet distances are determined discretely.

[0017] According to one implementation, said convolutional neural network comprises at least one convolution layer, at least one activation function, at least one max pooling layer and at least one fully connected layer.

[0018] According to one aspect, said machine learning method optimizes a mean square error between said training Fréchet distance and a Fréchet distance determined by said Fréchet distance model.

[0019] Advantageously, said Siamese architecture of said learning method comprises a concatenation layer of the two outputs of said one-dimensional convolutional neural network and at least one linear filter.

[0020] Advantageously, said positioning data of said journeys traveled, or possibly of said learning journeys, are acquired from measurements using a geolocation device, or from measurements of connection data to a telephone network.

[0021] According to an embodiment option, the method further comprises a step of preprocessing said positioning data.

[0022] According to one embodiment, said positioning data of said traveled paths and said learning paths are discretized into a number of points between 5 and 100, and preferably between 10 and 50.

[0023] Furthermore, the invention relates to a method for determining a mode of transport of a first journey for which the mode of transport is not known, in which the following steps are implemented: a. At least one similarity is determined between said first journey and a second journey for which the mode of transport is known by means of the method of determining a similarity according to one of the preceding characteristics; and b. If said determined similarity is less than a predetermined threshold, said mode of transport of said second journey is attributed to said first journey.

[0024] Furthermore, the invention relates to a method of mapping onto a representation of a transport network a first path not positioned on the transport network, said representation of a transport network comprising a plurality of strands, characterized in that the following steps are implemented: a. A similarity is determined between said first path t at least one strand of said transport network by means of the method of determining the similarity according to one of the preceding characteristics; and b. If, for at least one strand of said transport network, the determined similarity is less than a predetermined threshold, it is determined that said first path has traveled through said strand.

[0025] Other characteristics and advantages of the method according to the invention will appear on reading the following description of non-limiting examples of embodiments, with reference to: referring to the figures attached and described below. List of figures

[0026] [Fig.l]

[0027] [Fig.l] illustrates the steps of the method for determining the Fréchet distance according to one embodiment of the invention.

[0028] [Fig.2]

[0029] [Fig.2] illustrates the steps of the method for determining a mode of transport according to an embodiment of the invention.

[0030] [Fig.3]

[0031] [Fig.3] illustrates the steps of the method of mapping a route on a transport network according to one embodiment of the invention.

[0032] [Fig.4]

[0033] [Fig.4] illustrates the construction of a convolutional neural network according to one embodiment of the invention.

[0034] [Fig.5]

[0035] [Fig.5] illustrates the architecture of a Siamese network according to one embodiment of the invention.

[0036] [Fig.6]

[0037] [Fig.6] illustrates, for an example, a comparison of the calculation time of the Fréchet distance by a method of the prior art, and by the method according to an embodiment of the invention.

[0038] [Fig.7]

[0039] [Fig.7] illustrates four examples of journeys between a departure zone and an arrival zone.

[0040] [Fig. 8]

[0041] [Fig.8] illustrates, for another example, a comparison of the exact Fréchet distance and the Fréchet distance determined by the method according to an embodiment of the invention. Description of the embodiments

[0042] The present invention relates to a method for determining a similarity between two journeys traveled, in particular with a view to determining a mode of transport, carrying out a mapping method, controlling an autonomous vehicle, or an autonomous robot, a carpooling method, a vehicle sharing method, etc. In the present application, a journey traveled is a movement traveled by a vehicle, between an origin (departure) and a destination (arrival), the journey traveled being defined by its trajectory between the origin and the destination. For certain embodiments (in particular for the application of the Fréchet distance to a car- tospondence), the term "path traveled" can refer to one or more strands of a representation of a transport network, for example a road graph.

[0043] For the method according to the invention, the similarity is determined by the Fréchet distance. Thus, the invention is a method for determining a similarity between two paths traveled by means of a Fréchet distance.

