Patent Publication Number: US-2016232179-A1

Title: Recommending points of interests in a region

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This is a continuation of U.S. patent application Ser. No. 14/659,125, filed on Mar. 16, 2015 which is a continuation application which claims priority to commonly assigned, co-pending U.S. patent application Ser. No. 12/567,667, filed Sep. 25, 2009, now U.S. Pat. No. 9,009,177. Application Ser. No. 12/567,667 is fully incorporated herein by reference. 
    
    
     BACKGROUND 
     A wide range of traditional information retrieval is being offered to users by service providers or search engines. The traditional information retrieval services offered may allow a user to provide a set of keywords or terms to a search engine. In return, the search engine provides a list of items that are relevant to the keywords or the terms by retrieving text documents. 
     A problem that occurs with the traditional information retrieval, however, is when the user wants to find particular locations by representative categories in a geographical region. For example, the user travelling in a new city may have limited knowledge about the area. Since the user may also have limited time, it is highly desirable to find locations with a desired mixture of local sights and/or attractions to visit during this limited time. 
     Another problem with the traditional information retrieval is that it does not help identify geographical regions that may be considered potential high-risk areas prone to outbreak of diseases. Thus, the problem is not able to identify the high-risk areas to alert a traveler to avoid that geographical region. 
     SUMMARY 
     This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. 
     This disclosure describes geographical recommendation services that, for example, searches and recommends points of interests based on a user-specified region. Points of interests include spatial objects (e.g., buildings, landmarks, rivers, parks) and their distributions in a geographical region. The process searches for points of interests by partitioning a spatial map into grids to identify representative categories located in each of the grids. In response to the user-specified region, a set of geographical candidates containing the representative categories is retrieved. The process determines whether the user-specified region and the set of geographical candidates include similar representative categories and spatial distributions of the representative categories. Then the process recommends the top ranked geographical candidates that have similar content information to the user-specified region. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The Detailed Description is set forth with reference to the accompanying figures. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. The use of the same reference numbers in different figures indicates similar or identical items. 
         FIG. 1  is a schematic showing an illustrative environment for searching and recommending points of interests in a geographical region. 
         FIG. 2  is a block diagram showing an illustrative computing device usable with the environment of  FIG. 1 . 
         FIG. 3  is a block diagram showing an illustrative server usable with the environment of  FIG. 1 . 
         FIG. 4  is a flowchart showing an illustrative process identifying POIs with representative categories in geographical regions. 
         FIG. 5  is a schematic showing illustrative spatial distributions of POIs with representative categories. 
         FIG. 6 a    is a diagram showing illustrative mutual distance vectors. 
         FIG. 6 b    is a diagram showing illustrative reference distance vectors. 
         FIG. 7  is a schematic showing an illustrative quadtree and an inverted list. 
         FIG. 8  is a flowchart showing an illustrative process of searching and recommending top geographical regions with similar measures of content to the user-specified region. 
     
    
    
