DE102019006005A1 - Graph-based method for geolocation of the root causes of events recorded by a vehicle - Google Patents

Abstract

ermittelt. Für jede maximale Clique $\left({\widehat{C}}_l^{\left(k\right)}\right)$

wird ein maximaler Hotspot umfassend alle den Knoten (ν_i) der jeweiligen maximalen Clique $\left({\widehat{C}}_l^{\left(k\right)}\right)$

zugeordneten Ereignisse (e_i) gebildet, diesem eine Geoposition zugeordnet, die aus der Gesamtheit der den jeweiligen Ereignissen (e₁, e₂) des maximalen Hotspots zugeordneten Geopositionen ermittelt wird.

In a method for assigning a common geoposition to a plurality of events (e _i ) caused by a common root cause and detected by at least one vehicle, a geoposition of the vehicle is recorded for each individual event (e _i ). A distance measure is determined for pairs of different events (e _i , e _j , i ein j), which takes into account at least the geopositions of the events (e _i , e _j , i i j). At least one undirected connected graph (G) is formed, an event (e _i ) being assigned to a node (ν _i ) of the graph (G) if the distance between the event (e _i ) and at least one further event ( e _j , j ≠ i) does not exceed a maximum distance (d _max ) and each pair of different nodes (ν _i , ν _j , i ≠ j) is then assigned an edge (ε _{i, j} ) if the distance measure between the events (e _i , e _j , i ≠ j) associated with the nodes (ν _i , ν _j , i ≠ j) do not exceed the maximum distance (d _max ). For the at least one graph (G) is the set of all maximum cliques $\left({\widehat{\mathrm{C.}}}_l^{\left(k\right)}\right)$

determined. For every maximum clique $\left({\widehat{\mathrm{C.}}}_l^{\left(k\right)}\right)$

a maximum hotspot will encompass all the nodes (ν _i ) of the respective maximum clique $\left({\widehat{\mathrm{C.}}}_l^{\left(k\right)}\right)$

assigned events (e _i ), this is assigned a geoposition which is determined from the totality of the geopositions assigned to the respective events (e ₁ , e ₂ ) of the maximum hotspot.

Description

The invention relates to a method for assigning a common geoposition to a plurality of events caused by a common root cause and detected by at least one vehicle according to the preamble of claim 1.

With the sensors of vehicles, events and objects in the vehicle environment are increasingly being recorded, to which geolocation can be assigned. These are, for example, potholes, objects that can be detected by camera such as signs or traffic lights, objects that can be detected by radar such as bridges or objects that can be detected by means of Light Detection and Ranging (LIDAR), as well as landmarks that support vehicle localization. Such objects can also be detectable with a plurality of detection methods. System interventions of the assistance systems or Car2X events, that is to say events that take place in the vehicle, can also be recorded and can be assigned to a geoposition of the vehicle at the time the event occurs.

All of these objects or events have in common that their position in the world is recorded and stored at least once, but potentially several times, as the most accurate geolocation of at least one vehicle. However, every position measurement is always associated with an inaccuracy, so that in the case of multiple passes, a specific concrete event, for example driving through a pothole, a traffic light or the intervention of a driver assistance system, is always localized at more or less different geopositions. This scattering is caused, for example, by measurement errors of the Global Positioning System (GPS) and / or by indefinite latencies in the signal processing in the vehicle and prevents the pothole identified in several passes or the traffic light identified in several passes by simply comparing the respectively assigned geoposition as the same pothole or the same traffic light can be recognized. Likewise, the repeated triggering of an assistance system at a certain location is not easily recognized as a trigger due to the same circumstances.

Due to the measurement error, locally limited clusters of, for example, traffic light positions are generated. In the following it has to be decided whether the traffic light is the same or several traffic lights. The subsets to be investigated from the total amount of recorded events, which can potentially be assigned to a common root cause (pothole, traffic light), grow exponentially with the total number of measured events and thus elude a simple sequential analysis of such subsets.