[0044] The method according to the invention can be implemented for any type of vehicle: bicycle, motor vehicle, motorized two-wheeler, boat, hovercraft, scooter, etc. as well as pedestrian travel. However, the method according to the invention is particularly suitable for motorized vehicles, such as motor vehicles, heavy goods vehicles, buses, motorized two-wheelers, etc.

[0045] The method is implemented from a plurality of learning paths. These are paths that make it possible to construct the Fréchet distance model. This construction will be detailed in the remainder of the description. The learning paths correspond to the trajectory of a vehicle and are defined by positioning points (i.e. the location in space of points belonging to the trajectory / path). These positioning points can be acquired by means of a geolocation system, for example GPS for "Global Positioning System" which can be translated as global positioning system, or the Galileo system, or any similar system. The geolocation system can in particular be included in a smartphone or a connected object. Alternatively, the positioning points can be acquired from connection data to a telephone network.This may include the location of the antennas to which a mobile phone connected during the journey. For this type of data, the recorded geographic coordinates do not correspond to the actual positions of a user but rather to those of the antennas to which their mobile phone was connected during a telephone event (call, SMS, internet connection). These journeys may also contain artifacts such as echo phenomena between antennas when the phone connects to several antennas at the same time. As a non-limiting example, the number of learning journeys may be greater than 5000, or even greater than 10000 depending on the accuracy of the operating points of the learning journeys. This range allows a good compromise between the accuracy of the Fréchet distance model and the calculation time.

[0046] The method implements the following steps: 1. Determination of learning Fréchet distances 2. Discretization of the positioning data of the learning paths 3. Building a learning base 4. Construction of the Fréchet distance model 5. Acquisition of journeys traveled 6. Discretization of the positioning data of the journey paths 7. Determination of similarity (Fréchet distance)

[0047] These steps will be detailed in the remainder of the description. Learning steps 1 to 4 can be implemented only once, beforehand. Steps 5 to 7 are carried out online, and can be repeated for each new route traveled. These steps can be implemented by computer means, in particular a computer or a server, comprising at least one processor and a computer memory.

[0048] [Fig.l] illustrates, schematically and in a non-limiting manner, the steps of the method according to one embodiment of the invention. For the TRN learning phase, TAP learning paths are used, for each pair of learning paths, FAP learning Fréchet distances are determined analytically. A learning base B AP is then constructed, from which a learning method APP is implemented to construct a Fréchet distance model. Then, in line ONL, at least two TRA paths are acquired; and TRAj and the Fréchet distance model is applied to these paths to determine the Fréchet distance DF.

[0049] 1. Determination of learning Fréchet distances

[0050] In this step, learning Fréchet distances are analytically determined for each pair of learning paths using the positioning data. In other words, the learning Fréchet distances are determined by applying the mathematical equation for the Fréchet distance described above.

[0051] According to an implementation of the invention, the method may comprise a step of preprocessing the positioning data, for example by filtering, removing outliers, etc. Thus, it is possible to limit the noise and improve the accuracy of the learning. This step is particularly useful for the embodiment in which the positioning data is connection data to a telephone network.

[0052] According to one embodiment of the invention, the learning Fréchet distances can be determined discretely. By way of example, the steps described below can be applied:

[0053] We consider two paths P and Q represented by an ordered set of points n and m in a metric space (V, d) equipped with a metric d. We define the sequences corresponding to the points composing P and Q by ( pj _ pj and AQ) =(«r....... O

[0054] In the space a(P) X cr( 0), we define the coupling sequence C(P, Q) of the pairs of unique points of P and Q:

[0055] c(P, g) = (pa, q.), (paj qb^, ........, (pa[, qb^

[0056] The number £ of pairs of unique points between P and Q is obtained by respecting the conditions (example in [Fig.l]): 1. The first and last positions are related (aj = bj = 1) and (bL = m). 2. The only movements allowed are forward (no going back) i.e., at least one point on a path must be advanced to its successive point (for any pair of points); (^+1 ~ a< or a>+i ~ ai+t) and ( bi+r bi or bf+i bi+i).