     DETAILED DESCRIPTION 
     Overview 
     As discussed above, conventional services or search engines may not always provide an effective way of searching regions that are similar in content information to a region specified by the user. For example, in some instances, it may be difficult to identify how to measure similarities in content information between the regions. Moreover, conventional services or search engines may not be able to readily incorporate the distribution of the representative categories while trying to measure similarities between the regions. This disclosure describes various illustrative ways of searching to recommend geographical regions that are similar to a user-specified region or a query region on a spatial map. For example, by determining whether the user-specified region and a set of geographical candidates have similar content information including common geometric properties, common representative categories, and common spatial distributions of representative categories. The process provides the top ranked geographical regions from the set of geographical candidates, that have similar content information to the user-specified region. Thus, the techniques described in detail below provide ways to search and to recommend points of interests in regions that are similar to the user-specified region. 
     In an implementation, the techniques for searching and recommending similar regions employ a spatial vector space model. The vector space model measures similarity by analyzing whether the user-specified region and a candidate region have a significant overlap in their representative categories and whether the points of interests of the common representative categories among these two regions have a similar spatial distribution. The vector space model evaluates the similarity of the two regions by analyzing a cosine similarity of corresponding feature vectors of the two regions. Furthermore, to minimize the effects of scaling and to allow for rotation invariant, two new features capture the spatial distribution of points of interests: mutual distance vector or reference distance vector. 
     In another implementation, the techniques employ a quadtree-based heuristic region search approach. The quadtree process partitions the spatial map into a hierarchical structure and builds a quadtree structure for quick retrieval of points of interests in a region. For instance, the process uses these index structures to perform region search queries efficiently. Given the user-specified region, the process analyzes a shape and a size of the user-specified region and determines an appropriate quadtree layer to initiate a similar region search process. At the same time, the process may compute values for an inverse region frequency of category to derive the representative categories of the user-specified region. Next, a prune-and-refine process quickly reduces the search space that is unlikely to be in the top most similar regions. 
     While aspects of described techniques can be implemented in any number of different computing systems, environments, and/or configurations, implementations are described in the context of the following illustrative computing environment. 
     Illustrative Environment 
       FIG. 1  is a block diagram of an illustrative environment  100  in which the service provider or service engine searches and recommends geographic regions with similar points of interests (POIs). Points of interests may include spatial objects (e.g., buildings, landmarks, rivers, parks) in representative categories and their distributions in a geographical region. While representative categories include but are not limited to, restaurants, hotels, shopping malls, museums, theatres, golf courses, bowling alleys, landmarks, and the like. 
     The environment  100  includes an illustrative computing device  102 , which may take a variety of forms, including, but not limited to, a desktop computer, a portable handheld computing device (e.g., a personal digital assistant, a smart phone, a cellular phone), a thin client, a laptop computer, a media player, or any other device capable of connecting to one or more network(s)  104  to access network services, a network service provider, a web site, web entity, and the like. A user  106  may employ the illustrative computing device  102  to connect to the one or more network(s)  104 . 
     The one or more network(s)  104  represents any type of communications network(s), including multiple different types of networks, interconnected with each other and functioning as a single large network (e.g., the Internet or an intranet). The network  104  may include wire-based networks (e.g., cable), wireless networks (e.g., cellular, satellite, etc.), cellular telecommunications network(s), and IP-based telecommunications network(s) (e.g., Voice over Internet Protocol networks). The network  104  may use any number of protocols and configurations to enable the computing device  102  to access other devices, content, information, and resources. 
     The computing device  102  may include a geographical region module  108  to implement searching for geographic regions with similar POIs to the user-specified region, that may be accessed on the computing device  102 . In some implementations, this geographical region module  108  may be available as part of the web browser, may be incorporated into a search engine, or may be available as an application on the computing device  102 . In particular, the geographical region module  108  searches and provides recommendations of regions with similar POIs to the query region specified by the user  106 . The terms user-specified region and query region are used interchangeably to refer to the region that the user  106  specifies. 
     The user-specified region may be a place the user has visited, a place the user would like to visit, or a place the computing device specifies based at least in part on the user&#39;s present location as a center of a certain window size. In an implementation, the user  106  may draw a rectangle around the query region at the place he or she is visiting on the spatial map. Thus, the region identified in this rectangle is the query region  110  or the user-specified region  110 , such as a shopping mall. Shown is an example of a set of candidates that may be in a geographical region  112 . 
     Unlike a traditional text query that searches based on keywords, the geographical region module  108  finds the top most similar regions to the user-specified region using an algorithm. The algorithm identifies a set of candidates in the regions if there is similar content information of the POIs in the regions. The algorithm evaluates whether the POIs in the query region  110  and the set of candidates  112  have similarities that are measured by geometric properties, content properties, and spatial properties. The similarity measures look for common geometric properties (i.e., scales, shapes, sizes), common content properties (i.e., POIs categories, representative categories), and common spatial properties (i.e., distribution of POIs of representative categories, reference points). The algorithm performs the search promptly to provide the top candidates. In the illustrated example, the top regions  112  with similar POIs may be presented to the user  106  on a spatial map, as an enlarged view, or as a list. 
     The environment  100  may include one or more web site servers  114 ( 1 ),  114 ( 2 ), . . . ,  114 (S) which may be a representative set of servers that is accessible via the network(s)  104 . The geographical region servers  114  may be independent servers, or a collection of servers that are configured to perform larger scale functions (e.g., a server farm or a datacenter), or a set of servers configured to host one or more sites (e.g., web sites) accessible by the network  104 . In the illustrated example, the servers  114  may represent private servers that serve content and programming to the computing device  102 , the thin client, and the like. Alternatively, the servers  114 ( 1 )- 114 (S) may represent a wireless services provider that provides content to wireless devices. In still other implementations, the servers  114 ( 1 )- 114 (S) may be configured to host a service provider, such as a web site accessible by the computing device  102  via the Internet. 
     These various arrangements exhibit examples of environments where a server-side geographical region module  116  may be employed. In the illustrated example shown in  FIG. 1 , the user  106  operates the computing device  102  to connect via the network(s)  104  to the servers  114 . In this example, the geographical region module  108  is capable of receiving a list of candidates for geographical regions of similar POIs to the user-specified region. Thus, the geographical region module  108  process identifies regions with similar POIs in response to the user-specified region and provides the top geographical recommendations, as identified by the user  106 . 
     In another implementation, a server-side geographical region module  116  may be located on the geographical server  114  or may be part of an operating system browser on the server accessible by a computing device. In some instances, the geographical region module on the computing device may be executed with a server-side geographical region module to provide recommendations of geographical regions with similar POIs to the user-specified region. 
       FIG. 2  is a block diagram showing an exemplary communication device, such as the computing device  102 . As shown, the computing device  102  includes a processor  200 , a memory  202 , and one or more communication connections  204 . The communication connection(s)  204  may include a wide area network (WAN) module, a local area network module (e.g., WiFi), a personal area network module (e.g., Bluetooth), and/or any other suitable communication modules to allow the computing device  102  to communicate over the network(s)  104 . For example, the recommendations for the geographical regions with POIs may be delivered by the browser, sent to others through email, shared in text messaging, shared in instant messaging, or the like. 
     The memory  202  may also include an operating system  206  and a user interface (UI) module  208  that, when executed on the processor  200 , collectively facilitate presentation of a user interface on a display of the computing device  102 . The user interface module  208  may provide a visual representation of the spatial map, where the user  106  may draw a rectangle in one color (e.g., red color) to specify the query region  110 . For example, by providing a visual representation to the user  106  confirms the query region  110  selected may include the representative categories that are desired. This provides assurance to the user  106  when receiving the top recommendations for the geographical regions with POIs, that are similar to the user-specified region  110 . In an implementation, the similar geographical regions with POIs may be displayed with a second color (e.g., blue color). Thus, the user  106  may visually confirm there are similar representative categories and similar spatial distribution of POIs to the query region. 
