Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
  • G06F16/30—Information retrieval; Database structures therefor; File system structures therefor of unstructured textual data
  • G06F16/35—Clustering; Classification

Definitions

• the present invention relates to the field of topological searches and more particularly to a method and device for selecting functional entities in a topological space.
• such a selection process can be made more efficient by limiting the number of entities that will be searched.
• the distribution of entities in a topographical space allows for a grouping of the entities on the basis of location.
• the search and selection process becomes more complex when there are a number of entities distributed in a topological space which utilize different methods to perform their tasks and have differing ranges of effectiveness.
• the range of effectiveness of an entity for a specific function can be referred to as the entity's footprint.
• Specific applications can concentrate on only one method of performing a task or what can be referred to as the morphology of the entity. By concentrating on one particular morphology, the application can omit entities that perform the same function, albeit by a different method.
• different detection methods can include infrared, RF and visual morphologies. Concentration on only infrared methods of tracking this object can exclude a RF detector that can achieve the function of tracking that particular object. In other instances, depending on the type of object being tracked, visual detection might be unable to track the object while RF detection will accomplish that function. Thus, visual detection exists in a different functional domain than the RF detector. In addition, two different entities might utilize the same method of detection, but still have different functional domains. For example, light detectors might have different frequency ranges which would create different functional domains if the object being detected were light of a specific frequency.
• NP hard problems typically lead to time-consuming searches. Reducing this search space becomes a requirement when there is a time constraint in selecting appropriate entities.
• This invention utilizes standard physical space partitioning techniques along with entity characteristics to distribute them into limited size overlapping sets. Partitioning is performed based on the functionality and location of the entity rather than on the morphology of the entity. A membership value, ranging from 0 to 1 , is assigned to each entity associated with each set resulting in fuzzy characteristics for the sets. Dynamic variation in the range of effectiveness of the entity is accounted for by changing the memberships of the entities to the groups based on the varying range of effectiveness. A metric can be derived from the membership value list of each entity to enable a unique single dimensional comparison of two disparate entities that are described in many dimensions.
• the procedure of partitioning is the following: a distribution of the entities in a topographical space is provided as input.
• the input includes the type and functionality of each entity. Further, the variation of the entity range of effectiveness is input.
• the grid spacing is an independent parameter that is loosely tied to the range of the functional attribute of the particular grouping of entities. If the ranges of separate types of entities for the same functional characteristics are unequal, the smaller range is selected.
• the spacing parameter can be, and is, changed if required.
• a fuzzy set is created for each grid space of each functional attribute. All those entities of the particular functional attribute whose range of effectiveness overlap a portion of a grid space are assigned to be members of the particular fuzzy set associated with the grid space. The membership value of the entity to that group is determined. This procedure is completed for the entire group of entities that exist in the particular space. A change in the footprint of an entity results in the entity initially being removed from membership of all groups. The assignation is then recomputed based on the aforementioned procedure.
• a method for dynamically grouping limited range entities in a topological space comprising the steps of: determining functional domains for each entity in the topological space; partitioning the topological space into grids wherein the partitioning step is performed on the topological space for each different functional domain that exists; associating a group with each grid that corresponds to a unique functional domain and unique topological space; ascertaining a range of effectiveness for each entity wherein the ascertaining step is performed for each functional domain to which an entity belongs; comparing the range of effectiveness of each entity with each grid space that is associated with each group for each functional domain that the entity and group share in common; assigning each entity to be a member of each group whose compared range of effectiveness intersects the compared grid space that is associated with the group; and storing the group memberships of each entity.
• the method further comprises the steps of. identifying when a change of conditions for any entity occurs; the conditions including a change in function, a change in range of effectiveness and a change in location, and repeating the ascertaining, comparing, assigning and storing steps when the change occurs
• the grid dimensions for each functional domain correspond to the smallest range of effectiveness of the entities that belong to the functional domain
• the grid dimensions corresponding to the same functional domain are the same In accordance with another aspect of this embodiment of the invention, the grid dimensions corresponding to the same functional domain are determined independent of grid dimensions for different functional domains.
