Patent Publication Number: US-2021165410-A1

Title: Trajectory similarity search

Description:
BACKGROUND 
     The present disclosure relates to trajectory similarity analysis, and more specifically, to a method, a system, and a computer program product for trajectory similarity search. 
     With the boom of location-based services, a large volume of trajectories are generated. For example, Global Positioning System (GPS)-based trajectories of moving vehicles generates large volumes of trajectory data. Analysis of trajectory data have been used in various applications, such as, applications for: trajectory prediction, carpooling, route planning, and traffic analysis. 
     SUMMARY 
     Embodiments of the present invention disclose a computer-implemented method, a computer system, and a computer program product for trajectory similarity search. The present invention may include, in response to receiving, by one or more processors, a search request for at least one trajectory similar to a query trajectory, determining, by one or more processors, a respective similarity between a query trajectory and a plurality of trajectories by calculating, in a synchronized way, a spatial distance measure and a time difference measure between the query trajectory and the plurality of trajectories. The present invention may further include, identifying, by one or more processors, the at least one trajectory from the plurality of trajectories based on the respective similarity between the query trajectory and the plurality of trajectories. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       These and other objects, features and advantages of the present invention will become apparent from the following detailed description of illustrative embodiments thereof, which is to be read in connection with the accompanying drawings. The various features of the drawings are not to scale as the illustrations are for clarity in facilitating one skilled in the art in understanding the invention in conjunction with the detailed description. In the drawings: 
         FIG. 1  depicts a cloud computing node according to an embodiment of the present disclosure; 
         FIG. 2  depicts a cloud computing environment according to an embodiment of the present disclosure; 
         FIG. 3  depicts abstraction model layers according to an embodiment of the present disclosure; 
         FIG. 4  depicts a system in which embodiments of the present disclosure can be implemented; 
         FIG. 5  depicts a schematic diagram of an example for simplifying the query trajectory according to embodiments of the present disclosure; 
         FIG. 6A  depicts a schematic diagram of an example for mapping trajectories according to embodiments of the present disclosure; 
         FIG. 6B  depicts a schematic diagram of an example for merging grids according to embodiments of the present disclosure; 
         FIG. 7  depicts a schematic diagram of an example for indexing the grids and the plurality of trajectories according to embodiments of the present disclosure; 
         FIG. 8  depicts a schematic diagram of an example for trajectory similarity search according to embodiments of the present disclosure; 
         FIG. 9A  depicts a schematic diagram of one example for measuring the similarity between two trajectories according to embodiments of the present disclosure; 
         FIG. 9B  depicts a schematic diagram of another example for measuring the similarity between two trajectories according to embodiments of the present disclosure; 
         FIG. 10  depicts a schematic diagram of an example for determining respective similarities between the query trajectory and the plurality of trajectories according to embodiments of the present disclosure; and 
         FIG. 11  is an operational flowchart illustrating a trajectory similarity search process according to embodiments of the present disclosure. 
     
    
    
     Throughout the drawings, same or similar reference numerals represent the same or similar elements. 
     DETAILED DESCRIPTION 
     Some embodiments will be described in more detail with reference to the accompanying drawings, in which the embodiments of the present disclosure have been illustrated. However, the present disclosure can be implemented in various manners, and thus should not be construed to be limited to the embodiments disclosed herein. 
     It is to be understood that although this disclosure includes a detailed description on cloud computing, implementation of the teachings recited herein are not limited to a cloud computing environment. Rather, embodiments of the present disclosure are capable of being implemented in conjunction with any other type of computing environment now known or later developed. 
     Cloud computing is a model of service delivery for enabling convenient, on-demand network access to a shared pool of configurable computing resources (e.g. networks, network bandwidth, servers, processing, memory, storage, applications, virtual machines, and services) that can be rapidly provisioned and released with minimal management effort or interaction with a provider of the service. This cloud model may include at least five characteristics, at least three service models, and at least four deployment models. 
     Characteristics are as follows: 
     On-demand self-service: a cloud consumer can unilaterally provision computing capabilities, such as server time and network storage, as needed automatically without requiring human interaction with the service&#39;s provider. 
     Broad network access: capabilities are available over a network and accessed through standard mechanisms that promote use by heterogeneous thin or thick client platforms (e.g., mobile phones, laptops, and PDAs). 
     Resource pooling: the provider&#39;s computing resources are pooled to serve multiple consumers using a multi-tenant model, with different physical and virtual resources dynamically assigned and reassigned according to demand. There is a sense of location independence in that the consumer generally has no control or knowledge over the exact location of the provided resources but may be able to specify location at a higher level of abstraction (e.g., country, state, or datacenter). 
