BEST MODE FOR CARRYING OUT THE INVENTION

[0025] Embodiments of the present invention provide a method and system for accelerating calculations of force in physics-based visualization systems. Embodiments of the present invention also provide a method and system that can account for the similarity between data objects.

[0026] Embodiments of the present invention generally pertain to a two-pass procedure including a prediction step and a correction step. In the prediction step, the forces exerted on data objects by other data objects are calculated without considering the degree of similarity between the objects. As such, a technique that accelerates force computations (such as but not limited to Barnes-Hut) can be used in the prediction step.

[0027] In the correction step, forces are calculated for those data object pairs that have a certain (e.g., specified) degree of similarity, using a function that considers the similarity between data objects. These forces are used with the forces calculated in the prediction step to determine the actual forces on the data objects. For those data object pairs that have the specified degree of similarity, the forces calculated in the prediction step are subtracted and the forces calculated in the correction step are added.

[0028] In its various embodiments, the present invention can reduce the overall computational effort while striking an appropriate balance with accuracy. Suppose there are N data objects, and M pairs of data objects having the specified degree of similarity. A conventional approach (not utilizing the present invention) requires explicit force calculations for all N data objects and a computational effort on the order of N ² . According to one embodiment of the present invention, the computational effort is reduced to on the order of N log N (for the calculations performed using Barnes-Hut) plus M (for the explicit force calculations for the M pairs of data objects having the specified degree of similarity). The value of M can be varied by changing the value of the specified degree of similarity; by specifying a lower threshold for the degree of similarity, the value of M will increase. The threshold can be specified by a user to achieve a desired balance between computational speed and accuracy.

[0029] FIG. 2A illustrates data objects 20 , 21 , 22 , 23 and 24 in multi-dimensional space in accordance with one embodiment of the present invention. It is understood that although five data objects are illustrated in two-dimensional space, other than five data objects may be used and that other than two dimensions may be used in accordance with the present invention.

[0030] A non-zero degree of similarity between data objects can be indicated using a “link” or an “edge.” In FIG. 2 A, for example, link 30 is used to indicate that data objects 20 and 21 have a degree of similarity other than zero. Typically, similarity is normalized to a value between zero and one, so that data objects that have a maximum degree of similarity have a similarity equal to one, while a degree of similarity equal to zero indicates that the data objects are dissimilar. A degree of similarity not equal to (greater than) zero and less than one indicates that the data objects have some similarity. It is appreciated that the present invention can be used with other measures of similarity that may or may not be normalized.

[0031] In one embodiment, a threshold value can be defined such that pairs of data objects having a degree of similarity less than the threshold value can be considered to be dissimilar (e.g., they can be assumed to have a similarity value of zero). In this embodiment, a link or edge (e.g., link 30 ) can be used to indicate that two data objects (e.g., data objects 20 and 21 ) have a degree of similarity greater than (or greater than or equal to) the threshold value. As will be seen, when used with the various embodiments of the present invention, a threshold value can be specified by a user to achieve a desired balance between computational speed and accuracy; that is, a higher threshold value will likely increase the speed of the computations but accuracy may be affected.

[0032] In the example of FIG. 2 A, data object pairs 20 and 21 , 22 and 23 , and 23 and 24 have a degree of similarity greater than zero, while each of the other data object pairs (e.g., 20 and 22 , 20 and 23 , 20 and 24 , 21 and 22 , 21 and 23 , 21 and 24 , and 22 and 24 ) have a degree of similarity equal to zero. As mentioned above, in one embodiment, these latter pairs of data objects may have a degree of similarity not equal to zero but less than a threshold value, while the former pairs of data objects may have a degree of similarity greater than the threshold value.

[0033] FIG. 2B illustrates data objects 20 - 24 in multi-dimensional space with similarities set to zero in accordance with one embodiment of the present invention. By assuming the similarities are all equal to zero, the forces on the data objects can be calculated by applying a computationally efficient force computation technique such as Barnes-Hut. It is understood that another computationally efficient force computation technique such as a fast multipole expansion (FME) technique may be used in accordance with the present invention. Such techniques are known in the art.

[0034] FIG. 2C illustrates forces (exemplified by 40 ) on data objects 20 - 24 in multi-dimensional space, in which the forces are calculated with similarities set to zero using a technique such as Barnes-Hut, in accordance with one embodiment of the present invention.