• the assigning step further comp ⁇ ses the step of calculating a membership value for each entity in each group wherein the membership value is equal to the ratio of intersecting space to total space within the group
• the storing step stores the membership values of each entity for each group
• the repeating step is performed for only the entities in which a change in conditions has occurred
• a method for dynamically grouping limited range entities in a topological space comprising the steps of determining functional domains and range of effectiveness in each functional domain for each entity in the topological space; partitioning the topological space into functional grids wherein each grid corresponds to a unique functional domain and topological space; and assigning each entity to be a member of a group whose range of effectiveness intersects the space of a functional grid and the entity and grid share the same functional domain.
• a device to dynamically group limited range entities in a topological space comprising a data processor; the processor including a domain determiner to ascertain functional domains for each entity in the topological space; a partitioner to separate the topological space into grids for each functional domain; an identifier to assign each grid that has a unique functional domain and topological space to a unique group; a footprint determiner to ascertain the range of effectiveness of each entity for each functional domain that the entity belongs to; a comparator to compare the range of effectiveness of each entity with the space of each group when the entity and group share the same functional domain; an assignor to assign each entity as a member of each group whose range of effectiveness intersects the space of each the group; and a membership storer to store the group memberships in a memory storage device.
• Fig. 1 is a schematic representation of a procedure of one embodiment of the present invention
• Fig. 2 is an example that depicts the steps of footprint determination and grid creation developed in accordance with the present invention.
• Fig. 3 is an example that depicts the steps of entity to group assignment and membership determination in accordance with the present invention.
• Fig. 4 is an example that depicts the steps of footprint determination and grid creation when recalculating the group assignments due to changes in conditions in accordance with the present invention.
• Fig. 5 is an example that depicts the steps of entity to group assignment and membership determination when recalculating the group assignments due to changes in conditions in accordance with the present invention.
• Fig. 6 is a schematic representation of a procedure developed in accordance with the present invention that scans the partition space for the relevant entities.
• Fig. 7 is a schematic representation of a procedure developed in accordance with the present invention that will determine the entity similarities for each group.
• Fig. 8 is a graphical depiction of the combinatorial search space based on the number of entities and the number of groups in accordance with the present invention.
• Fig. 9 is a graphical depiction of the combinatorial search space based on the number of entities and the number of groups in accordance with the present invention.
• Fig. 1 illustrates a flow chart that shows one embodiment of the present invention that can be utilized on a data processing unit.
• the step of data input 101 is necessary to establish the working parameters and requires all the relevant information about the topological space in which the partitioning is to occur.
• the specific information regarding the footprint of each entity is not required at this stage.
• the required input is at this stage includes: 1) The topological description of the space of distribution in 3 dimensions, unchanging with time.
• a scaling factor for each functional domain that the entities are viable This is used to determine the grid spacing. If this is not provided, the factor may be assumed to be 1.
• the subject space can now be partitioned as indicated in the grid creation step 103.
• the subject space is partitioned according to the initial estimates of the functional domain spacing.
• the number of partitions in each dimension is a whole number and the dimensions of each grid space are equal to the dimensions of all the grid spaces in that functional domain.
• the effective dimension of each grid space is less than or equal to the initial estimate times the scaling factor specified for each functional domain.
• Figs. 2(a) - (c) shows an example of the grid creation step that depicts three entities in a two-dimensional space.
• a two dimensional space is utilized for illustrative purposes in Fig. 2, it is understood that the application of this procedure can be utilized in three-dimensional space.
• entities 1 and 2 are viable in one functional domain each, these domains not being the same.
• Entity 1 has the functional domain of A while entity 2 has the functional domain of B.
• the circle around each entity represents the entities' footprints.
• Entity 3 with viability in both functional domains, A and B. is shown with two footprints, one for each domain.
• Grid overlays are made for each functional domain.
• Figs. 2(b) and (c) grid overlays are shown for the two functional domains.
• Fig. 2(b) shows the overlay for the first domain
• Fig. 2(c) shows the grid overlay for the second domain.
• the grid size results in a 5 by 3 grid while functional domain A results in a 2 by 2 matrix.