     Rapid elasticity: capabilities can be rapidly and elastically provisioned, in some cases automatically, to quickly scale out and rapidly released to quickly scale in. To the consumer, the capabilities available for provisioning often appear to be unlimited and can be purchased in any quantity at any time. 
     Measured service: cloud systems automatically control and optimize resource use by leveraging a metering capability at some level of abstraction appropriate to the type of service (e.g., storage, processing, bandwidth, and active user accounts). Resource usage can be monitored, controlled, and reported providing transparency for both the provider and consumer of the utilized service. 
     Service Models are as follows: 
     Software as a Service (SaaS): the capability provided to the consumer is to use the provider&#39;s applications running on a cloud infrastructure. The applications are accessible from various client devices through a thin client interface such as a web browser (e.g., web-based e-mail). The consumer does not manage or control the underlying cloud infrastructure including network, servers, operating systems, storage, or even individual application capabilities, with the possible exception of limited user-specific application configuration settings. 
     Platform as a Service (PaaS): the capability provided to the consumer is to deploy onto the cloud infrastructure consumer-created or acquired applications created using programming languages and tools supported by the provider. The consumer does not manage or control the underlying cloud infrastructure including networks, servers, operating systems, or storage, but has control over the deployed applications and possibly application hosting environment configurations. 
     Infrastructure as a Service (IaaS): the capability provided to the consumer is to provision processing, storage, networks, and other fundamental computing resources where the consumer is able to deploy and run arbitrary software, which can include operating systems and applications. The consumer does not manage or control the underlying cloud infrastructure but has control over operating systems, storage, deployed applications, and possibly limited control of select networking components (e.g., host firewalls). 
     Deployment Models are as follows: 
     Private cloud: the cloud infrastructure is operated solely for an organization. It may be managed by the organization or a third party and may exist on-premises or off-premises. 
     Community cloud: the cloud infrastructure is shared by several organizations and supports a specific community that has shared concerns (e.g., mission, security requirements, policy, and compliance considerations). It may be managed by the organizations or a third party and may exist on-premises or off-premises. 
     Public cloud: the cloud infrastructure is made available to the general public or a large industry group and is owned by an organization selling cloud services. 
     Hybrid cloud: the cloud infrastructure is a composition of two or more clouds (private, community, or public) that remain unique entities but are bound together by standardized or proprietary technology that enables data and application portability (e.g., cloud bursting for load-balancing between clouds). 
     A cloud computing environment is service oriented with a focus on statelessness, low coupling, modularity, and semantic interoperability. At the heart of cloud computing is an infrastructure that includes a network of interconnected nodes. 
     Referring now to  FIG. 1 , a schematic of an example of a cloud computing node is shown. Cloud computing node  10  is only one example of a suitable cloud computing node and is not intended to suggest any limitation as to the scope of use or functionality of embodiments of the invention described herein. Regardless, cloud computing node  10  is capable of being implemented and/or performing any of the functionality set forth hereinabove. 
     In cloud computing node  10  there is a computer system/server  12  or a portable electronic device such as a communication device, which is operational with numerous other general purpose or special purpose computing system environments or configurations. Examples of well-known computing systems, environments, and/or configurations that may be suitable for use with computer system/server  12  include, but are not limited to, personal computer systems, server computer systems, thin clients, thick clients, hand-held or laptop devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputer systems, mainframe computer systems, and distributed cloud computing environments that include any of the above systems or devices, and the like. 
     Computer system/server  12  may be described in the general context of computer system-executable instructions, such as program modules, being executed by a computer system. Generally, program modules may include routines, programs, objects, components, logic, data structures, and so on that perform particular tasks or implement particular abstract data types. Computer system/server  12  may be practiced in distributed cloud computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed cloud computing environment, program modules may be located in both local and remote computer system storage media including memory storage devices. 
     As shown in  FIG. 1 , computer system/server  12  in cloud computing node  10  is shown in the form of a general-purpose computing device. The components of computer system/server  12  may include, but are not limited to, one or more processors or processing units  16 , a system memory  28 , and a bus  18  that couples various system components including system memory  28  to processor  16 . 
     Bus  18  represents one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. By way of example, and not limitation, such architectures include Industry Standard Architecture (ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, Video Electronics Standards Association (VESA) local bus, and Peripheral Component Interconnect (PCI) bus. 
     Computer system/server  12  typically includes a variety of computer system readable media. Such media may be any available media that is accessible by computer system/server  12 , and it includes both volatile and non-volatile media, removable and non-removable media. 