     Furthermore, the user interface module  208  of the computing device  102  may, in some implementations, visually present a list of the top geographical regions with POIs identified. This visual representation of a list allows the user  106  to visually verify that the representative categories have been identified for the geographical regions. For example, the list may describe Region Candidate  1  that includes restaurants, shopping malls, and theatres with their addresses, while Region Candidate  2  includes restaurants and hotels with their addresses. Thus, the user may quickly scan the list to select a region. 
     Furthermore, the computing device  102  may visually present the geographical regions with POIs in a representation with geographical coordinates, such as streets and highways. By visually illustrating what and where the representative categories are, helps the user  106  know what representative categories are available and where the representative categories are located. For example, the user  106  may be travelling in New York City, wants to find a restaurant close to a theatre. The user  106  may draw a rectangle around restaurants or theatres on a certain street located in Manhattan, representing the categories of the user-specified region  110 . In response, the geographical region module  108  in operation with the user interface module  208  provides and displays the top recommendations of geographical regions with POIs that are similar to the user-specified query  110 . The top recommended geographical regions may be shown with rectangles around the regions in different colors. For example, in an implementation, the rectangles may be based on colors ranging in order of rank. 
     The memory  202  may include a content storage  210  for locally storing representative categories of points of interests on the spatial map. The content stored may include representative categories identified through: spatial objects, published telephone listings, zip codes, city information, graphical representation of the set of geographical coordinates, and the like. Some of the information may include business entities, each having their own properties of name, category, and GPS coordinate. Storing the representative categories of points of interests in the content storage  210  offers the user  106  accessibility to the content, if there is no network service available. As mentioned, the servers  114  may host some or all of the content, such as the spatial maps, applications, and may store some or all of the content, based on the network service provider. 
     The computing device  102  as described above may be implemented in various types of systems or networks. For example, the computing device may be a part of, including but is not limited to, a client-server system, a peer-to-peer computer network, a distributed network, an enterprise architecture, a local area network, a wide area network, a virtual private network, a storage area network, and the like. 
       FIG. 3  is a schematic block diagram showing details of an exemplary geographical region server  114 . The geographical region server  114  may be configured as any suitable system capable of searching and providing recommendations for geographical regions with POIs similar to the user-specified region, which includes, but is not limited to, searching, receiving, storing, detecting, sharing, removing, and updating the content. In one exemplary configuration, the geographical region server  114  includes at least one processor  302  and a memory  304 . The geographical region server  116  may also include additional removable storage  306  and/or non-removable storage  308 . 
     Turning to the contents of the memory  304  in more detail, the memory  304  may store an operating system  310 , the server-side geographical region module  116 , a geographical region user interface module  312 , and one or more applications for implementing all or a part of the searching geographical region services. The geographical region user interface module  312  facilitates a representation of the geographical regions with POIs similar to the user-specified query region on a display of a user interface to receive selections from the user  106 . The server-side geographical region module  114  and the geographical region UI module  312  may be stored on the geographical region server  114 , in addition to or instead of the individual computing device  102 . 
     The memory  304  in this implementation may also include a quadtree module  314 , an extraction spatial logic  316 , a pruning logic  318 , a content storage  320 , and a communication connection(s)  322 . 
     The quadtree module  314  provides a heuristic region search approach. The quadtree module  314  partitions the spatial map into a hierarchical structure and builds a quadtree structure for quick retrieval of POIs. The quadtree module  314  uses the index structures to perform region search queries efficiently. Given a user-specified query, the process analyzes a shape and a size of the user-specified region and determines an appropriate quadtree layer to initiate the similar region search process. A detailed discussion of the quadtree follows in  FIG. 4  with an illustration in  FIG. 7 . 
     Once the starting level of the quadtree and the representative categories of the region are known, a prune-and-refine procedure occurs to remove the search space that is unlikely to be in the top-K most similar regions. The extraction spatial logic  316  extracts the representative categories from the search region. Occurring about the same time as the quadtree module  314  interacting, the extraction spatial logic  316  may compute category frequency values for each category on the user-specified query region and may maintain the top-m categories with the largest category frequency values. 
     The pruning logic  318  works in conjunction with the quadtree module  314 . The pruning logic  318  effectively prunes the region by storing key statistical information at each node in the quadtree structure. Each node maintains a lower bound and an upper bound which are useful for pruning the candidate regions by the pruning logic  318 . 
     The content storage  320  provides suitable storage options for the content based at least in part on storing representative categories for points of interests on the spatial map. The content stored may include representative categories identified through: spatial objects, published telephone listings, zip codes, city information, graphical representation of the set of geographical coordinates, and the like. The content storage  320  may also manage storage options for the content, such as the content from the computing device  102 , the content stored in the content storage  210 , and the content stored in the server-side content storage  320 . 
     The server  114  may also contain communications connection(s)  322  that allow the processor  302  to communicate with the computing device  102 , other network servers, network storage, and/or other devices on the network(s)  104 . The server  114  may also include one or more known input device(s), such as a keyboard, mouse, pen, voice input device, touch input device, etc., and output device(s), such as a display, speakers, printer, etc. All these devices are well known in the art and are not discussed at length here. 
     Any memory described herein may include volatile memory (such as RAM), nonvolatile memory, removable memory, and/or non-removable memory, implemented in any method or technology for storage of information, such as computer-readable instructions, data structures, applications, program modules, emails, and/or other content. Also, any of the processors described herein may include onboard memory in addition to or instead of the memory shown in the figures. The memory may include storage media such as, but not limited to, random access memory (RAM), read only memory (ROM), flash memory, optical storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by the respective systems and devices. 
     The geographical region server as described above may be implemented in various types of systems or networks. For example, the geographical region server may be a part of, including but is not limited to, a client-server system, a peer-to-peer computer network, a distributed network, an enterprise architecture, a local area network, a wide area network, a virtual private network, a storage area network, and the like. 
     Illustrative Processes 
       FIGS. 4 and 8  are flowcharts showing illustrative processes for performing a search for geographical regions with POIs that are similar to a user-specified region.  FIG. 4  is a flowchart based on at least in part on identifying the POIs, building a quadtree, and identifying the representative categories.  FIG. 8  is a flowchart based on at least in part on a user-specified region, performing representative categories pruning and spatial feature pruning, and recommending the top geographical regions with similar POIs. The processes are illustrated as a collection of blocks in logical flowcharts, which represent a sequence of operations that can be implemented in hardware, software, or a combination. For discussion purposes, the processes are described with reference to the computing environment  100  shown in  FIG. 1 , the computing device  102  shown in  FIG. 2 , and/or the geographical region server  114  shown in  FIG. 3 . However, the processes may be performed using different environments and devices. Moreover, the environments and devices described herein may be used to perform different processes. 
     For ease of understanding, the methods  400  and  800  are delineated as separate steps represented as independent blocks in  FIGS. 4 and 8 . However, these separately delineated steps should not be construed as necessarily order dependent in their performance. The order in which the process is described is not intended to be construed as a limitation, and any number of the described process blocks maybe be combined in any order to implement the method, or an alternate method. Moreover, it is also possible that one or more of the provided steps will be omitted. 
       FIG. 4  is a flowchart  400  based on at least in part on identifying the POIs, building a quadtree, and identifying the representative categories. As shown in  402 , the process  400  identifies POIs on the spatial map from POIs database. The POIs database may use information retrieved from including but not limited to: published telephone information with categories, zip code information, area code information, and the like. The entities in the POIs database that are within the query region are processed. The process may check the global position satellite (GPS) positions of each entities. 
     Equations used for the process are described below. An equation illustrates the search functionality and recommends geographical regions with similar content information. Using the spatial map, a query region Rq, two coefficients to control an area of a region u 1  and u 2 , the process finds the top-k most similar regions to Rq on the spatial map. The equation to find the area Ri is: 
     