[0035] FIG. 2D illustrates forces on data objects 20 - 24 in multi-dimensional space, in which the forces (exemplified by 50 ) are corrected to account for similarities in accordance with one embodiment of the present invention. In one embodiment, this is accomplished by updating the forces for those links having a non-zero degree of similarity (or a degree of similarity greater than the threshold). This is explained more fully in conjunction with FIGS. 3 and 4 , below.

[0036] FIG. 3A is a flowchart 300 showing a process for force computation in a physics-based visualization technique according to one embodiment of the present invention. Flowchart 300 includes processes of the present invention that, in one embodiment, are carried out by a processor under the control of computer-readable and computer-executable instructions. The computer-readable and computer-executable instructions reside, for example, in data storage features such as computer usable volatile memory, computer usable non-volatile memory, and/or a data storage device.

[0037] In step 305 , in the present embodiment, data objects are placed into initial positions in a rendering of multi-dimensional space. In one embodiment, the data objects are placed in equally spaced positions as if on a spherical surface. Alternatively, the data objects can be randomly placed within the multi-dimensional space.

[0038] In step 310 , in the present embodiment, data objects are placed according to their relative degree of support and similarity. The data objects are placed such that the distance between two data objects indicates the degree of support between the two objects. A directional arrow can be added between pairs of similar data objects that have a non-zero degree of similarity or a degree of similarity greater than some other threshold. Step 310 includes essentially prediction steps and a correction step, described further in conjunction with FIG. 3B .

[0039] FIG. 3B is a flowchart further describing step 310 of FIG. 3A according to one embodiment of the present invention. In this embodiment, steps 311 and 312 are essentially prediction steps and step 313 is essentially a correction step. In steps 311 and 312 , similarity is assumed to be zero for all links. Step 313 corrects for this assumption by updating the forces for those links in which similarity is not equal to zero (or in which similarity is greater than a specified threshold value).

[0040] In step 311 , in the present embodiment, force functions are replaced with functions that only depend on distance. Because energy is defined as the integral of force over space (or length or distance), it is recognized that force can also be derived as the gradient of a function for calculating energy. It is appreciated that there may be other types of functions used to calculate force, either directly or indirectly. In general, in accordance with the present embodiment of the present invention, the function or functions that are used to derive or calculate force in a physics-based visualization technique, either directly or indirectly, are replaced with a function that is dependent solely on the distance between data objects. This function may be different from the function used in the correction step (step 313 ). Alternatively, a function dependent on both distance and similarity may be used; however, similarity values of zero are used as inputs, or the coefficient of the similarity term can be set to zero. By calculating the forces using a function that does not consider similarity, the force calculation is amenable to the use of Barnes-Hut, FME, and the like.

[0041] In step 312 , according to the present embodiment of the present invention, the forces on data objects are calculated based on the simplifying assumptions introduced according to Barnes-Hut, FME, or another such technique known in the art. These techniques typically have a computational run time on the order of N or of N log N, where N represents the number of data objects.

[0042] In the present embodiment, step 313 is performed only for those links for which similarity is not equal to zero (or those links with similarity greater than the specified threshold value). In step 313 , an explicit force calculation dependent on both distance and similarity is performed for those links with similarity greater than zero (or greater than the threshold). For each such link, the force calculated in step 312 (as if the link had zero similarity) is subtracted, and the actual force from the explicit force calculation is added.

[0043] In the present embodiment, if M is the number of links with similarity other than zero (or above the threshold value), then the correction step (step 313 ) is only performed for M links. It is generally true that M is much less than N(N−1)/2.

[0044] Note that the threshold value can be defined to achieve a desired value for M. In effect, the value of the threshold (and hence the value of M) determines the amount by which the estimated forces (from step 312 ) need to differ from the actual forces in order to be considered in the correction step (step 313 ). For a higher threshold value (and therefore, a smaller M), there is a greater difference between the estimated forces and the actual forces. That is, by increasing the threshold value, a greater number of data object pairs will have their actual forces replaced with forces that are dependent only on distance.

[0045] Because the present embodiment of step 313 only involves M links, the computational run time is on the order of M. Accordingly, the total run time associated with the present embodiment is on the order of N plus M, or of N log N plus M, depending on the optimization technique used in step 312 . In one embodiment, further computational efficiency can be achieved by adjusting the parameter θ in Barnes-Hut (the parameter θ controls the granularity of the calculation in Barnes-Hut in a known manner). In general, by adjusting the values of M and/or θ, the user can achieve a desirable balance between computational accuracy and speed.