     System memory  28  can include computer system readable media in the form of volatile memory, such as random access memory (RAM)  30  and/or cache memory  32 . Computer system/server  12  may further include other removable/non-removable, volatile/non-volatile computer system storage media. By way of example only, storage system  34  can be provided for reading from and writing to a non-removable, non-volatile magnetic media (not shown and typically called a “hard drive”). Although not shown, a magnetic disk drive for reading from and writing to a removable, non-volatile magnetic disk (e.g., a “floppy disk”), and an optical disk drive for reading from or writing to a removable, non-volatile optical disk such as a CD-ROM, DVD-ROM or other optical media can be provided. In such instances, each can be connected to bus  18  by one or more data media interfaces. As will be further depicted and described below, memory  28  may include at least one program product having a set (e.g., at least one) of program modules that are configured to carry out the functions of embodiments of the invention. 
     Program/utility  40 , having a set (at least one) of program modules  42 , may be stored in memory  28  by way of example, and not limitation, as well as an operating system, one or more application programs, other program modules, and program data. Each of the operating system, one or more application programs, other program modules, and program data or some combination thereof, may include an implementation of a networking environment. Program modules  42  generally carry out the functions and/or methodologies of embodiments of the invention as described herein. 
     Computer system/server  12  may also communicate with one or more external devices  14  such as a keyboard, a pointing device, a display  24 , etc.; one or more devices that enable a user to interact with computer system/server  12 ; and/or any devices (e.g., network card, modem, etc.) that enable computer system/server  12  to communicate with one or more other computing devices. Such communication can occur via Input/Output (I/O) interfaces  22 . Still yet, computer system/server  12  can communicate with one or more networks such as a local area network (LAN), a general wide area network (WAN), and/or a public network (e.g., the Internet) via network adapter  20 . As depicted, network adapter  20  communicates with the other components of computer system/server  12  via bus  18 . It should be understood that although not shown, other hardware and/or software components could be used in conjunction with computer system/server  12 . Examples, include, but are not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data archival storage systems, etc. 
     Referring now to  FIG. 2 , illustrative cloud computing environment  50  is depicted. As shown, cloud computing environment  50  includes one or more cloud computing nodes  10  with which local computing devices used by cloud consumers, such as, for example, personal digital assistant (PDA) or cellular telephone  54 A, desktop computer  54 B, laptop computer  54 C, and/or automobile computer system  54 N may communicate. Nodes  10  may communicate with one another. They may be grouped (not shown) physically or virtually, in one or more networks, such as Private, Community, Public, or Hybrid clouds as described hereinabove, or a combination thereof. This allows cloud computing environment  50  to offer infrastructure, platforms and/or software as services for which a cloud consumer does not need to maintain resources on a local computing device. It is understood that the types of computing devices  54 A-N shown in  FIG. 2  are intended to be illustrative only and that computing nodes  10  and cloud computing environment  50  can communicate with any type of computerized device over any type of network and/or network addressable connection (e.g., using a web browser). 
     Referring now to  FIG. 3 , a set of functional abstraction layers provided by cloud computing environment  50  ( FIG. 2 ) is shown. It should be understood in advance that the components, layers, and functions shown in  FIG. 3  are intended to be illustrative only and embodiments of the invention are not limited thereto. As depicted, the following layers and corresponding functions are provided: 
     Hardware and software layer  60  includes hardware and software components. Examples of hardware components include: mainframes  61 ; RISC (Reduced Instruction Set Computer) architecture based servers  62 ; servers  63 ; blade servers  64 ; storage devices  65 ; and networks and networking components  66 . In some embodiments, software components include network application server software  67  and database software  68 . 
     Virtualization layer  70  provides an abstraction layer from which the following examples of virtual entities may be provided: virtual servers  71 ; virtual storage  72 ; virtual networks  73 , including virtual private networks; virtual applications and operating systems  74 ; and virtual clients  75 . 
     In one example, management layer  80  may provide the functions described below. Resource provisioning  81  provides dynamic procurement of computing resources and other resources that are utilized to perform tasks within the cloud computing environment. Metering and Pricing  82  provide cost tracking as resources are utilized within the cloud computing environment, and billing or invoicing for consumption of these resources. In one example, these resources may include application software licenses. Security provides identity verification for cloud consumers and tasks, as well as protection for data and other resources. User portal  83  provides access to the cloud computing environment for consumers and system administrators. Service level management  84  provides cloud computing resource allocation and management such that required service levels are met. Service Level Agreement (SLA) planning and fulfillment  85  provide pre-arrangement for, and procurement of, cloud computing resources for which a future requirement is anticipated in accordance with an SLA. 