       
         
           
             
               μ 
               1 
             
             ≤ 
             
               
                 Area 
                  
                 
                   ( 
                   
                     R 
                     i 
                   
                   ) 
                 
               
               
                 Area 
                  
                 
                   ( 
                   
                     R 
                     q 
                   
                   ) 
                 
               
             
             ≤ 
             
               
                 μ 
                 2 
               
               . 
             
           
         
       
     
     Ri is a return region or in a set of candidates and that any two regions do not have a large overlap. An expected size of returned similar regions may satisfy the following inequality:
         a* size of original region=&lt;size of returned region&lt;=b* size of original region. For example, a may be 0.7, b may be 1.3. These parameters may ensure the size of the returned regions are similar to the query region.       

     In an equation, P is the spatial map, and T is a set of POI categories, such that T={C 1 , C 2 , . . . C K }. Each POI may be labeled with multiple POI categories. For example, a building is labeled both as a cinema and a restaurant, if the building houses a cinema and has at least one restaurant inside. 
     In another equation, the POI database D is a set of POIs. Each POI, o in D is presented by a tuple o=&lt;p o ; To&gt;, where p o =(x o , y o ) denotes the location of o, and T o  is the set of o&#39;s POI categories. The process uses |C i | to denote the number of POI tuples with category C i . Thus the number of POI tuples with category may be represented as: 
       |C i |=|{o|Γ o =C i }∥
 
     A region RεP is a spatial rectangle bounded by 
     [Rx min ,Rxmax]×[Ry min ,Ry max ] A POI o {po|Γo} is believed to have occurred in region R if p o :εRD={o|p o  εRΛΓoεC i } is a set of objects with category Ci occurring in region R. 
     In block  404 , the process calculates the Category Frequency (CF) of the category Ci in region Rj, may be denoted as CF i;j . This is the fraction of the number of POIs with category Ci occurring in region Rj to the total number of POIs in region Rj, shown as: 
     
       
         
           
             
               CF 
               
                 i 
                 , 
                 j 
               
             
             = 
             
               
                 n 
                 
                   i 
                   , 
                   j 
                 
               
               
                 
                   ∑ 
                   
                     p 
                     = 
                     1 
                   
                   K 
                 
                  
                 
                     
                 
                  
                 
                   n 
                   
                     p 
                     , 
                     j 
                   
                 
               
             
           
         
       
         
         
           
             where ni;j is the points number of category Ci in region R j . The relevance of a category Ci depends on the distribution of POIs with category Ci on the entire map. These equations are used to identify the category frequency of the category in the region. 
           
         
       
    
     In block  406 , the process partitions the spatial map into grids (or regions) by imposing a g x ×g y  grid on the spatial map. The Inverse Region Frequency (IRF) of category Ci, may be denoted as IRFi. The IRF is a logarithm of a fraction of a total number of grids to a number of grids that contain POIs with category Ci. Shown is the equation for Inverse Region Frequency as: 
     
       
         
           
             
               IRF 
               i 
             
             = 
             
               log 
                
               
                 
                   
                     
                       g 
                       x 
                     
                     × 
                     
                       g 
                       y 
                     
                   
                   
                      
                     
                       { 
                       
                         
                           D 
                           i 
                           
                             R 
                             j 
                           
                         
                          
                         
                           
                             D 
                             i 
                             
                               R 
                               j 
                             
                           
                           ≠ 
                           ∅ 
                         
                       
                       } 
                     
                      
                   
                 
                 . 
               
             
           
         
       
     
     With CF and IRF calculated, the significance of a category in region R j , may be denoted as CF-IRF i,j . This equation identifies the representative categories by: 
     
       
      
       CF−IRF 
       i,j 
       =CF 
       i,j 
       ×IRF 
       i  
      
     
     Furthermore, a CFIRF vector space model represents each region by a set of representative categories&#39; CFIRF values. The information content of a candidate region, Ri and the query region, Rq, may be represented by vectors. The vector representations may be shown as: 
       {right arrow over ( R   l )}=( w   1,l   ,w   2,l   , . . . ,w   K,l ) 
       {right arrow over ( R   q )}=( w   2,q   ,w   2,q   , . . . ,w   K,q ) 
     where w h,1  and w k,q  are the CFIRF feature values of category C k  in regions Ri and Rq, respectively. Furthermore, ω=CF−IRF may be used. 
     The CF-IRF identifies the representative categories of a region including the query region and grid regions to be searched. When identifying the representative categories of the query region, the process determines a corresponding level of the quad-tree where the query should be searched. After the quadtree level is determined, the number of grids on the level is known and the CF-IRF may be calculated. The top m categories with relatively large CF-IRF values may be selected as the representative categories, where m is a predefined parameter. 
     The information content similarity of two regions, Ri and Rj, is the cosine similarity of the corresponding feature vectors of Ri and Rj. The spatial vector space model (SVSM) ranks the regions according to their cosine similarity measures, described as: 
     
       
         
           
             
               Sim 
                
               
                 ( 
                 
                   
                     R 
                     i 
                   
                   , 
                   
                     R 
                     j 
                   
                 
                 ) 
               
             
             = 
             
               
                 cos 
                  
                 
                   ( 
                   
                     
                       
                         R 
                         i 
                       
                       → 
                     
                     , 
                     
                       
                         R 
                         j 
                       
                       → 
                     
                   
                   ) 
                 
               
               = 
               
                 
                   
                     
                       
                         R 
                         i 
                       
                       → 
                     
                     · 
                     
                       
                         R 
                         j 
                       
                       → 
                     
                   
                   
                     
                        
                       
                         
                           R 
                           i 
                         
                         → 
                       
                        
                     
                     × 
                     
                        
                       
                         
                           R 
                           j 
                         
                         → 
                       
                        
                     
                   
                 
                 . 
               
             
           
         
       
         
         
           
             Using the equation shown above, the vector space model regards regions having similar CFIRF category values to be similar and ranks the regions according to their cosine similarity measures. 
           
         
       
    
     In block  408 , after partitioning the spatial map of this database, the process builds a hierarchical quadtree structure to facilitate the construction of multi-scale regions. In the quadtree, the root node denotes the map and each non-leaf node corresponds to one of the four partitioned cells from its parent&#39;s cell. At the lowest level, each leaf node corresponds to the partitioned cell with the smallest granularity. 
     The quadtree structure enables the efficient handling of multi-granularity similar region queries. This is because the process may adaptively select the different levels of granularity by accessing the quadtree nodes at an appropriate level. 
     From the quadtree  408 , the process moves to the right to apply category indexing as shown in block  410 . Category indexing may be used to conducting a search by indexing a particular category. This may be used as input for a layer selection in  FIG. 8 . From here, the process proceeds to block  412 . 
     In block  412 , the process constructs an inverted tree index on the representative categories to facilitate similar region search. The root node of the inverted tree has K entries, where each entry corresponds to a category. Each category, say Ci, of a non-leaf node is associated with a child node that has four entries. The entry value is 1 if the corresponding partitioned region has the Ci as a representative category; otherwise the entry value will be 0. This inverted list tree is recursively built until it reaches a leaf node of the quadtree structure or all four entries have value 0. Based on this inverted tree index, the process may quickly identify the cells that have similar categories to the query region. The inverted tree  412  is used as input for category-based pruning in  FIG. 8 . 
     In block  414 , the process identifies representative categories of a region for the query region and grid regions to be searched. Based on determining the number of grids in the level described above, the process moves to identify whether these are representative categories. The process determines the corresponding level of quad-tree where the geographical regions should be searched. Once this level of quad-tree is determined, the number of grids on each level is known to calculate the CF-IRF. 
     In block  416 , the process extracts spatial features from the representative categories. The process allows effective region pruning by storing the key statistical information at each node in the quadtree. Each node maintains the lower bound and upper bound of feature entries. The feature entries are defined as the lower bound feature vector of a node B, denoted as Blb, is (f1, lb, f2, lb, . . . fn, lb), where fi,lb is the minimum i-th feature entry of all descendant nodes of B. The upper bound feature vector of a node B, denoted as Bub, is (f1, ub, f2, ub, fn, ub) where fi, ub is the maximum i-th feature value of all descendant nodes of B. 
     Depending on the similarity measure that is adopted, the bounds may be one of the following:
         min(Ci)/max(Ci): The minimum/maximum number of POIs of category Ci in the region corresponding to node B;   min(h(Ci; Cj)Imax(h(Ci; CA): The minimum/maximum mutual distance of category pair Ci and Cj in the region corresponding to node B;   min(Ii)/max(i): The minimum/maximum reference distance vector of representative categories in the region corresponding to node B;
 
These bounds are useful for pruning the candidate regions as stated in Lemma 1 shown below.
       