[0057] For a given coupling sequence C, the largest distance among the pairs of points / \ defines the coupling distance:

[0058] || C|| ^^(p^

[0059] In the space of all possible coupling sequences, Q,pq, the discrete Fréchet distance between P and Q is the minimum distance among all distances in &P, Q: C)= min ||C || CGQ

[0061] According to an implementation of the invention, the learning Fréchet distance can be determined by dynamic programming. 2. Discretization of learning paths

[0062] In this step, the positioning data of the learning paths are discretized in one dimension. The use of a discretization, therefore of a single dimension, for the learning paths allows the use of a one-dimensional learning method which makes it possible to construct and use the Fréchet distance model more quickly, while limiting the necessary computing resources, such as memory and processors. By this discretization, each learning path is made up of a number of points of dimensions two or three. Conversely, in the method described in the document “Janit Anjaria, Hong Wei, Hao Li, Shlok Mishra, and Hanan Samet. 2021. TrajDistLeam: leaming to compute distance between trajectories. In Proceedings of the 14th ACM SIGSPATIAL International Workshop on Computational Transportation Science (IWCTS '21).Association for Computing Machinery, New York, NY, USA, Article 4, 1-9”, paths are represented by two-dimensional trajectories images.

[0063] According to an implementation of the invention, the learning paths can be discretized into a number of points between 5 and 100, and preferably initially between 10 and 50. Thus, we obtain a good compromise between the precision of the Fréchet distance model, calculation time and necessary computer resources.

[0064] As an example, each discretized learning path can take the following form:

[0065] Trad = ( Xj Xy ... XN ) with Trad the discretized path, N the number of points of the discretization, Xi the coordinates of the ith point of the discretization. 3. Building the learning base

[0066] During this step, a learning base is constructed which includes the positioning data of the learning paths discretized in step 2, and the learning Fréchet distances determined in step 1. In other words, the learning base includes for each pair of learning paths, discretized positioning data and the learning Fréchet distance obtained analytically. 4. Construction of the Fréchet distance model

[0067] In this step, a Fréchet distance model is constructed using a machine learning method, trained on the learning base constructed in step 3. The Fréchet distance model associates a Fréchet distance with discretized positioning data of a pair of paths. In other words, the Fréchet distance model has discretized positioning data of a pair of paths as input and has a Fréchet distance as output.

[0068] According to the invention, the machine learning method implements a Siamese architecture of a one-dimensional convolutional neural network. The Siamese architecture is also called a Siamese neural network, or twin neural network. This architecture is an artificial neural network that uses the same weights while working in tandem on two different inputs to calculate comparable outputs. In other words, the Siamese architecture comprises the application of the same one-dimensional convolutional neural network to each path, then a concatenation of the outputs of this convolutional neural network makes it possible to determine the Fréchet distance.

[0069] According to one aspect of the invention, the convolutional neural network may comprise at least one convolution layer which allows particular characteristics to be extracted, at least one activation layer, at least one max-pooling layer (layer allowing sub-sampling) to reduce the spatial dimension, and at least one fully connected layer forming a linear filter. Preferably, the convolutional neural network may comprise a plurality of convolution layers. In this case, a sequence formed by the convolution layer, the activation layer and the max-pooling layer may be repeated for each convolution layer.

[0070] [Fig.4] illustrates, schematically and in a non-limiting manner, a design of a one-dimensional convolutional neural network according to one embodiment. The one-dimensional convolutional neural network CNN 1D has as input the discretized data of a TRA path and as output the particular characteristics of this path. The one-dimensional convolutional neural network CNN 1D comprises at least one convolution sequence SEQ and one fully connected layer EC. The convolution sequence SEQ comprises a convolution layer, an activation layer and a max-pooling layer.

[0071] According to variants not shown, the one-dimensional convolutional neural network may comprise a plurality of convolution sequences and / or a plurality of fully connected layers.