     Workloads layer  90  provides examples of functionality for which the cloud computing environment may be utilized. Examples of workloads and functions which may be provided from this layer include: mapping and navigation  91 ; software development and lifecycle management  92 ; virtual classroom education delivery  93 ; data analytics processing  94 ; transaction processing  95 ; and trajectory similarity search  96 . Hereinafter, reference will be made to  FIGS. 4-11  to describe details of the trajectory similarity search  96 . 
     As described previously, a large volume of trajectories are generated from location-based services. For example, Global Positioning System (GPS)-based trajectories of moving vehicles generates large volumes of trajectory data. Analysis of trajectory data have been used in various applications, such as, applications for: trajectory prediction, carpooling, route planning, and traffic analysis. 
     Effectively and efficiently searching a growing trajectory database for similar trajectories to a query trajectory is a challenging task. In order to measure a similarity between a query trajectory and another trajectory, some traditional schemes compute spatial similarity and temporal similarity independently, and then compute an overall similarity by summing the weighted spatial and temporal similarities. As such, two trajectories having a high spatial similarity, but a low temporal similarity may have the same overall similarity as another two trajectories having a high temporal similarity but a low spatial similarity. 
     Embodiments of the present disclosure address the problems described above by providing a new solution for conducting a search for trajectory similarity. In embodiments of the present disclosure, the similarity between two trajectories may be measured by synchronously matching their spatial distance against time difference. Further, with this new similarity measurement, a grid-based indexing of the trajectories and partitioning of the query trajectory may be enabled to overcome the challenge of searching for similar trajectories over a large number of trajectories. Thus, embodiments of the present disclosure improve the effectiveness and efficiency of searching for trajectory similarity. 
     With reference now to  FIG. 4 , a system  400  in which embodiments of the present disclosure can be implemented is shown. It is to be understood that the structure and functionality of the system  400  are described only for the purpose of illustration without suggesting any limitations as to the scope of the present disclosure. 
     As shown in  FIG. 4 , the system  400  may generally comprise a similarity search apparatus  420  and a database processing apparatus  450 . The similarity search apparatus  420  and/or the database processing apparatus  450  may be implemented by computer system/server  12  of  FIG. 1 . In some embodiments, the solution for trajectory similarity search may comprise two phases: an offline phase and an online phase. 
     During the offline phase, the database processing apparatus  450  may obtain a plurality of trajectories from a trajectory database  440  and generate an index structure  460  for indexing the plurality of trajectories. The index structure  460  may be provided to the similarity search apparatus  420  for the following trajectory similarity search. During the online phase, the similarity search apparatus  420  may receive a request to search for at least one trajectory similar to a query trajectory  410  from the plurality of trajectories in the trajectory database  440 . The similarity search apparatus  420  may determine respective similarities between the query trajectory  410  and the plurality of trajectories based on the index structure  460 , and select the at least one trajectory (such as, top-K most similar trajectories, where K≥1) from the plurality of trajectories based on the similarities between the query trajectory  410  and the plurality of trajectories. The similarity search apparatus  420  may present a search result  430  indicating the at least one trajectory similar to the query trajectory  410 . 
     As shown in  FIG. 4 , the similarity search apparatus  420  may comprise a simplification unit  421  and a search unit  423 . The database processing apparatus  450  may comprise a gridding unit  451 , a grid merging unit  452  and an indexing unit  453 . It is to be understood that the structures and functionalities of the similarity search apparatus  420  and/or the database processing apparatus  450  are described only for the purpose of illustration without suggesting any limitations as to the scope of the present disclosure. The similarity search apparatus  420  and/or the database processing apparatus  450  may include additional units not shown in  FIG. 4  and/or omit some units shown in  FIG. 4 . For example, in some embodiments, the simplification unit  421  as shown in  FIG. 4  can be omitted. Alternatively, or in addition, in some embodiments, the grid merging unit  452  as shown in  FIG. 4  can be omitted. 
     In some embodiments, the simplification unit  421  may simplify the query trajectory  410 , so as to generate the simplified query trajectory  422 . The simplified query  422  may be provided to the search unit  423  for trajectory similarity search. In some embodiment, the query trajectory  410  may comprise a plurality of query points indicating respective locations of a moving object (such as, a moving vehicle) at different time points. The simplification unit  421  may partition the query trajectory  410  into a plurality of line segments by connecting a part of the locations. That is, the simplified query trajectory  422  can be represented by the plurality of line segments. 