     Lemma 1: Let {right arrow over (R q )}=(f 1,q ,f 2,q , . . . , f n,q ) to be the feature vector of query region, σ to be the cosine similarity threshold of top-k regions. A node B can be pruned if for any feature entry fi,q, there is 
     
       
         
           
             
               
                 f 
                 
                   i 
                   , 
                   ub 
                 
               
               · 
               
                 f 
                 
                   i 
                   , 
                   q 
                 
               
             
             ≤ 
             
               
                 δ 
                 n 
               
               · 
               
                  
                 
                   
                     B 
                     → 
                   
                   lb 
                 
                  
               
               · 
               
                 
                    
                   
                     
                       R 
                       q 
                     
                     → 
                   
                    
                 
                 . 
               
             
           
         
       
     
     Proof: Let fi;j to be the i-th feature entry of region Rj where R i εB. Then fi,lb≦fi,j≦fi,ub and |{right arrow over (B)} lb |≦|{right arrow over (R j )}|≦|{right arrow over (B)} ub |. Assume that: 
     
       
         
           
             
               
                 f 
                 
                   i 
                   , 
                   ub 
                 
               
               · 
               
                 f 
                 
                   i 
                   , 
                   q 
                 
               
             
             ≤ 
             
               
                 δ 
                 n 
               
               · 
               
                  
                 
                   
                     B 
                     → 
                   
                   lb 
                 
                  
               
               · 
               
                 
                    
                   
                     
                       R 
                       q 
                     
                     → 
                   
                    
                 
                 . 
               
             
           
         
       
     
     For the i-th feature entry fi,j, the process has 
     
       
         
           
             
               
                 f 
                 
                   i 
                   , 
                   j 
                 
               
               · 
               
                 f 
                 
                   i 
                   , 
                   q 
                 
               
             
             ≤ 
             
               
                 f 
                 
                   i 
                   , 
                   ub 
                 
               
               · 
               
                 f 
                 
                   i 
                   , 
                   q 
                 
               
             
             ≤ 
             
               
                 δ 
                 n 
               
               · 
               
                  
                 
                   
                     B 
                     → 
                   
                   lb 
                 
                  
               
               · 
               
                  
                 
                   
                     R 
                     q 
                   
                   → 
                 
                  
               
             
             ≤ 
             
               
                 δ 
                 n 
               
                
               
                 
                    
                   
                     
                       R 
                       j 
                     
                     → 
                   
                    
                 
                 · 
                 
                   
                      
                     
                       
                         R 
                         q 
                       
                       → 
                     
                      
                   
                   . 
                 
               
             
           
         
       
     
     By summing up the inequalities, the process shows: 
       {right arrow over ( R   j )}·{right arrow over ( R   q )}=Σ o=1   n   f   p,j   ·f   p,q ≦δ·|{right arrow over ( R   j )}|·|{right arrow over ( R   q )}|
 
     Based on this, cos({right arrow over (R j )},{right arrow over (R q )})≦δ, which means that any region Rj under B will not have a larger similarity than the top-k region similarity threshold. 
     With Lemma 1, the process may prune all node B that have no chance of satisfying the similarity threshold δ. For example, suppose the quadtree node B has four child nodes, B 1 , B 2 , B 3 , and B 4 . Each feature vector of child node has five entries. 
       {right arrow over ( B   1 )}=(0.1,0.3,0.1,0.8,0.0) 
       {right arrow over ( B   2 )}=(0.1,0.7,0.2,0.7,0.0) 
       {right arrow over ( B   3 )}=(0.0,0.3,0.1,0.8,0.2) 
       {right arrow over ( B   4 )}=(0.2,0.4,0.2,0.6,0.1) 
     The process has {right arrow over (B)} lb =(0.0, 0.3, 0.1, 0.6, 0.0) and {right arrow over (B)} ub =(0.2, 0.7, 0.2, 0.8, 0.2). Let the feature vector of query region is {right arrow over (R q )}=(0.9, 0.1, 0.9, 0.1, 0.8) and δ=0.95. The result is 
     
       
         
           
             
               
                 δ 
                 n 
               
               · 
               
                  
                 
                   
                     B 
                     → 
                   
                   lb 
                 
                  
               
               · 
               
                  
                 
                   
                     R 
                     q 
                   
                   → 
                 
                  
               
             
             = 
             
               0.2468 
               . 
             
           
         
       
     
     Thus, the node B can be pruned because each feature entry product of{right arrow over (R q )} and {right arrow over (B)} ub  is less than 0.2468. 
     Block  418  calculates feature bounds which helps speed up the search. Once the feature bounds are identified, this may be applied in category-based pruning in  FIG. 8 . 
       FIG. 5  is a schematic showing illustrative spatial distributions with representative categories  500 . The illustrations  500  represent geometric properties (i.e., scales and shapes), content properties (i.e., POIs categories and representative categories), and spatial properties (i.e., distribution of POIs of representative categories and reference points). As mentioned previously, similarity measure determines whether the regions are similar. 
     In this implementation, restaurants may be represented by triangles, stores may be represented by circles, and theatres may be represented by stars. An example of a query region is shown in  502  with restaurants, stores, and a theatre closely distributed. 
     Shown along  504  are spatial distributions of restaurants, stores, and theatres in a) a shopping mall and b) a shopping street. This illustrates common representative categories of restaurants, stores, and theatres. However, the two illustrations show different scales, such as a small scale for the shopping mall while a large scale for the shipping street. Furthermore, the spatial distributions of the shopping mall and the shopping street are very different as the distributions of the POIs for each category are drastically different in the two figures. Thus, the shopping mall and the shopping street are not similar. However, the shopping mall is similar to the query region  502  and would be selected as having common representative categories, common size and scale, and common spatial distributions. 
     Shown along  506  are spatial distributions of restaurants, stores, and theatres in a c) living area and in an d) university town. This illustrates the living area and the university town are not similar because the overlap in their common categories is only 2 out of 3. The common categories are restaurants represented by triangles and stores represented by circles. There are no theatres represented by stars but includes rectangles. Furthermore, there are different shapes, the living area is in a small rectangle while the university town would include multiple rectangles. These spatial distributions of the POIs corresponding to the representative categories may be differentiated by the spatial vector space model. To minimize the effects of scaling and to allow for rotation invariant, the process uses two features to capture the spatial distributions of these POIs: mutual distance vector and reference distance vector. 
       FIG. 6 a    is a diagram showing illustrative mutual distance vectors  600 . The mutual distance vector  600  represents a mutual distance between two sets of POIs, P and Q. The mutual distance between P and Q is an average distance of all the points in P to the nearest point of Q. Vectors  600  show the nearest neighbor distances from P to Q (shown in dash lines), such as P 1  to Q 1 , P 2  to Q 1 , and P 3  to Q 2 . Vectors  600  also show the nearest neighbor distances from Q to P (shown in solid lines), such as Q 1  to P 1 , Q 3  to P 3 , and Q 2  to P 3 . In this example, the mutual distance h(P;Q) is the average distance of dash lines and h(Q; P) is the average distance of solid lines. 
     Shown below is an equation to measure the mutual distance of h(P;Q): 
     