[0072] According to an implementation of the invention, the Siamese architecture may comprise for each path a one-dimensional convolutional neural network, then a concatenation layer, and at least one fully connected layer to form a linear filter. Furthermore, when the Siamese architecture comprises several fully connected layers, this Siamese architecture may comprise an activation layer between two fully connected layers. A linear layer increases the representation capacity of the neural network (by finding complex combinations of features extracted by the convolution layers). Adding a non-linear activation function to the output of the linear filters makes it possible to introduce non-linearity into this representation.Adding two fully connected layers followed by an activation layer allows for linear combinations and nonlinear combinations that are twice as complex.

[0073] The last fully connected layer of the Siamese architecture allows to obtain a single scalar output, in this case the estimated Fréchet distance.

[0074] [Fig.5] illustrates, schematically and in a non-limiting manner, a Siamese architecture according to an implementation of the invention. A one-dimensional convolutional neural network CNN 1D is applied to a first path TRA;. The same one-dimensional convolutional neural network CNN 1D is applied to a second path TRAj. Then, the outputs of the 1D CNN convolutional neural networks are concatenated CCT, then at least one fully connected layer EC is implemented to determine the Fréchet distance DF.

[0075] According to variants not shown, the Siamese architecture may comprise at least two fully connected layers, and an activation layer between each pair of fully connected layers.

[0076] According to one embodiment of the invention, the machine learning method can optimize a mean square error between the training Fréchet distance and the Fréchet distance from the Fréchet distance model. constructed. This mean squared error is sensitive to outliers. Alternatively, the mean absolute error can be used for the machine learning method.

[0077] According to one embodiment, the learning paths of the learning base can be segmented by batch (also called group or batch). This segmentation by batch makes it possible to browse the base more quickly while each time identifying very different learning paths. In addition, this segmentation makes it possible to avoid problems linked to a lack of computer storage space.

[0078] According to one embodiment option, several epochs (from the English "epoch" which designates the complete passage of the data set of the learning base) may be provided for the training method. The number of epochs reflects the number of passages of the algorithm during the training phase. Preferably, the epoch may be composed of an aggregation of several batches of data and iterations. According to a non-limiting example, the optimization algorithm implemented may be the stochastic gradient descent (SGD) algorithm, also called gradual descent, which is an iterative algorithm based on the calculation of an error gradient. Other similar algorithms may be implemented. 5. Acquisition of journeys traveled

[0079] During this step, positioning data of at least two journeys traveled by a vehicle are acquired. In other words, positioning data of at least two journeys traveled are obtained, for which it is desired to determine the Fréchet distance separating them. The journeys traveled are defined by the trajectory of a vehicle, characterized by positioning points (i.e. the location in space). These positioning points can be acquired by means of a geolocation system, for example GPS for "Global Positioning System" which can be translated as global positioning system, or the Galileo system, or any similar system. The geolocation system can be included in a smartphone, in a vehicle, or a connected object. Alternatively, the positioning points can be acquired from connection data to a telephone network.This may include the location of the antennas to which a mobile phone connected during the journey. For this type of data, the recorded geographic coordinates do not correspond to the actual positions of a user but rather to those of the antennas to which their mobile phone was connected during a telephone event (call, SMS, internet connection). These journeys may also contain artifacts such as echo phenomena between antennas when the phone connects to several antennas at the same time. For these examples, the acquisition of the journeys traveled corresponds to a measurement step of the . location of points belonging to the vehicle's movement. 6. Discretization of the journeys traveled

[0080] In this step, the positioning data of the paths traveled are discretized into one dimension. Using a discretization, therefore a single dimension, for the paths traveled makes it possible to use the Fréchet distance model more quickly, while limiting the necessary computing resources, such as memory and processors. By this discretization, each path traveled is made up of a number of points of dimensions two or three. Conversely, in the method described in the document “Janit Anjaria, Hong Wei, Hao Li, Shlok Mishra, and Hanan Samet. 2021. TrajDistLearn: learning to compute distance between trajectories. In Pro-ceedings of the 14th ACM SIGSPATIAL International Workshop on Computational Transportation Science (IWCTS '21). Association for Computing Machinery, New York, NY, USA, Article 4, 1-9”, paths are represented by two-dimensional trajectory images.