[0046] FIG. 4 is a flowchart 400 of a process for calculating forces on data objects in a physics-based visualization system in accordance with one embodiment of the present invention. Flowchart 400 includes processes of the present invention that, in one embodiment, are carried out by a processor under the control of computer-readable and computer-executable instructions. The computer-readable and computer-executable instructions reside, for example, in data storage features such as computer usable volatile memory, computer usable non-volatile memory, and/or a data storage device.

[0047] In step 410 , according to the present embodiment of the present invention, forces are calculated for data objects in the physics-based visualization system according to the distance between the data objects and without considering the similarity between the data objects. These forces are referred to herein as “first forces” to distinguish them from the forces that are calculated as a function of both the distance and similarity between data objects. These latter forces are referred to herein as “second forces.”

[0048] In the present embodiment, the first forces are calculated by assuming that all of the data object pairs have a similarity of zero. In one embodiment, this is accomplished by setting all values of similarity to zero. Alternatively, functions for calculating the first forces as a function of only distance can be derived from functions that are known in the art. In one embodiment, if the function being used to calculate forces includes a similarity term, the similarity term is zeroed out (for example, the coefficient of the similarity term is set equal to zero) to remove this term from the function. Thus, according to the present embodiment of the present invention, the first forces can be calculated using the simplifying assumptions introduced according to Barnes-Hut, FME, or another technique known in the art. That is, by calculating the first forces without considering similarity, the force calculation is amenable to the use of Barnes-Hut, FME, and the like.

[0049] In step 420 , in the present embodiment, second forces are calculated for those data object pairs that have a degree of similarity not equal to zero or that is greater than a specified threshold value. It is important to note that, in the present embodiment, the second forces are only calculated for a subset of the total set of data object pairs. For example, with reference back to FIG. 2 A, second forces are calculated only for the data object pairs 20 and 21 , 22 and 23 , and 23 and 24 .

[0050] In the present embodiment, the second forces are calculated using a function that considers similarity between data objects. In one embodiment, a function that is dependent on both the distance between data objects and their similarity is used. Such functions are known in the art. The function used to calculate the second forces may be the same function as that used in step 410 (before the similarity terms are zeroed out). Alternatively, the function used to calculate the second forces may a different function than that used in step 410 ; that is, the function of step 410 may be a first function dependent only on the distance between data objects, and the function of step 420 may be a second function different from the first function in that the second function is dependent on both distance and similarity.

[0051] In step 430 , in the present embodiment, the net forces on each data object are calculated using the first forces and the second forces, considering the similarity between data objects. When there is a degree of similarity between two data objects, the first force (the force that is a function only of distance) is subtracted, and the second force (the force that is a function of distance and similarity) is added.

[0052] With reference back to FIGS. 2A through 2D , one embodiment of the present invention is illustrated for data objects 21 and 24 . According to the present embodiment, first forces (as in step 410 of FIG. 4 ) are calculated for data objects 21 and 24 without considering similarity (e.g., by setting similarity to zero). As such, the simplifying assumptions of Barnes-Hut (or like techniques) can be used to calculate the first forces. In the example of FIG. 2 B, data objects 22 and 23 can be treated as a single object for the calculations of first forces (dependent only on distance) exerted on data objects 21 and 24 . That is, using Barnes-Hut for example, the first forces exerted on data object 21 are due to the forces exerted by data objects 20 and 24 and by a “superobject” representing data objects 22 and 23 . Similarly, the first forces exerted on data object 24 are due to the forces exerted by data objects 20 and 21 and by a superobject representing data objects 22 and 23 .

[0053] Next, according to the present embodiment, second forces dependent on both distance and similarity are calculated for the data object pairs that have a degree of similarity greater than zero (or greater than the threshold). Continuing the example from the preceding paragraph, in which the method of the present invention is illustrated for data objects 21 and 24 , the second forces would include the force exerted by data object 20 on data object 21 , the force exerted by data object 22 on data object 24 , and the force exerted by data object 23 on data object 24 .

[0054] Then, according to the present embodiment, the net forces on data objects 21 and 24 are determined. For data object 21 , the first force (dependent only on distance) exerted on data object 21 by data object 20 is subtracted, and the second force (dependent on distance and similarity) exerted on data object 21 by data object 20 is added. Thus, the net force on data object 21 includes the first force from data objects 22 and 23 (treated as a superobject according to Barnes-Hut), the first force from data object 24 , and the second force from data object 20 . Similarly, the net force on data object 24 includes the first force from data object 20 , the first force from data object 21 , the second force from data object 22 , and the second force from data object 23 .