       
         
           
             
               h 
                
               
                 ( 
                 
                   P 
                   , 
                   Q 
                 
                 ) 
               
             
             = 
             
               
                 1 
                 
                    
                   P 
                    
                 
               
                
               
                 
                   ∑ 
                   
                     p 
                     ∈ 
                     P 
                   
                 
                  
                 
                     
                 
                  
                 
                   
                     min 
                     
                       q 
                       ∈ 
                       Q 
                     
                   
                    
                   
                       
                   
                    
                   
                     dist 
                      
                     
                       ( 
                       
                         p 
                         , 
                         q 
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     where dist(p,q) is the Euclidean distance function. 
     A small mutual distance of h(P;Q) means that all the POIs in sets P and Q are close. The mutual distance is also consistent with the Hausdorff distance, which is a widely used distance function in pattern recognition. 
     A region R can be characterized by the mutual distances among the sets of POIs in R. Given K number of representative categories, R can be represented as a vector of K2 entries, denoted as {right arrow over (H R )}=(h 11 , h 12 , . . . , h KK ), where hij is the mutual distance of the set of POIs in R with category Ci to the set of POIs in R with category Cj. 
     Note that the mutual distance is an asymmetric metric, i.e., h(P,Q)≠h(Q,P). The process may also measure the closeness within a set of POIs of the same category, say P={p 1 , p 2 , . . . , p m } as follows: 
     
       
         
           
             
               h 
                
               
                 ( 
                 
                   P 
                   , 
                   P 
                 
                 ) 
               
             
             = 
             
               
                 1 
                 
                    
                   P 
                    
                 
               
                
               
                 
                   ∑ 
                   
                     
                       p 
                       i 
                     
                     ∈ 
                     P 
                   
                 
                  
                 
                   
                     min 
                     
                       
                         pj 
                         ∈ 
                         P 
                       
                       , 
                       
                         j 
                         ≠ 
                         i 
                       
                     
                   
                    
                   
                     
                       dist 
                        
                       
                         ( 
                         
                           
                             p 
                             i 
                           
                           , 
                           
                             q 
                             j 
                           
                         
                         ) 
                       
                     
                     . 
                   
                 
               
             
           
         
       
         
         
           
             As mentioned above, a small mutual distance of h(P;P) implies that the POIs of P are close to each other. On the other hand, a large h(P;P) means that the POIs of P have a sparse distribution. 
           
         
       
    
     While the mutual distance vector  600  accurately captures the spatial distribution among the POIs of different categories in a region R, it has been observed that most users tend to use some reference points for determining region similarity. With this in mind, the process captures the spatial distributions of the POIs with respect to a set of reference points. This is based on the observation that users usually compare the distribution by the distances between the POIs and the region icons or corners. 
       FIG. 6 b    is a diagram showing illustrative reference distance vectors  602 . Shown are five reference points, O 1 , O 2 , O 3 , O 4 , O 5 , four corners, and the center, as the reference set.  FIG. 6B  illustrates the five reference points and the distances of two POIs, P and Q, to the reference set. 
     The similarity of regions is determined by the similarity of feature vector sets. Given two regions Ri and Rj and their feature vector sets I R     i   ={{right arrow over (I 1,i )}, . . . , {right arrow over (I c,i )}} and i R     j   ={{right arrow over (I 1,j )}, . . . , {right arrow over (I c,j )}} the similarity is computed by selecting the best similar feature vector from I R     j    for each feature vector in I R     i   , and compute the average similarity value. The reference distance is an average distance of all the points in P/Q to each of the reference points. Given a region R, a set of POIs P, and a set of reference points O={O 1 , O 2 , O 3 , . . . O 4 }. The distance of P to the i-th reference point o i εO is measured by: 
     
       
         
           
             
               r 
                
               
                 ( 
                 
                   P 
                   , 
                   
                     o 
                     i 
                   
                 
                 ) 
               
             
             = 
             
               
                 1 
                 
                    
                   P 
                    
                 
               
                
               
                 
                   ∑ 
                   
                     p 
                     ∈ 
                     P 
                   
                 
                  
                 
                   
                     dist 
                      
                     
                       ( 
                       
                         p 
                         , 
                         
                           o 
                           i 
                         
                       
                       ) 
                     
                   
                   . 
                 
               
             
           
         
       
     
     Assume region R has K different categories of POIs. The process uses ri,j to denote the distance of POIs with category Ci to the reference point Oi. The distance of K categories to the reference point Oi is a vector of K entries, shown below: 
       {right arrow over ( I   i )}=( r   1,i   ,r   2,i   , . . . ,r   K,i )         The distance of K categories to the reference set O is a set of vectors, shown as:       
       I={{right arrow over (I 1 )}, . . . ,{right arrow over (I c )}} 
     The selection of reference points is application dependent. The process may need at least reference points to uniquely determine a position on the spatial plane. The larger number of reference points will give a more accurate representation of the spatial distributions among the POIs, while incurring more computational cost. 
       FIG. 7  illustrates an exemplary quadtree  700  and an exemplary inverted list  702  for a process similar to the one described  FIG. 4 . The quadtree  700  and the inverted list  704  partitions geographical spaces into grids based on the quadtree. Each quadtree node stores the features bound of its four adjacent children. The feature bound is calculated in a bottom-up manner. 
     For example, the shadowed areas in the quadtree  700  correspond to the shadowed nodes in the inverted list  702 . In the first level, shadow area  1  in quadtree  700  corresponds to the shadow area  1  in the inverted list  702 . In the second level, shadow areas  12  and  13  in the quadtree  700  corresponds to 1,1, in the inverted list  702 . 
     A search strategy is described based on the quadtree structure. Given a query region, the process adjusts the search granularity on the quadtree based on the query region by accessing the lowest level of the quadtree. The lowest level of the quadtree has an area that is greater than μ 1 ×area(R q ). 
     An algorithm, algorithm 1 is shown below to give an illustration of the region search. The purpose is to select a bucket of level lsearch in the quadtree as a seed and gradually expand this bucket to a region of suitable shape and large similarity value. 
     