• only those entity footprints that are viable in the relevant domains are shown. Consequently, entity 1 is seen to have no footprint or activity in functional domain B and entity 2 has no footprint or activity in functional domain A. Entity 3 is active in both domains and has separate footprints for both.
• the dimensions of grid spaces across functional domains are not related and may differ.
• An optional means of partitioning the grid space is to use binary space partition trees. This will enable a marginally faster search through the partitioned data spaces. However, this is not relevant to the issue of assigning entities to partitioned sets.
• This invention includes partitioning procedures such as binary space partitioning trees or quad- and oct-trees. However, for the sake of simplicity, only the linear partitioning and entity assignation procedure is described.
• the next step 105 is group creation in which a group is associated with each grid space.
• the group characteristics are then assigned, prior to any entity membership determination.
• Group characteristics can include the following:
• Fig. 3(a)-(e) the functional domain grids that were created in Fig. 2 are now assigned.
• the functional domain grids of Figs. 2(b) and (c) are enumerated for reference.
• the numbering of the groups corresponds to the number of the grid spaces - this relationship remaining one-to-one and unchanging for the duration of the procedure.
• Each group number corresponds to a unique topological and functional partition. While group 1 and 16 share the same topological space they are assigned to groups differently based on the functional domain.
• the footprints are then determined for each entity.
• a footprint is determined for each functional domain in which an entity exists.
• the footprint specifies the topological range of effectiveness.
• the next steps are the Entity to Group Assignment step 109 and the Membership
• Determination step 11 1 wherein each entity and its footprint is compared with each group grid space. Entities are compared with only those groups in whose functional domains the entities are viable. This limits the assignation time to some degree.
• the relevant footprint of the entity for the particular functional domain is utilized in determining if any portion of the footprint and group grid space intersects. If there is an overlap of these defined areas, the entity is tagged as being a member of that particular group.
• the membership of the entity to the group is computed as the area of overlap divided by the whole area of the associated grid space. Referring to Fig. 3. the table presented therein demonstrates Entity to Group assignment and Membership Determination results. Group assignment for each entity is followed by the computation of membership value. Fig.
• 3(c) has a table that lists the approximate membership values for the example shown. This value is a ratio of the volume of intersection of the footprint and grid space divided by the grid space volume. Since entity 1 only exists in the functional domain of A which has only been assigned to groups 16-19, entity l's membership in groups 1-15 is nonexistent as represented by the value of 0.00.
• the lists of entities and associated membership values are stored in memory or other storage facility in a computer in step 113.
• This core database can be changed depending on any changes in the initial conditions that were used in creating the list of entities and associated membership values. Such changes can include 1) a change in the footprint of an entity or 2) a change in location of a particular entity.
• a set of flags is maintained that determines whether the situation requires one or more of the entities to behave in a manner that is divergent from that which is currently in operation.
• the switching of any of these flags triggers a re-evaluation of the particular entity or set of entities as indicated by decision box 1 15 in Fig. 1.
• a change in the footprint which may be a characteristic of the entire set, would cause the entire set of entities for the particular functional domain to be re-assigned.
• a change in a particular entity for example, the movement, addition or termination thereof, will cause a re-allocation for only that entity.
• grid spacing stays constant, even when the flags are switched.
• the methodology does not exclude the possibility of altering grid spacing during the operation of the algorithm. In the current embodiment this would require a re-iteration of the algorithm from step 103 onwards, requiring the recreation of grids, re-formation of groups and reallocation of each of the entities to groups.
• the dynamic maintenance of the entity allocation to the grid spaces does not preclude the storage of various scenarios in non-volatile memory. Predictable variation of entity footprints that occur frequently may be used for pre-computing the group allocation of these entities to save on repeated computation during operation of this procedure.
• the dynamic variation of entity footprints and the corresponding changes in coverage and entity membership are described in Figs 4 (a)-(d) and 5 (a)-(c).
• Fig. 4(a) shows the original trio of entities from Fig. 2.
• Fig. 4(b) shows a change in the footprints for each of these entities based on some phenomenon The source of this phenomenon may be internal or external and is not relevant to the procedure.