Clustering methods are known from the prior art, which summarize closely located geopositions in clusters. Such a known method is published as Density-Based Spatial Clustering of Applications with Noise (DBSCAN) method, for example in Martin Ester, Hans-Peter Kriegel, Jörg Sander, Xiaowei Xu: A density-based algorithm for discovering clusters in large spatial databases with noise. In: Evangelos Simoudis, Jiawei Han, Usama M. Fayyad (ed.): Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD-96). AAAI Press, 1996, ISBN 1-57735-004-9, pages 226-231.

The document DE 10 2015 002 158 A1 describes a method for determining traffic density information in a motor vehicle that is to be taken into account in a function of a vehicle system and that describes the traffic density in the surroundings of the motor vehicle, wherein radar data describing objects in the surroundings of the motor vehicle are recorded by means of at least one radar sensor that is based on the surroundings of the motor vehicle and is based on semiconductor technology , an environment map containing the detected objects classified into static and dynamic objects is determined by evaluating the radar data, and the traffic density information is determined from at least some of the positions of dynamic objects contained in the environment map.

A common geoposition can be assigned to a plurality of events that are recorded by at least one vehicle, with a single geoposition being recorded for each individual event and the events being caused by a common root cause. For example, the recorded events can be numbered in the order in which they were recorded.

der Kardinalität k bezeichnet. Potenziell bildet ein solcher Hotspot alle auf eine gemeinsame Grundursache, der eine einzige, gemeinsame Geoposition zuzuordnen ist, zurückführbaren Ereignisse ab.Each lexicographically sorted set of k different events is called a hotspot $H_i^{\left(k\right)}$

the cardinality k. Such a hotspot potentially depicts all events attributable to a common root cause to which a single, common geoposition can be assigned.

From the power set of the set of all recorded events, all subsets of cardinality one can be formed and lexicographically sorted assigned to a homogeneous hotspot list, which only includes hotspots of the same cardinality.

der homogenen Hotspotliste H^(k) dann ein neuer Hotspot $h_j^{\left(k+1\right)}$

umfassend die lexikografisch sortierte Vereinigungsmenge der Ereignisse beider Hotspots $h_i^{\left(k\right)},h_{i+1}^{\left(k\right)}$

erzeugt und der neuen homogenen Hotspotliste H^(k+1) hinzugefügt wird, wenn das Maximum der mindestens anhand der Geopositionen der Ereignisse paarweise ermittelten Entfernungen zwischen den Ereignissen eine vorbestimmte maximale Entfernung d_max nicht überschreitet. Mit anderen Worten: in einen bereits gebildeten Hotspot, dem eine Menge von Ereignissen zugeordnet ist, wird unter Bildung eines neuen Hotspots dann ein neues Ereignis aufgenommen, wenn dadurch die größtmögliche Entfernung zwischen zwei Ereignissen die vorbestimmte maximale Entfernung nicht überschreitet. Damit ist sichergestellt, dass die Ausdehnung eines Hotspots die vorgegebene maximale Entfernung d_max nicht überschreitet. Starting with the cardinality one (k = 1), a homogeneous hotspot list H ^{(k) of} a cardinality k can be continuously created using a subsequent incremental procedure to form a new homogeneous hotspot list H ^{(k + 1) of} the next higher cardinality k + 1 in that from two lexicographically sorted hotspots $H_i^{\left(k\right)},H_{i+1}^{\left(k\right)}$

the homogeneous hotspot list H ^(k) then a new hotspot $H_j^{\left(k+1\right)}$

includes the lexicographically sorted union of the events of both hotspots $H_i^{\left(k\right)},H_{i+1}^{\left(k\right)}$

is generated and added to the new homogeneous hotspot list H ^{(k + 1)} when the maximum of the distances between the events determined in pairs at least on the basis of the geopositions of the events is a predetermined maximum distance d _max does not exceed. In other words, a new event is added to a hotspot which has already been formed and to which a number of events are assigned, with the formation of a new hotspot if the greatest possible distance between two events does not thereby exceed the predetermined maximum distance. This ensures that the expansion of a hotspot is the specified maximum distance d _max does not exceed.