       
         
           
               
             
               
                   
               
               
                 Algorithm 1: RegionSearch(R q , T, s, k) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   input : 
                 Query region R q ; 
               
               
                   
                   
                 Quadtree T; 
               
               
                   
                   
                 Number of return regions s; 
               
               
                   
                   
                 Number of representative categories m. 
               
               
                   
                   output: 
                 Top-k similar regions 
               
            
           
           
               
               
            
               
                   
                  1 Compute the search level l search  on T based on R q ; 
               
               
                   
                  2 CM = ExtractCategory(R q ); 
               
               
                   
                  3 Adjust({right arrow over (R)} q , CM); 
               
               
                   
                  4 R =  |; 
               
               
                   
                  5 δ = 0; 
               
               
                   
                  6 SearchQTree({right arrow over (R)} q , T.root, δ, R); 
               
               
                   
                  7 return R i   
               
               
                   
                  8 Procedure SearchQTree(R q , B, δ, R, CM) 
               
               
                   
                  9 if B has CM catagories    B cannot be primed by 
               
               
                   
                   Lemma 1 then 
               
            
           
           
               
               
               
            
               
                   
                 10  | 
                 if B level &lt; l search  then 
               
            
           
           
               
               
               
               
            
               
                   
                 11  | 
                  | 
                 foreach child node B′ ∈ B do 
               
               
                   
                 12  | 
                  | 
                  |_SearchQTree(R q , B′, δ, R); 
               
            
           
           
               
               
               
            
               
                   
                 13  | 
                 else 
               
            
           
           
               
               
               
               
            
               
                   
                 14  | 
                  | 
                 R =RegionExpansion(R q , B′); 
               
               
                   
                 15  | 
                  | 
                 R = R ∪ R; 
               
               
                   
                 16  | —   
                  | —   
                 update δ; 
               
            
           
           
               
               
            
               
                   
                 17 Function RegionExpansion(R q ,R) 
               
               
                   
                 18 repeat 
               
            
           
           
               
               
               
            
               
                   
                 19  | 
                 foreach dir ∈ {LEFT, RIGHT, DOW N, U P} do 
               
            
           
           
               
               
               
               
            
               
                   
                 20  | 
                  | 
                 R″ = expand(R, dir); 
               
               
                   
                 21  | 
                  | —   
                 dir = arcmax( Sim(R q ,R″)); 
               
            
           
           
               
               
               
            
               
                   
                 22  | 
                 R′ = expand(R, dir); 
               
            
           
           
               
               
            
               
                   
                 23 until Sim (R q , R) ≦ Sim(R q , R′); 
               
               
                   
                 24 return R′ 
               
               
                   
                   
               
            
           
         
       
     
     Line 1 computes the proper search level on the quadtree T. The bucket of search level will be greater than the minimal area of returned regions. Line 2 extracts the representative categories from the search region Rq. The function ExtractCategory computes the CFIRF values for each category on Rq and only maintains the top-m categories with the largest CFIRF values. Line 3 adjusts the feature vector of Rq. If the feature vectors are category CFIRF vectors or reference feature vectors, the entries which correspond to the top-m representative categories remains and the other entries are set to be zero. If the feature vector are mutual influence feature vector, the entries which correspond to the top-m representative category pairs remain and the other entries are set to zero. 
     Line 4 and Line 5 initialize the return region set to be an empty set and the similarity threshold δ to be 0. Line 6 calls procedure SearchQTree to find and to prune the candidate regions. Line 9 of Algorithm 1 is the validity checking for the top-k regions. A bucket is valid only if 1) it contains the CM representative categories, and 2) it cannot be pruned by Lemma 1. The inverted tree structure and the feature bounds of buckets facilitate the validity checking. If a bucket is valid, this bucket may contain at least one top-k similar region, which means that its child nodes need to be processed further. 
     Line 13 recursively calls the procedure to process the child node if has a depth less than lsearch. Otherwise, the process may stop at the level of/search because the buckets at the lower levels are too small to be candidate regions. Line 14 expands the bucket of lsearch by calling the function RegionExpansion. Line 15 inserts the expanded region R to the top-k region set R. If R has no overlap with the existing top-k regions, R is inserted into R. Note that R only maintains k regions which have the largest cosine similarity values. Line 16 updates the similarity threshold I based on k-th largest similarity value in R. 
     Lines 17-24, the RegionExpansion function treats a region as a seed and tries to expand the seed in four candidate directions, and selects the optimal expanded region which give the largest similarity value. The step width of each expansion is the cell side of the quadtree leaf node in order to minimize the scope of expansion, which eventually approach the local most similar region. The expansion is repeatedly performed till there is no increase in the similarity value (Line 23). Finally, Line 7 returns the top-k regions. If the number of regions in R is less than k, the process may decrease the value of m by 1 in Line 9, and search the cells which share exact m i 1 common representative categories and do not pruned by Lemma 1. The process repeatedly decreases the m value by 1 till the number of return regions in R reaches k. 
       FIG. 8  is a flowchart illustrating an exemplary process  800  of searching to recommend the geographical regions having the top similar scores from the set of candidates that are similar to the user-specified region. To search and to provide recommendations of geographical regions with similar POIs to the user-specified region, the process looks for properties that are similar. The process measures properties based on at least on geometric properties (i.e., scales and shapes), content properties (i.e., POI categories and representative categories), and spatial properties (i.e., distribution of POIs of representative categories and reference points). 
     At block  802 , the query region or the user-specified region is identified or selected by the user  106 , by highlighting the query region on the spatial map. In an implementation, the user  106  may specify the POIs by drawing a rectangle around the query region on the spatial map. The region highlighted within the rectangle is the user-specified region or the query region. For example, the user is travelling in Seattle, Wash., accesses the spatial map for Seattle, and selects sights or attractions specific to the Seattle region, such as the Space Needle. The user-specified region with the POI is the Space Needle, which may be highlighted by a red color rectangle. The process may retrieve similar POIs in the geographic region on the spatial map, identifying the geographical regions with the top most similar scores. The process searches and recommends sights or attractions specific to the Seattle region, such as the Pike Place Market, the Waterfront, the Woodland Park Zoo, the Seattle Art Museum, and the like. The POIs in the geographical region that are similar in content to the POIs in the user-specified region may be shown with blue lines around them. 
     In block  804 , the process detects the representative categories based on using the equations described above in  404  and  406  to calculate category frequency CF, inverse region frequency IRF, and significance of a category in a region CF-IRF. For convenience, the equations are reproduced below: 
     
       
         
           
             
               CF 
               
                 i 
                 , 
                 j 
               
             
             = 
             
               
                 n 
                 
                   i 
                   , 
                   j 
                 
               
               