• Fig. 4(d) shows the altered footprints overlap with the grid spaces Note that the grid spaces remain constant
• the parameters that change are the membership of the entities to these groups and the associated membership values This is shown in Figs 5(a) and (b) with the associated membership values in Fig. 5(c)
• the creation of the group allocation database provides an easily accessible and efficiently sorted set of entities Optimization procedures requiring a set of entities can operate more efficiently by being able to search only from a limited group of valid entities
• Optimization procedures requiring a set of entities can operate more efficiently by being able to search only from a limited group of valid entities
• the required search among the complete set of entities available is reduced to a limited set
• the procedure scans through the relevant grid spaces
• the specific group in which the queried location lies contains all the entities that are likely to be within range of the location
• all the groups that refer to each of the grid spaces include possible candidate entities.
• the relevant groups are merged together to create an exclusive set.
• the list of entities determined by the described algorithm has a higher than average likelihood of being within range of the queried location than the entire set of entities. Moreover, for the particular functional domain, only these entities in the list are possible candidates.
• the search order is now through a list of "M" groups, rather than
• the relevant search engine to determine an appropriate entity may now scan the resulting exclusive and non-repeated set of entities. Assuming that this is the "optimal" entity for the task at hand, the current techniques provide a means of ordering the remainder of the limited set according to a similarity function. This single-dimensional ordering in the multi-dimensional search space enables the search engine to select the best "alternative" entity without further computation.
• Iff a. and b belong to at least one common group.
• M a Membership value of Entity A in the "/ "th group; M b Membership value of Entity B in the "/"th group; m Total, non-repeated number of groups that Entities A or B is a member of.
• the similarity between entities is a derived value that is indirectly determined from their partitioned group membership. Identical entities, i.e., those that have the same location, functional domains and ranges in those domains will have a similarity of 1, while those that do not belong to any common groups will have a similarity of 0.
• the entities in a group are ordered according to the procedure in Fig. 7.
• the similarity function usage is a viable indicator for entities that are close together, ergo, those that are in the same or neighborhood groups.
• Entities in widely separated groups will come up with similarities of 0, regardless of distance - in essence implying that this is a metric to measure the similarity of a tuple of entities and not the dissimilarity of any tuple of entities. Entities with high similarity will be able to be substituted one for the other, when performing a given function. Entities with similarity of zero will not be able to be substituted one for the other.
• the size of the search space can be characterized by the following equation:
• Equation (3) Consider a two dimensional area, 20 units by 20 units (400 square units) in dimension that contains a randomly distributed set of morphologically and functionally identical entities. The functional range of each of these entities is a constant circle of radius 1 unit. There is no dynamic variation or multiple functionality.
• a series of random entities were generated in the topological space, 100, 500, 1000 and 5000. This procedure was repeated twice to have two cases for each entity set number.
• the topological space was then divided, for each entity set, into firstly 400 spaces (20 x 20, 1 unit grid groups), then 100 (10 x 10, 2 unit grid groups), 25 (5 x 5, 4 unit grid groups) and 1 (1 x 1 , no grid or group).
• the following chart indicates the average number of entities per group for each category.
• the smallest and largest number of entities that were found in any group accompanies the average number of entities in parentheses.
• group allocation was performed and the average number of entities for each entity set number was determined. This was then rounded to the closest integer larger than the number.
• the spread indicates the lowest and highest number of entities belonging to a group.
• the effective search space for each of these cases is then a search through the list of groups and then a combinatorial search through the entity list of the specific group. Since a standard search through a list of " «" length is "n/2" (it is less for a binary space partitioned procedure), the effective space for a set of entities within range of a specific point in space is:
• equation 4 can be written as
• Figs. 8 and 9 these results are graphically displayed to demonstrate the effects of this type of grouping.
• four separate plots for the increase in search space are shown with no groups (farthest back), 25 groups, 100 groups and 400 groups (nearest).
• Fig. 9 plots the change in the search space for each increase in groups created.
• the combinatorial search space decrease with the creation of more groups.
• the search space becomes greater once the number of groups exceeds the number of entities.
• the search space starts to increase for any number of entities when the number of groups exceeds the number of entities.

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