U.S. patent application number 14/108267 was filed with the patent office on 2014-06-26 for computer-implemented system and method for correcting a rendering of clusters.
This patent application is currently assigned to FTI Technology LLC. The applicant listed for this patent is FTI Technology LLC. Invention is credited to Dan Gallivan.
Application Number | 20140176556 14/108267 |
Document ID | / |
Family ID | 34523439 |
Filed Date | 2014-06-26 |
United States Patent
Application |
20140176556 |
Kind Code |
A1 |
Gallivan; Dan |
June 26, 2014 |
Computer-Implemented System and Method For Correcting A Rendering
Of Clusters
Abstract
A computer-implemented system and method for correcting a
rendering of clusters is provided. A pair of clusters is selected
within a representation. A span between centers of the clusters is
determined. Radii for each of the clusters in the pair is
identified. The radii are summed and at least one of the clusters
in the pair is moved within the representation when the span
exceeds the sum.
Inventors: |
Gallivan; Dan; (Bainbridge
Island, WA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
FTI Technology LLC |
Annapolis |
MD |
US |
|
|
Assignee: |
FTI Technology LLC
Annapolis
MD
|
Family ID: |
34523439 |
Appl. No.: |
14/108267 |
Filed: |
December 16, 2013 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
13112928 |
May 20, 2011 |
8610719 |
|
|
14108267 |
|
|
|
|
12060005 |
Mar 31, 2008 |
7948491 |
|
|
13112928 |
|
|
|
|
11728636 |
Mar 26, 2007 |
7352371 |
|
|
12060005 |
|
|
|
|
11110452 |
Apr 19, 2005 |
7196705 |
|
|
11728636 |
|
|
|
|
09944475 |
Aug 31, 2001 |
6888548 |
|
|
11110452 |
|
|
|
|
Current U.S.
Class: |
345/440 |
Current CPC
Class: |
G06T 17/00 20130101;
G06T 11/206 20130101; G06T 11/20 20130101 |
Class at
Publication: |
345/440 |
International
Class: |
G06T 11/20 20060101
G06T011/20 |
Claims
1. A computer-implemented system for correcting a rendering of
clusters, comprising: a selection module to select a pair of
clusters within a representation; a determination module to
determine a span between centers of the clusters; an identification
module to identify radii for each of the clusters in the pair and
summing the radii; an orientation module to move at least one of
the clusters in the pair within the representation when the span
exceeds the sum; and a processor to execute the modules.
2. A system according to claim 1, wherein each of the clusters is
oriented within the representation at a distance from a common
origin.
3. A system according to claim 2, further comprising: a
representation module to further orient each cluster in the
representation at a fixed angle along a common axis drawn through
the common origin.
4. A system according to claim 2, wherein the orientation module
increases the distance of the at least one cluster by multiplying
the distance of that cluster by a variable coefficient.
5. A system according to claim 2, further comprising: a coefficient
module to identify a fixed coefficient; a distance determination
module to determine a further distance for each of the clusters in
the pair by multiplying the identified fixed coefficient by the
distance of that cluster from the common origin; and the
orientation module to reorient each of the clusters away from the
common origin based on the further determined distance.
6. A system according to claim 2, wherein the span is
proportionately increased relative to the reorientation of the
clusters.
7. A system according to claim 2, further comprising: a
representation module to increase the distance of the clusters as a
similarity of concepts represented by each cluster decreases.
8. A system according to claim 1, wherein the clusters each
comprise a non-circular shape having a convex volume and the center
comprises a center of mass.
9. A system according to claim 8, further comprising: a segment
module to determine a segment from the center of mass to a point
along the span drawn between the centers of mass for the pair as
the radii for each of the non-circular clusters in the pair.
10. A system according to claim 1, wherein the radii of each
cluster signifies a number of documents attracted to that
cluster.
11. A computer-implemented method for correcting a rendering of
clusters, comprising the steps of: selecting a pair of clusters
within a representation; determining a span between centers of the
clusters; identifying radii for each of the clusters in the pair;
summing the radii; and moving at least one of the clusters in the
pair within the representation when the span exceeds the sum,
wherein the steps are performed on a suitably-programmed
computer.
12. A method according to claim 11, wherein each of the clusters is
oriented within the representation at a distance from a common
origin.
13. A method according to claim 12, further comprising: further
orienting each cluster in the representation at a fixed angle along
a common axis drawn through the common origin.
14. A method according to claim 12, further comprising: increasing
the distance of the at least one cluster by multiplying the
distance of that cluster by a variable coefficient.