                 
                   ∑ 
                   
                     p 
                     = 
                     1 
                   
                   K 
                 
                  
                 
                     
                 
                  
                 
                   n 
                   
                     p 
                     , 
                     j 
                   
                 
               
             
           
         
       
       
         
           
             
               IRF 
               i 
             
             = 
             
               log 
                
               
                 
                   
                     g 
                     x 
                   
                   × 
                   
                     g 
                     y 
                   
                 
                 
                    
                   
                     { 
                     
                       
                         D 
                         i 
                         
                           R 
                           j 
                         
                       
                        
                       
                         
                           D 
                           i 
                           
                             R 
                             j 
                           
                         
                         ≠ 
                         ∅ 
                       
                     
                     } 
                   
                    
                 
               
             
           
         
       
       
         
           And 
         
       
       
         
           
             
               CF 
                
               
                 - 
               
                
               
                 IRF 
                 
                   i 
                   , 
                   j 
                 
               
             
             = 
             
               
                 CF 
                 
                   i 
                   , 
                   j 
                 
               
               × 
               
                 IRF 
                 i 
               
             
           
         
       
     
     In block  806 , a layer selection receives input from the category indexing  410 . The layer selection  806  analyzes a shape and a size of the user-specified region and determines an appropriate quadtree layer to initiate the similar region search process. During this time, the process computes the CFIRF values to derive the representative categories of the user-specified region. Thus, the layer selection  806  identifies the quadtree layer based on the information received from the user-specified region and the category index information. Once the starting level of the quadtree and the representative categories of the user-specified region are known, a prune-and-refine procedure may reduce the search space that is not likely to be in the top-k most similar geographical regions. 
     Turning to block  808 , the process performs representative categories pruning on the set of candidates. Representative category-based pruning includes receiving input of the representative categories and information from the quadtree layer along with content received from the inverted tree list  412  and feature bounds  418 . The category-based pruning determines there is some overlap of representative categories with the user-specified region. 
     The process performs category-based pruning  808  on the set of candidates. For example, a candidate region may have some overlaps of representative categories with the query region. An equation to determine overlap based at least in part on cosine similarity. For pruning, the cosine similarity should exceed a threshold, as shown in the equation below: 
     
       
         
           
             
               Cosine 
                
               
                 ( 
                 
                   
                     
                       R 
                       j 
                     
                     → 
                   
                   , 
                   
                     
                       R 
                       q 
                     
                     → 
                   
                 
                 ) 
               
             
             = 
             
               
                 
                   
                     
                       R 
                       j 
                     
                     → 
                   
                   · 
                   
                     
                       R 
                       q 
                     
                     → 
                   
                 
                 
                   
                      
                     
                       R 
                       j 
                     
                      
                   
                   · 
                   
                      
                     
                       R 
                       q 
                     
                      
                   
                 
               
               &lt; 
               δ 
             
           
         
       
     
     Block  810  performs spatial feature-based pruning. For spatial feature-based pruning  810 , the equations to consider are: 
     
       
         
           
             
               cosine 
                
               
                 ( 
                 
                   
                     
                       h 
                       j 
                     
                     ⇀ 
                   
                   , 
                   
                     
                       h 
                       q 
                     
                     ⇀ 
                   
                 
                 ) 
               
             
             = 
             
               
                 
                   
                     
                       h 
                       j 
                     
                     ⇀ 
                   
                   · 
                   
                     
                       h 
                       q 
                     
                     ⇀ 
                   
                 
                 
                   
                      
                     
                       
                         h 
                         j 
                       
                       ⇀ 
                     
                      
                   
                   · 
                   
                      
                     
                       
                         h 
                         q 
                       
                       ⇀ 
                     
                      
                   
                 
               
               &lt; 
               δ 
             
           
         
       
       
         
           
             
               cosine 
                
               
                 ( 
                 
                   
                     
                       I 
                       j 
                     
                     ⇀ 
                   
                   , 
                   
                     
                       I 
                       q 
                     
                     ⇀ 
                   
                 
                 ) 
               
             
             = 
             
               
                 
                   
                     
                       I 
                       j 
                     
                     ⇀ 
                   
                   · 
                   
                     
                       I 
                       q 
                     
                     ⇀ 
                   
                 
                 
                   
                      
                     
                       
                         I 
                         j 
                       
                       ⇀ 
                     
                      
                   
                   · 
                   
                      
                     
                       
                         I 
                         q 
                       
                       ⇀ 
                     
                      
                   
                 
               
               &lt; 
               
                 δ 
                 . 
               
             
           
         
       
     
     As mentioned earlier, the pruning process may be sped up based on Lemma
         1. For brevity, Lemma 1 will not be reproduced here but the discussion follows as discussed in  416 .       

     Block  812  expands the region. The process selects the seeds regions that do not need to be pruned. The process expands the seed regions using the functionality shown below: 
     
       
         
           
               
               
             
               
                   
                   
               
             
            
               
                   
                 Function RegionExpansion(R q ,R) 
               
               
                   
                 repeat 
               
            
           
           
               
               
               
            
               
                   
                  | 
                 foreach dir ∈ {LEFT, RIGHT, DOWN, UP} do 
               
            
           
           
               
               
               
               
            
               
                   
                  | 
                  | 
                 R″ = expand(R, dir); 
               
               
                   
                  | 
                  | —   
                 dir = arcmax( Sim(R q ,R″)); 
               
            
           
           
               
               
               
            
               
                   
                  | 
                 R′ = expand(R, dir); 
               
            
           
           
               
               
            
               
                   
                 until Sim(R q , R) ≦ Sim(R q , R′); 
               
               
                   
                 return R′ 
               
               
                   
                   
               
            
           
         
       
     
     Block  814  provides recommendations for the top ranking geographical regions that have similar content information to the user-specified region. 
     In another implementation, the user may specify an area that is considered an area identified for a particular disease. Based on the user-specified area for this area, the process may identify the areas that are prone to the particular disease. Thus, travelers may desire to avoid areas that may be prone to this particular disease or potential to breakouts. 
     As discussed above, certain acts in processes  400  and  800  need not be performed in the order described, may be modified and/or may be omitted entirely, depending on the circumstances. Various instructions, methods, techniques, applications, and modules described herein may be implemented as computer-executable instructions that are executable by one or more computers, servers, or telecommunication devices. Generally, program modules include routines, programs, objects, components, data structures, etc. for performing particular tasks or implementing particular abstract data types. These program modules and the like may be executed as native code or may be downloaded and executed, such as in a virtual machine or other just-in-time compilation execution environment. The functionality of the program modules may be combined or distributed as desired in various implementations. An implementation of these modules and techniques may be stored on or transmitted across some form of computer-readable media. 
     Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described. Rather, the specific features and acts are disclosed as illustrative forms of implementing the claims.