       FIG. 5  depicts a schematic diagram of an example for simplifying the query trajectory according to embodiments of the present disclosure. As shown in  FIG. 5 , for example, the query trajectory  410  may include a plurality of query points  411 - 1 ,  411 - 2  . . .  411 - 16  (collectively referred to as “query points  411 ” or individually referred to as “query point  411 ”), each of which may represent a location where a moving object passed at a corresponding time point. For example, a query point  411  can be represented as &lt;p i , t i &gt;, where t i  represents a time point and p i  represents the location (such as, longitude and latitude coordinates) of a moving object at the time point t i . 
     In some embodiments, the simplification unit  421  may connect a part of the query points  411 , such as, the points  411 - 1 ,  411 - 5 ,  411 - 10  and  411 - 16  shown in  FIG. 5 , to generate the simplified query trajectory  422 . In  FIG. 5 , for example, the simplified query trajectory  422  may include a line segment S 1  which connects the points  411 - 1  and  411 - 5 , a line segment S 2  which connects the points  411 - 5  and  411 - 10 , and a line segment S 3  which connects the points  411 - 10  and  411 - 16 . 
     The number of line segments in the simplified query trajectory  422  should be proper. If there are too many line segments, an excessive search cost will be caused in the following trajectory similarity search; while if there are too few line segments, many similar trajectories will be found in the following trajectory similarity search, resulting in a high candidate maintenance cost. In some embodiments, a cost model can be designed to approximately find the best simplification, so as to balance the search cost and the candidate maintenance cost. Any algorithm (such as, a greedy algorithm) currently known or to be developed in the future for implementing such cost model can be used. The scope of the present disclosure is not limited in this aspect. 
     With reference back to  FIG. 4 , in some embodiments, each of the plurality of trajectories in the trajectory database  440  may comprise a set of locations points indicating respective locations of a moving object (such as, a moving vehicle) at different time points and thus may be represented as a set of line segments connecting the set of locations points. In some embodiments, the gridding unit  451  may divide a three-dimensional spatial-temporal space into a first set of grids, and then map respective sets of line segments corresponding to the plurality of trajectories into the first set of grids. The grid merging unit  452  may merge a plurality of neighboring grids in the first set of grids shared by at least two of the plurality of trajectories, so as to generate a second set of grids. The indexing unit  453  may generate the index structure  460  for indexing the second set of grids and the plurality of trajectories mapped to the second set of grids. 
       FIG. 6A  depicts a schematic diagram of an example for mapping a plurality of trajectories into a set of grids according to embodiments of the present disclosure. In the example as shown in  FIG. 6A , only for the purpose of simplicity, a set of grids divided from a two-dimensional space (for example, excluding a temporal dimension) are shown, which can be indexed as a1, a2 . . . a5, b1, b2 . . . b5, . . . , e1, e2 . . . e5. A plurality of trajectories T 1 , T 2  and T 3  are mapped to the set of grids. Taking the trajectory T 2  as an example, T 2  can be represented as: c1→c2→c3→c4→c5. It can be seen that, the grids c2, c3 and c4 are shared by the plurality of trajectories T 1 , T 2  and T 3 . In some embodiments, in order to further accelerate the trajectory similarity search, neighboring grids shared by the plurality of trajectories can be merged into one grid.  FIG. 6B  depicts a schematic diagram of an example for merging grids according to embodiments of the present disclosure. As shown in  FIG. 6B , the grids c2, c3 and c4 are merged into one grid, for example, represented as K 1 . Taking the trajectory T 2  as an example again, T 2  can be represented as: c1→K 1 →c5. Any algorithm currently known or to be developed in the further can be used for implementing such merging, including but not limited to a heuristic algorithm. 
       FIG. 7  depicts a schematic diagram of an example for indexing the grids and the plurality of trajectories according to embodiments of the present disclosure. As shown in  FIG. 7 , the trajectories T 1 , T 2  and T 3  have been mapped to the grids a1, a2 . . . a5, b1, b2 . . . b5, . . . , e1, e2 . . . e5, and the neighboring grids c2, c3 and c4 shared by the trajectories T 1 , T 2  and T 3  have been merged into one grid. Then, the indexing structure  460  can be built over all of the grids. In some embodiments, as shown in  FIG. 7 , the indexing structure  460  can be implemented by a R-tree. In the following, the indexing structure  460  can also be referred to as the R-tree  460 . It is to be understood that, in other embodiments, the indexing structure  460  can be implemented by a different data structure. 