15. A method according to claim 12, further comprising: identifying
a fixed coefficient; determining a further distance for each of the
clusters in the pair by multiplying the identified fixed
coefficient by the distance of that cluster from the common origin;
and reorienting each of the clusters away from the common origin
based on the further determined distance.
16. A method according to claim 12, further comprising:
proportionately increasing the span relative to the reorientation
of the clusters.
17. A method according to claim 12, further comprising: increasing
the distance of the clusters as a similarity of concepts
represented by each cluster decreases.
18. A method according to claim 11, wherein the clusters each
comprise a non-circular shape having a convex volume and the center
comprises a center of mass.
19. A method according to claim 18, further comprising: determining
a segment from the center of mass to a point along the span drawn
between the centers of mass for the pair as the radii for each of
the non-circular clusters in the pair.
20. A method according to claim 11, wherein the radii of each
cluster signifies a number of documents attracted to that cluster.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This patent application is a continuation of
commonly-assigned U.S. patent application Ser. No. 13/112,928,
filed May 20, 2011, pending; which is a continuation of U.S. Pat.
No. 7,948,491, issued May 24, 2011; which is a continuation of U.S.
Pat. No. 7,352,371, issued Apr. 1, 2008; which is a continuation of
U.S. Pat. No. 7,196,705, issued Mar. 27, 2007; which is a
continuation of U.S. Pat. No. 6,888,548, issued May 3, 2005, the
priority dates of which are claimed and the disclosures of which
are incorporated by reference.
FIELD
[0002] The present invention relates in general to data
visualization and, in particular, to a system and method for
correcting a rendering of clusters.
BACKGROUND
[0003] Computer-based data visualization involves the generation
and presentation of idealized data on a physical output device,
such as a cathode ray tube (CRT), liquid crystal diode (LCD)
display, printer and the like. Computer systems visualize data
through the use of graphical user interfaces (GUIs) which allow
intuitive user interaction and high quality presentation of
synthesized information.
[0004] The importance of effective data visualization has grown in
step with advances in computational resources. Faster processors
and larger memory sizes have enabled the application of complex
visualization techniques to operate in multi-dimensional concept
space. As well, the interconnectivity provided by networks,
including intranetworks and internetworks, such as the Internet,
enable the communication of large volumes of information to a
wide-ranging audience. Effective data visualization techniques are
needed to interpret information and model content
interpretation.
[0005] The use of a visualization language can enhance the
effectiveness of data visualization by communicating words, images
and shapes as a single, integrated unit. Visualization languages
help bridge the gap between the natural perception of a physical
environment and the artificial modeling of information within the
constraints of a computer system. As raw information cannot always
be digested as written words, data visualization attempts to
complement and, in some instances, supplant the written word for a
more intuitive visual presentation drawing on natural cognitive
skills.
[0006] Effective data visualization is constrained by the physical
limits of computer display systems. Two-dimensional and
three-dimensional information can be readily displayed. However,
n-dimensional information in excess of three dimensions must be
artificially compressed. Careful use of color, shape and temporal
attributes can simulate multiple dimensions, but comprehension and
usability become difficult as additional layers of modeling are
artificially grafted into the finite bounds of display
capabilities.
[0007] Thus, mapping multi-dimensional information into a two- or
three-dimensional space presents a problem. Physical displays are
practically limited to three dimensions. Compressing
multi-dimensional information into three dimensions can mislead,
for instance, the viewer through an erroneous interpretation of
spatial relationships between individual display objects. Other
factors further complicate the interpretation and perception of
visualized data, based on the Gestalt principles of proximity,
similarity, closed region, connectedness, good continuation, and
closure, such as described in R. E. Horn, "Visual Language: Global
Communication for the 21.sup.st Century," Ch. 3, MacroVU Press
(1998), the disclosure of which is incorporated by reference.
[0008] In particular, the misperception of visualized data can
cause a misinterpretation of, for instance, dependent variables as
independent and independent variables as dependent. This type of
problem occurs, for example, when visualizing clustered data, which
presents discrete groupings of data which are misperceived as being
overlaid or overlapping due to the spatial limitations of a
three-dimensional space.