[0081] According to an implementation of the invention, the paths traveled can be discretized into a number of points between 5 and 100, and preferably between 10 and 50. Thus, a good compromise is obtained between precision of the Fréchet distance model, calculation time and necessary computer resources.

[0082] As an example, each discretized path traveled can take the following form:

[0083] Trad= (X[ X^, ... XN^ XN ) with Trad the discretized path, N the number of points of the discretization, X, the coordinates of the ith point of the discretization.

[0084] 7. Determination of similarity (Fréchet distance)

[0085] In this step, the Fréchet distance and therefore the similarity between the two paths traveled discretized in step 6 are determined using the Fréchet distance model constructed in step 4. In other words, the Fréchet distance model is applied to the discretized positioning data of the paths traveled, and the Fréchet distance between the two paths traveled is obtained. Thanks to the model, the Fréchet distance and therefore the similarity can be obtained quickly without requiring significant computing resources (memory, processor).

[0086] For the embodiment for which more than two paths traveled are acquired in step 5, during this step, a Fréchet distance can be determined between each pair of acquired and discretized paths. The method according to the invention is particularly interesting for this embodiment, due to the reduced calculation time and the limited requirements in computing resources (memory and processor).

[0087] Furthermore, the invention relates to a method for determining a mode of transport of a first journey for which the mode of transport is not known. For this method, the following steps can be implemented: a. At least one similarity (i.e. a Fréchet distance) is determined between the first journey and a second journey for which the mode of transport is known by means of the method for determining a similarity (i.e. a Fréchet distance) according to any one of the variants described previously; and b. If the determined similarity is lower than a predetermined threshold, the mode of transport of the second journey is attributed to the first journey (in other words, the mode of transport of the first journey to be characterized is that of the second journey).

[0088] However, if the determined Fréchet distance is greater than the predetermined threshold, no mode of transport is assigned to the first journey. In this case, steps a and b can be repeated from another second journey.

[0089] Alternatively, step a can be performed for several second journeys: a Fréchet distance is calculated between the first journey and each second journey. For this embodiment, during step b, the mode of transport of the second journey which minimizes the similarity (the Fréchet distance) to the first journey can be assigned (preferably if this Fréchet distance is less than the predetermined threshold).

[0090] Thus, the method according to the invention makes it possible to quickly determine, without significant IT requirements, a mode of transport for a first journey to be characterized.

[0091] [Fig.2] illustrates, schematically and in a non-limiting manner, the steps of the method for determining a mode of transport according to one embodiment. The steps identical to the method of [Fig.l] are not detailed again. In this case, the first route is the route TRAi and the second route is the route TRAj. The Fréchet distance model MOD determines the Fréchet distance DF between the route to be characterized and the characterized route, if this Fréchet distance is less than a predetermined threshold, then a mode of transport MDT is determined for the first route TRAi. Optionally, if the Fréchet distance is greater than the predetermined threshold, the steps can be repeated with another second route TRAj.

[0092] The invention also relates to a method for map matching (from the English "map matching" or correspondence with a map) of a first journey with a representation of a transport network, in particular a road network. This method aims to project at least one journey onto a cartographic reference to determine the transport routes taken by the vehicle, for example on a road graph, a railway graph, etc. The transport network representation comprises a plurality of strands, which is an elementary subdivision of the transport network between two consecutive nodes of the transport network. For example, a strand of the road network can be a road between two consecutive intersections, between two consecutive signs, between an intersection and a sign, or a part of a motorway between two consecutive exits, etc. Thus, a fine division of the road network is available, and a model that is adapted to the road network without microscopic data. The road network can be represented by a graph, called a road graph. The road graph is composed of a set of edges (strands also called arcs) and nodes, the nodes being able to represent the intersections, and the edges the portions of roads between the intersections. The road graph can be obtained from an online service ("webservice") mapping, for example Here ™ (Here Apps LLC, Netherlands) which provides the graph edges as pure geometric objects. Preferably, the road graph is consistent with the road network (all physical connections between two roads, and only these, are represented by the graph nodes), as time-invariant as possible. In addition, the road graph can be simplified, by not taking into account road portions such as dead ends, paths in parks or cycle paths, depending on the type of the vehicle considered (e.g. for the motor vehicle embodiment, cycle paths may not be taken into account).