     As shown in  FIG. 7 , the R-tree  460  may include a root node  461 , which represents all of the grids. The R-tree  460  may also include one or more Minimal Bounding Rectangle (MBR) nodes  462 - 1 ,  462 - 2  acting as child nodes of the root node  461 , each containing at least one grid and/or at least one MBR node (such as, the MBR node  462 - 3 ). Each leaf node of the R-tree  460  may correspond to one grid. Further, each leaf node corresponding to a grid may be associated with an inverted list, which records identifiers of trajectories mapped to the grid. As shown in  FIG. 7 , for example, the inverted list associated with the grid a2 may record the identifier of the trajectory T 1 ; the inverted list associated with the grid b2 may record the identifier of the trajectory T 1 ; the inverted list associated with each of the grids c2, c3 and c4 may record the identifiers of the trajectories T 1 , T 2  and T 3 ; . . . and so on. Additionally, in some embodiments, in order to save storage space occupied by the index structure  460 , the inverted lists associated with the grids can be further simplified. For example, in  FIG. 7 , each of the grids c2, c3 and c4 is associated with the same inverted list T 1 →T 2 →T 3 . By representing the inverted list T 1 →T 2 →T 3  as K 1 , the inverted lists associated with the grids can be further simplified, as shown in  FIG. 7 . 
     With reference back to  FIG. 4 , as described above, the simplified query trajectory  422  and the index structure  460  can be provided to the search unit  423  for trajectory similarity search. In some embodiments, the query trajectory  422  may correspond to a plurality of line segments (such as, the line segments S 1 , S 2  and S 3  as shown in  FIG. 5 ). The search unit  423  may map the plurality of line segments into the grids indexed by the index structure  460 . Then, for each of the plurality of line segments, the search unit  423  may determine at least one grid associated with the each of the plurality of line segments by searching the index structure  460 , and determine at least one similarity between the line segment and the at least one grid. 
       FIG. 8  depicts a schematic diagram of an example for trajectory similarity search according to embodiments of the present disclosure. As shown in  FIG. 8 , the line segments S 1 , S 2  and S 3  of the query trajectory  422  are mapped to the grids indexed by the index structure  460 . At least one grid associated with each of the line segments S 1 , S 2  and S 3  can be determined by searching the index structure  460 . As used herein, a grid associated with a line segment can also be referred to as a “local candidate” of the line segment. Then, at least one similarity between the each of the line segments S 1 , S 2  and S 3  and the at least one grid can be determined, as will be further described in detail with reference to  FIGS. 9A-9B  in the following. The local candidates of each of the line segments S 1 , S 2  and S 3  can be ranked based on similarities between the local candidates and the each of the line segments S 1 , S 2  and S 3 . For example, as shown in  FIG. 8 , the local candidates of each of the line segments S 1 , S 2  and S 3  are ranked in descending order of similarity to the each of the line segments S 1 , S 2  and S 3 . 
     In some embodiments, in order to determine a similarity between a line segment (such as, S 1 , S 2  or S 3 ) and a grid, the search unit  423  may determine, from the plurality of trajectories (such as, T 1 , T 2  and T 3 ), a trajectory mapped to the grid; and then determine a similarity between the line segment and the trajectory mapped to the grid. The search unit  423  may determine the similarity between the line segment and the grid based on the similarity between the line segment and the trajectory mapped to the grid. 
       FIG. 9A  depicts a schematic diagram of an example for measuring the similarity between two trajectories  910  and  920  according to embodiments of the present disclosure. 
     As shown in  FIG. 9A , the trajectory  910  includes a plurality of points P 1 , P 2  . . . P 6 , while the trajectory  920  includes a plurality of points Q 1 , Q 2  and Q 3 . Each point on the trajectories  910  and  920  may indicate a location (such as, longitude and latitude coordinates) and a time point. Taking the point Q 2  on the trajectory  920  as an example, the search unit  423  may try to find another point Q 2 ′ on the trajectory  910  such that the similarity between the points Q 2  and Q 2 ′ is maximized. The similarity between the points Q 2  and Q 2 ′ can be determined as: 
       θ* e   −ΔD +(1−θ)* e   −ΔT   (1)
 
     where ΔD represents a spatial distance between the points Q 2  and Q 2 ′ (that is, the distance between the locations indicated by the points Q 2  and Q 2 ′), ΔT represents a time difference between the points Q 2  and Q 2 ′ (that is, the time difference between the time points indicated by the points Q 2  and Q 2 ′), and θ∈ [0,1] is a parameter to control the relative importance of the spatial and time differences. By maximizing the similarity as shown in the above formula (1), the search unit  423  can determine the point Q 2 ′ (such as, its location and time point) on the trajectory  910  which matches the point Q 2  as well as their similarity. Likewise, for another point Q 1  or Q 3  on the trajectory  910 , the search unit  423  can find a corresponding point Q 1 ′ or Q 3 ′ on the trajectory  910  and determine the similarity between the matching points. The similarity between the matching points can be used to determine the similarity between the trajectories  910  and  920 . That is, in the embodiments of the present disclosure, the similarity between two trajectories can be determined by measuring the spatial distance and time difference between the two trajectories in a synchronized way. 