This step of forming new hotspots with a cardinality incremented by one is carried out again when the newly formed homogeneous hotspot list H ^{(k + 1)} comprises at least two hotspots of cardinality k + 1. The formation of new hotspots is completed in a finite number of steps, since the greatest possible cardinality of a hotspot is determined by the total number of events and is therefore finite.

In a subsequent filter step, those whose associated set of events is a subset of at least one other set of events which is assigned to another hotspot are eliminated from the set of all hotspots formed in this way. As a result of this filtering step, there remain maximum hotspots whose event set is not a subset of any other hotspots.

For each of the maximum hotspots formed in this way, a common geoposition is determined from the totality of the geopositions assigned to the respective events. This common geoposition is assigned to a basic cause common to all events of a maximum hotspot.

If a common geoposition is assigned to a plurality of events caused by a common root cause and detected by at least one vehicle, a single geoposition can be recorded for each individual event. An index is then assigned to each recorded event in such a way that events are brought into a total order by sorting the indices.

An event pair list of event pairs is created. Each pair of events includes a first event e ₁ with a first index and a different second event e ₂ with a second index. The event pair list is formed in such a way that it contains all event pairs in which the first index is greater than the second index and in which a distance d (e ₁ , e ₂ ) between the first and the second determined at least on the basis of the geopositions of the two events Event a predetermined maximum distance d _max does not exceed.

Furthermore, in this embodiment, at least one search circle area is determined for each event pair of this event pair list by the intersection of a first circle around the geoposition of the first event e ₁ with the diameter equal to the predetermined maximum distance d _max with a second circle of the same diameter around the geoposition of the second event e ₂ is determined and around the intersection thus found a circle with the diameter equal to the predetermined maximum distance d _max is placed.

Is the distance between the first event e ₁ and the second event e ₂ less than the predetermined maximum distance d _max , two search circle areas for the pair of events are determined in this way. Is the distance between the first event e ₁ and the second event e ₂ equal to the predetermined maximum distance d _max , a single search circle area for the pair of events is determined in this way.

A hotspot list comprising at least one hotspot is created, a hotspot in each case comprising all events which occur in or on the edge of a search circle area assigned to an event pair of the event pair list C ₁ , C ₂ lie. Depending on the geometric distribution of the events, hotspots can also be assigned different cardinalities to this hotspot list. Therefore, this hotspot list is not necessarily homogeneous.

In a filter step, those hotspots are eliminated from the hotspot list that are assigned a set of events that are a real subset of at least one other set of events that are assigned to another hotspot in the hotspot list, so that only maximum hotspots remain on the filtered hotspot list .

Thus, in this embodiment of the method, a common geoposition is determined for each of the maximum hotspots found in this way from the total geopositions of the events associated with this hotspot.

The invention is based on the object of specifying an improved method for assigning a common geoposition to a plurality of events caused by a common root cause and detected by at least one vehicle.

The object is achieved according to the invention by the features of independent claim 1.

In a method for assigning a common geoposition to a plurality of events of an event set caused by a common root cause and recorded by at least one vehicle, at least one individual geoposition of the vehicle is recorded as a characteristic for each individual event. This geoposition corresponds to the position of the vehicle at the time when the event occurred or was recorded. This position can be determined, for example, using a satellite-based navigation system.

In the method, a distance measure is determined for each pair of different events, which takes into account at least the geopositions of the events. For example, the Euclidean distance between geopositions of different events can be determined.

A node is assigned to an event if and only if the distance between this event and at least one other event does not exceed a maximum distance.

An edge is assigned to a pair of different nodes if and only if the distance between the events assigned to these different nodes does not exceed the maximum distance.

At least one undirected coherent graph is formed, which comprises all nodes connected to one another via at least one edge. It is possible that a plurality of disjoint subsets of nodes are formed from the event set, which are connected only within a subset via at least one edge, so that each of these subsets is assigned a coherent graph.

The amount of all maximum cliques is determined for each graph. A subset of nodes of the graph that are completely networked with each other is called a clique. A clique is a maximum clique if the addition of any further nodes from the graph leads to the loss of complete networking. In other words: there is no node outside the maximum clique that is complete with it, that is: connected to each node of the maximum clique via an edge.