[0093] For this method, the following steps can be implemented: a. A similarity (i.e. Fréchet distance) is determined between the first to be positioned on a representation of a transport network and at least one strand of the transport network, by means of the method for determining the similarity (Fréchet distance) according to any one of the variants described previously, for which one of the two paths traveled is considered as a strand of the representation of the transport network; and b. If, for at least one strand of the transport network, the determined Fréchet distance is less than a predetermined threshold, it is determined that said first path has traveled said strand.

[0094] However, if the determined Fréchet distance is greater than the predetermined threshold, it is determined that the strand considered is not crossed by the first path.

[0095] By repeating these steps for several strands of the transport network, it is possible to determine several or even all of the strands crossed by the first path.

[0096] The method for determining similarity according to the invention can further be used in a method for controlling an autonomous vehicle, or an autonomous robot, a carpooling method, a vehicle sharing method. Furthermore, the Fréchet distance obtained by the method according to the invention can be used for a method for recognizing shapes and objects, a method for monitoring / controlling a biomechanical system, a screening method in biology for recognizing similarity between molecular structures, a signal control method, for example for matching musical signals, etc. Examples

[0097] The characteristics and advantages of the method according to the invention will appear more clearly on reading the application example below.

[0098] For the first example, in order to evaluate the gain in calculation time of the method according to the invention, distance matrices of different dimensions are constructed from the discrete Fréchet distance.

[0099] The dimension of the matrix "2 is fixed by the number of paths n. The distance matrices provide information on the similarity between the paths where each value Tj) corresponds to the discrete Fréchet distance between trajectories Ti and Th. For this example, the computation time required to determine the Fréchet distance is determined as a function of the number of paths. [Fig.6] illustrates a curve of the computation time t in s as a function of the number of paths Nb. Curve AA indicates the computation time used for the method for determining the Fréchet distance according to the prior art by dynamic programming, and curve INV indicates the computation time used for the method according to the invention. [Fig.6] also illustrates the acceleration factor Fa as a function of the number of paths Nb. The computation time of the method according to the invention is very insensitive to the size of the distance matrix, whereas that obtained by the classic AA method increases quadratically in proportion to the number of paths. For example, for 300 paths, we find: A ^Fréchet, exact — 300) — 1374 S and A fpréchet, approximate 300) 1 3 S. Let an acceleration factor > 100.

[0100] For the second example, we consider four paths between a departure zone and an arrival zone. [Fig.7] illustrates, schematically, the departure zone D, the arrival zone and the four paths T1 to T4. We determine for each pair of paths the Fréchet distance by means of the classic method according to the prior art (dynamic programming). Table 1 presents these Fréchet distances:

[0101] [Tables 1] D Fréchet Tl T2 T3 T4 Tl 0 - - - T2 2.21 0 - - T3 1.95 0.95 0 - T4 2.21 0.99 1.34 0

[0102] Then, the Fréchet distance is determined using the method according to one embodiment of the invention. Table 2 shows these Fréchet distances:

[0103] [Tables] D Fréchet Tl T2 T3 T4 Tl 0 - - - T2 2.34 0 - - T3 2.12 0.82 0 - T4 2.15 0.95 1.01 0

[0104] It is noted that the method according to the invention makes it possible to preserve the minimum and maximum values. In addition, the errors are small: the average absolute error is 0.11 and the average square error is 0.02. As a result, the method according to the invention makes it possible to precisely determine the Fréchet distance.