     In some embodiments, the search for matching points across two trajectories can be performed in a unidirectional way, as shown in  FIG. 9A . Alternatively, in some embodiments, the search for matching points across two trajectories can be performed in a bidirectional way, as shown in  FIG. 9B . 
     As shown in  FIG. 9B , for the points Q 1 , Q 2  and Q 3  on the trajectory  920 , the search unit  423  may determine matching points Q 1 ′, Q 2 ′ and Q 3 ′ on the trajectory  910 . Additionally, for the points P 1 , P 2  . . . P 6  on the trajectory  910 , the search unit  423  may determine matching points P 1 ′, P 2 ′ . . . P 6 ′ on the trajectory  920 . For example, as shown in  FIG. 9B, 7  pairs of matching points can be found across the trajectories  910  and  920 , which are (P 1 , Q 1 ), (P 3 , P 3 ′), (P 2 , P 2 ′), (Q 2 ′, Q 2 ), (P 5 , P 5 ′), (P 4 , P 4 ′) and (P 6 , Q 3 ). 
     In some embodiments, in response to determining pairs of matching points across the trajectories  910  and  920 , the search unit  423  can determine the similarity between the trajectories  910  and  920  based on respective similarities of these matching point pairs. In some embodiments, the similarity between two trajectories can be determined as a value, for example, by aggregating respective similarities of matching point pairs. Alternatively, the similarity between two trajectories can be determined as a range defined by an upper bound and a lower bound. For example, the upper bound can be determined as the maximum one of the similarities of these matching point pairs; while the lower bound can be determined as the minimum one of the similarities of these matching point pairs. 
     As such, with reference back to  FIG. 8 , for each of the line segments S 1 , S 2  and S 3 , respective similarities between the line segment and the local candidates of the line segment can be determined. Then, the search unit  423  can determine respective similarities between the query trajectory and the plurality of trajectories by aggregating the similarities between the plurality of line segments and their local candidates based on the index structure. 
       FIG. 10  depicts a schematic diagram of an example for determining respective similarities between the query trajectory and the plurality of trajectories according to embodiments of the present disclosure. In  FIG. 10 , for example, the similarity between a line segment and its local candidate is represented as a range defined by an upper bound (UB) and a lower bound (LB). It is to be understood that, this is merely for the purpose of illustration, without suggesting any limitations to the scope of the present disclosure. 
     As shown in  FIG. 10 , Table  1010  shows similarities between the line segment S 1  and its local candidates. By searching the index structure  460  as shown in  FIG. 7 , the trajectory associated with each local candidate can be determined, as shown in Table  1010 . Table  1020  shows similarities between the line segment S 2  and its local candidates. Table  1030  shows similarities between the line segment S 3  and its local candidates. The search unit  423  can determine respective similarities between the query trajectory  422  and the plurality of trajectories (also referred to as “global candidates” of the query trajectory  422 ) by aggregating the similarities between the line segments S 1 , S 2 , S 3  and their local candidates. For example, if the similarity bounds of a local candidate of a line segment exceed predetermined thresholds, the local candidate will be popped out to a global candidate list as shown in Table  1040 , where the original trajectory identifier associated with the local candidate will replace the identifier of the local candidate. The similarity between the query trajectory  422  and its global candidate can be determine by summing respective similarities between the line segments S 1 , S 2 , S 3  and their local candidates in the global candidate list, as shown in Table  1040 . 
     With reference back to  FIG. 4 , in some embodiments, in response to determining the similarities between the query trajectory  410  and the plurality of trajectories in the trajectory database  440 , the search unit  423  may select the at least one trajectory (such as, top-K most similar trajectories, where K≥1) from the plurality of trajectories based on the determined similarities. The search unit  423  may then present the search result  430  indicating the at least one trajectory. 
       FIG. 11  depicts a flowchart of an example method  1100  for trajectory similarity search according to embodiments of the present disclosure. For example, the method  1100  may be implemented by computer system/server  12  of  FIG. 1 . It is to be understood that the method  1100  may also comprise additional blocks (not shown) and/or may omit the illustrated blocks. The scope of the present disclosure described herein is not limited in this aspect. 
     At block  1110 , a method receives a request to search for at least one trajectory similar to a query trajectory from a plurality of trajectories. 