Methods for determining maximum cliques in a graph are known from the prior art, for example from the publication Coen Bron and Joep Kerbosch. 1973. Algorithm 457: finding all cliques of an undirected graph. Commun. ACM 16, 9 (September 1973), pages 575-577, DOI = http: //dx.doi.org/10.1145/362342.362367 and from the publication E. Tomita, A. Tanaka, Haruhisa Takahashi. The worst-case time complexity for generating all maximal cliques and computational experiments. Theoretical computer science 363 (2006), pages 28-42, DOI = https: //doi.org/10.1016/j.tcs.2006.06.015.

For each maximum clique of each graph formed in this way, a maximum hotspot is formed by combining events that are assigned to one of the nodes of the respective maximum clique in a set of events.

A common geoposition is determined for each of the maximum hotspots found in this way from the geopositions of the entirety of the events associated with the respective maximum hotspot. For example, the geometric center of gravity of all events contained in the maximum hotspot can be assigned to such a maximum hotspot.

The invention provides a graph-based method for the particularly quick and efficient determination of hotspots.

One advantage of the method according to the invention is that the effort required to form hotspots or subsets of events that can potentially be traced back to a common root cause is reduced compared to the prior art. Another advantage is that hotspots formed by the method according to the invention have a particularly high accuracy of fit to the interesting but unknown geolocations of basic causes, which are the basis of the events observed by means of sensors or detection of control signals. An advantage over clustering methods known from the prior art is that events combined in a maximum hotspot have a small, over the maximum distance d _max controllable local spread. This will avoided that a large number of individually independent basic causes with slightly different but distinguishable geolocation were combined in a single cluster. For example, this prevents independent, distinguishable root causes, which are arranged as a chain, for example, along a street, from being combined into a single cluster. This improves the local resolution of root causes compared to the prior art.

In one embodiment, the method is carried out by a distributed system of computers, at least one vehicle computer being arranged in a vehicle and being set up to record and / or calculate parameters or features of events relating to this vehicle and to communicate with at least one central computer, and wherein a central computer is set up for communication with at least one vehicle computer, for merging the events recorded by the at least one vehicle computer and for determining the maximum cliques of the at least one graph formed from these events.

Advantageous embodiments of the invention are the subject of the dependent claims.

Exemplary embodiments of the invention are explained in more detail below with reference to drawings.

• 1 schematisch in geometrischen Abständen voneinander erfasste Ereignisse und
• 2 schematisch einen Graphen umfassend Knoten, die Ereignissen zugeordnet wurden.

Show:

• 1 events and recorded schematically at geometric distances from one another
• 2nd schematically shows a graph comprising nodes that have been assigned to events.

Corresponding parts are provided with the same reference symbols in all figures.

The occurrence of an event is detected by means of at least one sensor of a vehicle e _i determined. An event e _i can be determined, for example, by driving through a pothole using a chassis sensor. An event e _i can also be determined as an intervention of a vehicle assistance system in the control of the vehicle. Alternatively, an event e _i can be determined by a vehicle surroundings sensor system, for example as a traffic light signal, a street equipment or a landmark. The vehicle surroundings sensor system can comprise, for example, a camera or a light detection and ranging (LIDAR) sensor.

Every event e _i comprises a geoposition by a geopositioning device of the vehicle at the moment the event is determined e _i was intended for the vehicle. The particular and the event e _i Associated geoposition is generally flawed, that is, it deviates from the physical geoposition of the event e _i causally triggering physical condition. In other words: the geoposition assigned to a shock absorber punching through generally differs from the geoposition of the pothole that triggers the shock absorber's punching through; the geoposition determined as an example for a traffic light generally deviates from the physical geoposition of the traffic light mast. Of course, are also for other events e _i Deviations between the determined geoposition and the actual geoposition, which is attributable to the root cause, are possible.

Events e _i can include further parameters, for example information about the vehicle and / or a time stamp. In one embodiment, an event includes e _i in addition to the geoposition, a speed vector likewise determined by the geopositioning device of the vehicle, the direction of which describes the current direction of movement of the vehicle and the amount of which describes the current speed of movement of the vehicle.