[0055] Thus, in accordance with the present invention, a portion of the data objects can be modeled as superobjects using techniques such as Barnes-Hut, reducing the total number of explicit force calculations that need to be performed and thereby reducing the run time needed to place data objects in a physics-based visualization system. The present invention thus provides a method and system for accelerating calculations of force in physics-based visualization systems while accounting for both the distance and the similarity between data objects.

[0056] The present invention may be utilized in a number of applications. These applications include but are not limited to: market basket analysis of the similarity of products used/purchased by consumers; customer behavior analysis of the similarity of customers; text mining in which the similarity of documents is analyzed; multidimensional scaling algorithms; large graph layouts of abstract, multidimensional graphs; and physical simulations of complex force fields in which force or other phenomena depend on more than one parameter.

[0057] FIG. 5A is a block diagram on one embodiment of a system 500 upon which embodiments of the present invention may be implemented. Client system 501 and server system 502 are computer systems coupled in a network in a known manner. Client 501 and server 502 may be physically in separate locations (e.g., remotely separated from each other). It is appreciated that, although only a single client and a single server are shown, the present invention can be utilized with any number of such systems.

[0058] System 500 may represent a portion of a communication network located within a firewall of an organization or corporation (an “Intranet”), or system 500 may represent a portion of the World Wide Web or Internet using any of the various network protocols. Client 501 and server 502 may also be coupled via their respective input/output ports (e.g., serial ports) or via wireless connections. In essence, client 501 and server 502 are coupled in some manner that provides the capability for them to exchange data. In the present embodiment, a physics-based visualization engine 530 is implemented on client 501 and a data integration engine 510 is implemented on server 502 . However, it is appreciated that both of these functions may be implemented either on client 501 or on server 502 , or that these functions may be distributed over a number of additional clients and servers (not shown).

[0059] An objective of physics-based visualization engine 530 is to generate a multi-dimensional display of data objects on display 540 . Display 540 is a display device suitable for creating graphic images. A multi-dimensional display generated by physics-based visualization engine 530 provides a friendly means of visualizing the relationships between large volumes of transactional data represented by the data objects. Physics-based visualization engine 530 is further described in conjunction with FIG. 5 C, below.

[0060] Continuing with reference to FIG. 5 A, data integration engine 510 essentially functions to organize raw transactional data into a form that allows for further manipulation and analysis. For example, data integration engine 510 may aggregate (sum) instances of the raw data over time, eliminate duplicate entries, filter out instances of data based on specified conditions, and the like.

[0061] FIG. 5B illustrates the data flow through a system 500 for analyzing and visualizing data in accordance with one embodiment of the present invention. As described by FIG. 5 A, the various functions illustrated by FIG. 5B can be executed on a single device, or execution of these functions may be distributed over a number of different devices.

[0062] In FIG. 5 B, transactional data include raw transactional data resulting from business and financial transactions including electronic commerce (e-commerce) transactions. The transactional data are analyzed and transformed into data objects by data integration engine 510 . In the present embodiment, the data objects are further processed by physics-based visualization engine 530 to generate a multi-dimensional display of data objects on display 540 .

[0063] Referring now to FIG. 5 C, physics-based visualization engine 530 includes an initialization module 531 , a placement module 532 , and an optional clustering module 533 . In this embodiment, the initialization module 531 places data objects into their initial positions in a rendering of multi-dimensional space. In one embodiment, the data objects are placed in equally spaced positions as if on a spherical surface. Alternatively, the data objects can be randomly placed within the multi-dimensional space.

[0064] In the embodiment of FIG. 5 C, placement module 532 moves the data objects such that the distances between any two of the data objects is indicative of the degree of support between those two objects. As described above, the degree of support between two data objects is proportionate to the force exerted by these data objects on each other. According to the present embodiment, placement module 532 uses the processes for force computation described above in conjunction with FIGS. 3A, 3B and 4 , above. In one embodiment, placement module 532 adds a directional arrow between pairs of similar data objects to indicate that they have a degree of similarity that is non-zero and/or greater than a specified threshold, as described above. In another embodiment, clustering module 533 then clusters related data objects into groups.

[0065] The preferred embodiment of the present invention is thus described. While the present invention has been described in particular embodiments, it should be appreciated that the present invention should not be construed as limited by such embodiments, but rather construed according to the following claims.