     At block  1120 , respective similarities between the query trajectory and the plurality of trajectories are determined by measuring spatial distances and time differences between the query trajectory and the plurality of trajectories in a synchronized way. 
     At block  1130 , the at least one trajectory is determined from the plurality of trajectories based on the similarities between the query trajectory and the plurality of trajectories. 
     Alternatively, or in addition, at block  1140 , an indication of the at least one trajectory is presented as a response to the request. 
     In some embodiments, prior to determining the similarities between the query trajectory and the plurality of trajectories, the query trajectory is simplified. 
     In some embodiments, the query trajectory indicates a plurality of locations of a moving object at different time points, and simplifying the query trajectory comprises: dividing the query trajectory into a plurality of line segments by connecting a part of the plurality of locations. 
     In some embodiments, each of the plurality of trajectories indicates a set of locations of a moving object at different time points and corresponds to a set of line segments connecting the set of locations, and the method  1100  further comprises: prior to determining the similarities between the query trajectory and the plurality of trajectories, dividing a three-dimensional spatial-temporal space into a first set of grids; mapping respective sets of line segments corresponding to the plurality of trajectories into the first set of grids; generating a second set of grids by merging a plurality of neighboring grids in the first set of grids shared by at least two of the plurality of trajectories; and generating an index structure for indexing the second set of grids and the plurality of trajectories mapped to the second set of grids. 
     In some embodiments, the index structure includes a R-tree. 
     In some embodiments, the query trajectory indicates a plurality of locations of a moving object at different time points and corresponds to a plurality of line segments connecting the plurality of locations, and determining the similarities between the query trajectory and the plurality of trajectories comprises: mapping the plurality of line segments corresponding to the query trajectory into the second set of grids; for each of the plurality of line segments, determining at least one grid associated with the each of the plurality of line segments from the second set of grids by searching the index structure, and determining at least one similarity between the each of the plurality of line segments and the at least one grid; and deriving the similarities between the query trajectory and the plurality of trajectories from aggregating respective similarities determined for the plurality of line segments based on the index structure. 
     In some embodiments, determining the at least one similarity between the line segment and the at least one grid comprises: for each of the at least one grid, determining a trajectory mapped to the each of the at least one grid from the plurality of trajectories by searching the index structure; determining a similarity between the line segment and the trajectory; and determining a similarity between the line segment and the each of the at least one grid based on the similarity between the line segment and the trajectory. 
     In some embodiments, the line segment includes a first point indicating a first location and a first time point, and determining the similarity between the line segment and the trajectory comprises: determining a second point indicating a second location and a second time point from the trajectory by maximizing a first similarity between the first point and the second point, wherein the first similarity is determined based on a spatial distance between the first location and the second location and a time difference between the first time point and the second time point; and determining the similarity between the line segment and the trajectory based on the first similarity. 
     In some embodiments, the trajectory includes a third point indicating a third location and a third time point, and determining the similarity between the line segment and the trajectory comprises: determining a fourth point indicating a fourth location and a fourth time point from the line segment by maximizing a second similarity between the third point and the fourth point, wherein the second similarity is determined based on a spatial distance between the third location and the fourth location and a time difference between the third time point and the fourth time point; and determining the similarity between the line segment and the trajectory based on at least one of the first similarity and the second similarity. 
     It can be seen that, embodiments of the present disclosure provide a new solution for trajectory similarity search. In this solution, the similarity between two trajectories is measured by synchronously matching their spatial distance against time difference. Further, with this new similarity measurement, to overcome the challenge of search similar trajectories over a huge number of trajectories, grid-based indexing of the trajectories and partitioning of the query trajectory are enabled, so as to improve effectiveness and efficiency of trajectory similarity search. 
     It should be noted that the trajectory similarity search according to embodiments of this disclosure could be implemented by computer system/server  12  of  FIG. 1 . 
     The present disclosure may be a system, a method, and/or a computer program product at any possible technical detail level of integration. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present disclosure. 
     The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire. 
     Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing/processing device. 
     Computer readable program instructions for carrying out operations of the present disclosure may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuitry, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++, or the like, and procedural programming languages, such as the “C” programming language, Python programming language, or similar programming languages. The computer readable program instructions may execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure. 
     Aspects of the present disclosure are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer readable program instructions. 
     These computer readable program instructions may be provided to a processor of a computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks. 
     The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the blocks may occur out of the order noted in the Figures. For example, two blocks shown in succession may, in fact, be accomplished as one step, executed concurrently, substantially concurrently, in a partially or wholly temporally overlapping manner, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions. 
     The descriptions of the various embodiments of the present disclosure have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.