An evaluation device or a backend is used to receive events e _i set up that are transmitted by at least one vehicle. The evaluation device assigns each event e _i reversibly clearly an index i = 1 , 2nd , ... n to. In one embodiment, the index i determined by n events e _l be consecutively numbered in the order of receipt by the evaluation device.

About two events e _i , e _j can be a spatial distance as a measure of similarity d _{i, j} = d (e _i , e _j ) can be determined, where d _{i, j} = 0 for i = j and d _{i, j} ≥ 0 for i ≠ j is. In one embodiment, the spatial distance d (e _i , e _j ) is the Euclidean distance between the geopositions of the events e _i , e _j determined, but metrics other than a Euclidean distance are also possible.

In an alternative embodiment, the similarity measure d (e _i , e _j ) includes not only the distance between the geopositions but also the direction vectors of the events e _i , e _j on. For example, a maximum angular distance can be specified such that two spatially close events e _i , e _j , i ≠ j, are only similar to one another, even if the two each have an event e _i linked driving directions include an angle that is smaller than the predetermined maximum angular distance.

Similarly, others can be related to events e _l , e _j determined parameters, for example the respectively determined amount of speed, are included in the calculation of the similarity measure d _{i, j} = d (e _i , e _j ). For example, the distance d (e _i , e _j ) can be formed as a weighted sum of the Euclidean distance of the geopositions and the sine value of the angle included by the speed vectors. It is also possible that a similarity measure or distance criterion d _{i, j} = d (e _i , e _j ) is formed, which additionally takes into account the direction of travel of the vehicle at the time an event is triggered.

1 shows an event set E = {e _i }, i = 1, 2, ... 7 of different events e _i . For each pair of events e _i , e _j , i ≠ j, the similarity measure d _{i, j} = d (e _i , e _j ) = d _{j, i} = d (e _j , e _l ) is determined. In 1 the events e _i , i = 1 ... 7 are shown at a geometric Euclidean distance that corresponds to the respective similarity measure d _{l, j} .

A coherent _{subset of} events E _dist ⊆ E is determined, which includes all events e _i ∈ E for which there is at least one other event e _j ∈ E such that the similarity measure or the distance between the event e _i and the other event e _j a predetermined maximum distance d _max does not exceed: $$d\left(e_i,e_j\right)\le d_{max}.$$

Such events e _i , e _j with d (e _i , e _j ) ≤ d _max should be referred to as neighboring events.

In other words: from all other events e _i distant (that is, not neighboring) "outliers" like that in 1 event shown as an example e ₇ are not in the contiguous subset of events E _dist added. The predetermined maximum distance d _max can be global, that is: for all possible pairs of events e _i , e _j be determined. However, in one embodiment of the method it is also possible to have a maximum distance d _max depending on the events e _i , e _j to determine the distance dimension d ( e _i , e _j ) with the maximum distance d _max to be compared. For example, a maximum distance determined specifically for a pair d _max take into account the average of the vehicle speeds, which in each case at the event e _i and at the event e _j were determined. This can take into account, for example, two events e _i , e _j , in the similarity measure d (e _i , e _j ) of a difference in the vehicle speeds, are more similar for the same vehicle speed difference if the vehicle speed as a whole (that is: on average between the two events e _i , e _j ) is lower.

From the contiguous subset of events E _dist becomes an undirected graph G comprising a set of nodes V = {ν _i } and edges ε _{i, j} formed by every event el ∈ E _dist exactly one knot ν _i is assigned and two nodes ν _i , ν _j then with an edge ε _{i, j} be connected if the similarity or distance measure d _{i, j} between the nodes ν _i , ν _j associated neighboring events e _i , e _j the predetermined maximum distance d _max does not exceed.

One to which in 1 presented contiguous subset of events E _dist corresponding graph G is in 2nd shown. It is therefore every knot ν _l of the graph G over a sequence of edges ε _{i, j} , ε _{j, k} , ... ε _{l, m} with every other knot ν _m of the graph G connected, in other words: the graph G is connected.