[0105] For a third example, we consider 160 journeys between the same departure zone and the same arrival zone. We can construct, for this example, the curve of [Fig.8] of the Fréchet distance obtained by the method according to the invention DHNV as a function of the DFE obtained by the method of the prior art. We note the good correlation of the results. In this situation also, the errors are small, the average absolute error is 0.20 and the average square error is 0.06. Thus, the method according to the invention is robust.

Claims

Claims

1. Method for determining a similarity between at least one pair of paths (TRA;, TRAj) traveled, the method being implemented from a plurality of learning paths (TAP) defined by positioning data, characterized in that the following steps are implemented: a. Analytically, Fréchet training distances (FAP) are determined for each pair of training paths (TAP) using said positioning data of said training paths (TAP); b. The said positioning data of the said learning paths (TAP) are discretized; c. A learning base (BAP) is constructed which includes said discretized positioning data of said learning paths (TAP) and said determined learning Fréchet distances (FAP); d. A Fréchet distance model (MOD) is constructed using a learning method (APP) trained on said learning base (BAP), said Fréchet distance model (MOD) associating a Fréchet distance with positioning data of a pair of paths (TRA;, TRAj ), said learning method (APP) implementing a Siamese architecture of a one-dimensional convolutional neural network (1 D CNN); e. Positioning data of at least two traveled paths (TRA;, TRAj) are acquired; f. The said positioning data acquired for the said at least two journeys traveled (TRA;, TRAj) are discretized; and g. A similarity is determined between at least one pair of said traveled paths (TRA;, TRAj) by means of said Fréchet distance model (MOD) and said positioning data of said traveled paths (TRA;, TRAj), said similarity being said Fréchet distance (DF) determined by said Fréchet distance model.

2. A method of determining a similarity according to claim 1, in which determines the said learning Fréchet distances (FAP) in a discrete manner.

3. Method for determining a similarity according to one of the preceding claims, wherein said convolutional neural network (CNN 1D) comprises at least one convolution layer (CV), at least one activation function (CA), at least one max pooling layer (MP) and at least one fully connected layer (EC).

4. A method for determining a similarity according to one of the preceding claims, wherein said machine learning method optimizes a mean square error between said training Fréchet distance (FAP) and a Fréchet distance determined by said Fréchet distance model.

5. Method for determining a similarity according to one of the preceding claims, in which said Siamese architecture of said learning method comprises a concatenation layer (CCT) of the two outputs of said one-dimensional convolutional neural network (1D CNN) and at least one linear filter (EC).

6. Method for determining a similarity according to one of the preceding claims, in which said positioning data of said journeys traveled, or possibly of said learning journeys, are acquired from measurements by means of a geolocation device, or from measurements of connection data to a telephone network.

7. Method for determining a similarity according to one of the preceding claims, wherein the method further comprises a step of preprocessing said positioning data.

8. Method for determining a similarity according to one of the preceding claims, in which said positioning data of said traveled paths (TRA;, TRAj) and of said learning paths (TAP) are discretized into a number of points between 5 and 100, and preferably between 10 and 50.

9. Method for determining a mode of transport of a first journey for which the mode of transport is not known, characterized in that the following steps are implemented: a. At least one similarity is determined between said first journey and a second journey for which the mode of transport is known by means of the method for determining a si- militaryity according to one of the preceding claims; and b. If said determined similarity is less than a predetermined threshold, said mode of transport (MDT) of said second journey is attributed to said first journey.

10. Method of mapping onto a representation of a transport network a first path not positioned on the transport network, said representation of a transport network comprising a plurality of strands, characterized in that the following steps are implemented: a. A similarity is determined between said first path t and at least one strand of said transport network by means of the similarity determination method according to one of claims 1 to 8; b. If, for at least one strand of said transport network, the determined similarity is less than a predetermined threshold, it is determined that said first path has traveled through said strand (COR).

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