In general, however, it is not from a knot ν _i any other knot ν _m directly over a single edge ε _{i, m} reachable. For example, in 2nd graphs shown G the knots ν ₁ and ν ₄ who have favourited Knots ν ₁ and ν ₅ who have favourited Knots ν ₂ and ν ₄ who have favourited Knots ν ₃ and ν ₅ or the knots ν ₂ and ν ₅ not across a single edge ε _{i, m} connected. This means that the respectively assigned events e _i , e _m have a similarity or distance measure that is the predetermined maximum distance d _max exceeds.

gebildet werden. Eine Clique $C_l^{\left(k\right)}$

ist eine Teilmenge der Kardinalität k, umfassend Knoten v_{l 1} , v_{l 2} , ...v_{l k} , die zu einem vollständig vernetzten Teilgraphen des Graphen G gehört. Mit anderen Worten: jeder zu einer Clique $C_l^{\left(k\right)}$

gehörende Knoten v_{l i} ist mit jedem anderen zur selben Clique $C_l^{\left(k\right)}$

gehörenden Knoten v_{l j} ,i ≠ j über eine Kante ε_{l l} ,l_j verbunden.From the knot set V can cliques ${\mathrm{C.}}_l^{\left(k\right)}\subseteq V$

be formed. A clique ${\mathrm{C.}}_l^{\left(k\right)}$

is a subset of cardinality k, including nodes v _{l 1} , v _{l 2nd} , ... v _{l k} leading to a fully networked subgraph of the graph G heard. In other words: everyone to a clique ${\mathrm{C.}}_l^{\left(k\right)}$

belonging nodes v _{l i} is with the same clique with everyone else ${\mathrm{C.}}_l^{\left(k\right)}$

belonging knot v _{l j} , i ≠ j over an edge ε _{l l} , l _j connected.

der Kardinalität 2. Ebenso bilden die Knotenmengen {ν₁, ν₂, ν₃}, {ν₂, ν₃, ν₆}, {ν₁, ν₃, ν₆) sowie {ν₁, ν₂, ν₆} je eine Clique $C_l^{\left(3\right)}$

der Kardinalität 3. Dagegen bilden die Knoten ν₃ , ν₄ , ν₅ , keine Clique $C_l^{\left(k\right)},$

da der Knoten ν₃ und der Knoten ν₅ nicht über eine Kante ε_3,5 miteinander verbunden sind.Every pair of over an edge ε _{i, j} interconnected nodes ν _i , ν _j thus forms a clique ${\mathrm{C.}}_l^{\left(\mathrm{2nd}\right)}$

of cardinality 2nd . Likewise, the knot sets {ν ₁ , ν ₂ , ν ₃ }, {ν ₂ , ν ₃ , ν ₆ }, {ν ₁ , ν ₃ , ν ₆ ) and {ν ₁ , ν ₂ , ν ₆ } each form a clique ${\mathrm{C.}}_l^{\left(\mathrm{3rd}\right)}$

of cardinality 3rd . In contrast, the nodes form ν ₃ , ν ₄ , ν ₅ , no clique ${\mathrm{C.}}_l^{\left(k\right)},$

there the knot ν ₃ and the knot ν ₅ not over an edge ε _3.5 are interconnected.

wird als maximale Clique bezeichnet, wenn die Hinzunahme irgendeines weiteren Knoten ν_i ∈ V, ${\nu }_i\notin {\widehat{C}}_l^{\left(k\right)}$

zu einem Teilgraphen führt, der nicht vollständig vernetzt ist. Mit anderen Worten: jeder weitere, nicht zur maximalen Clique ${\widehat{C}}_l^{\left(k\right)}$

gehörende Knoten ν_i korrespondiert zu einem Ereignis e_i , das zu mindestens einem Ereignis e_{l 1} ,e_{l 2} , ... e_{l k} der zur maximalen Clique ${\widehat{C}}_l^{\left(k\right)}$

korrespondierenden Ereignismenge E ein Ähnlichkeits- oder Abstandsmaß aufweist, welches die vorbestimmte maximale Entfernung d_max überschreitet. Somit vereint eine maximale Clique ${\widehat{C}}_l^{\left(k\right)}=\left\{{\nu }_{l_1},{\nu }_{l_2},\dots {\nu }_{l_k}\right\}$

eine größtmögliche Menge von Ereignissen {e_{l 1} e_{l 2} , ... e_{l k} }, die entsprechend der maximalen Entfernung d_max ausreichend ähnlich sind.A clique ${\widehat{\mathrm{C.}}}_l^{\left(k\right)}=\left\{{\mathrm{<figure-callout\; id="1"\; label="\nu \; l"\; filenames="DE102019006005A1\_0034.png"\; state="\{\{state\}\}">\nu \; </figure-callout>}}_{l_{}},{\nu }_{l_{\mathrm{2nd}}},...{\nu }_{l_k}\right\}$

is called the maximum clique if the addition of any further node ν _i ∈ V, ${\nu }_i\notin {\widehat{\mathrm{C.}}}_l^{\left(k\right)}$

leads to a subgraph that is not fully networked. In other words: every further one, not to the maximum clique ${\widehat{\mathrm{C.}}}_l^{\left(k\right)}$

belonging nodes ν _i corresponds to an event e _i that lead to at least one event e _{l 1} , e _{l 2nd} , ... e _{l k} the maximum clique ${\widehat{\mathrm{C.}}}_l^{\left(k\right)}$

corresponding set of events E has a similarity or distance measure which is the predetermined maximum distance d _max exceeds. Thus, a maximum clique united ${\widehat{\mathrm{C.}}}_l^{\left(k\right)}=\left\{{\mathrm{<figure-callout\; id="1"\; label="\nu \; l"\; filenames="DE102019006005A1\_0034.png"\; state="\{\{state\}\}">\nu \; </figure-callout>}}_{l_{}},{\nu }_{l_{\mathrm{2nd}}},...{\nu }_{l_k}\right\}$

the greatest possible number of events {e _{l 1} e _{l 2nd} , ... e _{l k} } corresponding to the maximum distance d _max are sufficiently similar.

zugeordneten Ereignisse {e_{l 1} ,e_{l 2} ...e_{l k} } bildet einen maximalen Hotspot ${\widehat{h}}_l^{\left(k\right)}$

der Kardinalität $k=\left|{\widehat{h}}_l^{\left(k\right)}\right|.$

In other words, the amount of a maximum clique ${\widehat{\mathrm{C.}}}_l^{\left(k\right)}$

assigned events {e _{l 1} , e _{l 2nd} ... e _{l k} } forms a maximum hotspot ${\widehat{H}}_l^{\left(k\right)}$

of cardinality $k=\left|{\widehat{H}}_l^{\left(k\right)}\right|.$

From the in 2nd graphs shown G can therefore be seen as maximum cliques: $\begin{array}{ccc}{\widehat{\mathrm{C.}}}_1^{\left(\mathrm{2nd}\right)}=\left\{{\nu }_{\mathrm{3rd}},{\nu }_{\mathrm{4th}}\right\},& {\widehat{\mathrm{C.}}}_{\mathrm{2nd}}^{\left(\mathrm{2nd}\right)}=\left\{{\nu }_{\mathrm{4th}},{\nu }_5\right\},& {\widehat{\mathrm{C.}}}_{\mathrm{3rd}}^{\left(\mathrm{4th}\right)}=\left\{{\mathrm{<figure-callout\; id="1"\; label="\nu "\; filenames="DE102019006005A1\_0034.png"\; state="\{\{state\}\}">\nu </figure-callout>}}_1,{\nu }_{\mathrm{2nd}},{\nu }_{\mathrm{3rd}},{\nu }_6\right\}.\end{array}$

eines Graphen G sind aus dem Stand der Technik bekannt, beispielsweise aus der Veröffentlichung Coen Bron und Joep Kerbosch. 1973. Algorithm 457: finding all cliques of an undirected graph. Commun. ACM 16, 9 (September 1973), Seiten 575-577, DOI=http://dx.doi.org/10.1145/362342.362367 sowie in der Veröffentlichung E. Tomita, A. Tanaka, Haruhisa Takahashi. The worst-case time complexity for generating all maximal cliques and computational experiments.Procedure for determining maximum cliques ${\widehat{\mathrm{C.}}}_l^{\left(k\right)}$

of a graph G are known from the prior art, for example from the publication Coen Bron and Joep Kerbosch. 1973. Algorithm 457: finding all cliques of an undirected graph. Commun. ACM 16, 9 (September 1973), pages 575-577, DOI = http: //dx.doi.org/10.1145/362342.362367 and in the publication E. Tomita, A. Tanaka, Haruhisa Takahashi. The worst-case time complexity for generating all maximal cliques and computational experiments.

Theoretical computer science 363 (2006), pages 28-42, DOI = https: //doi.org/10.1016/j.tcs.2006.06.015. Implementations of such methods are also available.

aus einer gegebenen Menge von Ereignissen E bestimmt werden können.The invention thus provides a method with which maximum hotspots are particularly simple and with little computation and implementation effort ${\widehat{H}}_l^{\left(k\right)}$

from a given set of events E can be determined.

Reference list

clique

maximum clique

d _{i, j}

spatial distance

d _max

maximum distance

E

Event set

E _dist

Event subset

e _i, i = 1 ... 7

event

G

graph

ν _i , i = 1 ... 7

node

ε _{i, j} , i, j = 1 ... 7, i ≠ j

Edge

QUOTES INCLUDE IN THE DESCRIPTION

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Patent literature cited

• DE 102015002158 A1 [0006]

Claims (3)

Caused method for assigning a common geo to a plurality of through a common root cause and, characterized by at least one vehicle sensed events (e _i), wherein at least a single geo the vehicle is detected to each event (e _i) as a feature in that, that - for each pair of different events (e _i , e _j , i ≠ j) a distance measure is determined which takes into account at least the geopositions of the events (e _i , e _j , i ≠ j), - one event (e _i ) then a node (ν _i ) is assigned if the distance between the event (e _i ) and at least one further event (e _i , j ≠ i) does not exceed a maximum distance (d _max ), - each pair of different nodes (ν _i , ν _j , i ≠ j) an edge (ε _{i, j} ) is assigned if the distance between the events (e _i , e _j , i ≠ j) assigned to the nodes (ν _i , ν _j , i ≠ j) j) the maximum distance (d _max ) does not exceed, - at least one undirected coherent graph (G) is formed, which comprises all nodes (ν _i , ν _j , i ≠ j) interconnected via at least one edge (ε _{i, j} ), - for each graph (G) the set of all maximum cliques $\left({\widehat{\mathrm{C.}}}_l^{\left(k\right)}\right)$

is determined, with a maximum clique $\left({\widehat{\mathrm{C.}}}_l^{\left(k\right)}\right)$

is determined as a fully networked subgraph of the respective graph (G), which cannot be extended by any further node (ν _i ) of the graph (G) without losing the property of complete networking, - for each maximum clique $\left({\widehat{\mathrm{C.}}}_l^{\left(k\right)}\right)$

each graph (G) a maximum hotspot comprising all the nodes (ν _i ) of the respective maximum clique $\left({\widehat{\mathrm{C.}}}_l^{\left(k\right)}\right)$

assigned events (e _i ) is formed and - for each of the maximum hot spots found in this way, a common geoposition is determined from the totality of the geopositions assigned to the respective events (e ₁ , e ₂ ). Procedure according to Claim 1 , characterized in that an event (e _i ) additionally comprises the direction of travel of the vehicle, the distance measure assigned to each pair of different events (e _i , e _j , i ≠ j) at least the geopositions and the directions of travel of the events (e _i , e _j , i ≠ j) are taken into account. Method according to one of the preceding claims, characterized in that a maximum distance (d _max ) specific for a pair of events (e _i , e _j , i ≠ j) from the events (e _i , e _j , i ≠ j) assigned characteristics is determined.

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