[0009] Consider, for example, a group of clusters, each cluster
visualized in the form of a circle defining a center and a fixed
radius. Each cluster is located some distance from a common origin
along a vector measured at a fixed angle from a common axis through
the common origin. The radii and distances are independent
variables relative to the other clusters and the radius is an
independent variable relative to the common origin. In this
example, each cluster represents a grouping of points corresponding
to objects sharing a common set of traits. The radius of the
cluster reflects the relative number of objects contained in the
grouping. Clusters located along the same vector are similar in
theme as are those clusters located on vectors having a small
cosine rotation from each other. Thus, the angle relative to a
common axis' distance from a common origin is an independent
variable with a correlation between the distance and angle
reflecting relative similarity of theme. Each radius is an
independent variable representative of volume. When displayed, the
overlaying or overlapping of clusters could mislead the viewer into
perceiving data dependencies where there are none.
[0010] Therefore, there is a need for an approach to presenting
arbitrarily dimensioned data in a finite-dimensioned display space
while preserving independent data relationships. Preferably, such
an approach would maintain size and placement relationships
relative to a common identified reference point.
[0011] There is a further need for an approach to reorienting data
clusters to properly visualize independent and dependent variables
while preserving cluster radii and relative angles from a common
axis drawn through a common origin.
SUMMARY
[0012] The present invention provides a system and method for
reorienting a data representation containing clusters while
preserving independent variable geometric relationships. Each
cluster is located along a vector defined at an angle .theta. from
a common axis x. Each cluster has a radius r. The distance
(magnitude) of the center c.sub.i of each cluster from a common
origin and the radius r are independent variables relative to other
clusters and the radius r of each cluster is an independent
variable relative to the common origin. The clusters are selected
in order of relative distance from the common origin and optionally
checked for an overlap of bounding regions. Clusters having no
overlapping regions are skipped. If the pair-wise span s.sub.ij
between the centers c.sub.i and c.sub.j of the clusters is less
than the sum of the radii r.sub.i and r.sub.j, a new distance
d.sub.i for the cluster is determined by setting the pair-wise span
s.sub.ij equal to the sum of the radii r.sub.i and r.sub.j and
solving the resulting quadratic equation for distance d.sub.i. The
operations are repeated for each pairing of clusters.
[0013] An embodiment provides a computer-implemented system and
method for correcting a rendering of clusters. A pair of clusters
is selected within a representation. A span between centers of the
clusters is determined. Radii for each of the clusters in the pair
is identified. The radii are summed and at least one of the
clusters in the pair is moved within the representation when the
span exceeds the sum.
[0014] Still other embodiments of the present invention will become
readily apparent to those skilled in the art from the following
detailed description, wherein is described embodiments of the
invention by way of illustrating the best mode contemplated for
carrying out the invention. As will be realized, the invention is
capable of other and different embodiments and its several details
are capable of modifications in various obvious respects, all
without departing from the spirit and the scope of the present
invention. Accordingly, the drawings and detailed description are
to be regarded as illustrative in nature and not as
restrictive.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] FIG. 1 is a block diagram showing a system for generating a
visualized data representation preserving independent variable
geometric relationships, in accordance with the present
invention.
[0016] FIG. 2 is a data representation diagram showing, by way of
example, a view of overlapping clusters generated by the cluster
display system of FIG. 1.
[0017] FIG. 3 is a graph showing, by way of example, the polar
coordinates of the overlapping clusters of FIG. 2.
[0018] FIG. 4 is a data representation diagram showing, by way of
example, the pair-wise spans between the centers of the clusters of
FIG. 2.
[0019] FIG. 5 is a data representation diagram showing, by way of
example, an exploded view of the clusters of FIG. 2.
[0020] FIG. 6 is a data representation diagram showing, by way of
example, a minimized view of the clusters of FIG. 2.
[0021] FIG. 7 is a graph, showing, by way of example, the polar
coordinates of the minimized clusters of FIG. 5.
[0022] FIG. 8 is a data representation diagram showing, by way of
example, the pair-wise spans between the centers of the clusters of
FIG. 2.
[0023] FIG. 9 is a flow diagram showing a method for generating a
visualized data representation preserving independent variable
geometric relationships, in accordance with the present
invention.
[0024] FIG. 10 is a routine for reorienting clusters for use in the
method of FIG. 9.
[0025] FIG. 11 is a flow diagram showing a routine for calculating
a new distance for use in the routine of FIG. 10.
[0026] FIG. 12 is a graph showing, by way of example, a pair of
clusters with overlapping bounding regions generated by the cluster
display system of FIG. 1.
[0027] FIG. 13 is a graph showing, by way of example, a pair of
clusters with non-overlapping bounding regions generated by the
cluster display system of FIG. 1.
[0028] FIG. 14 is a routine for checking for overlapping clusters
for use in the routine of FIG. 10.
[0029] FIG. 15 is a data representation diagram showing, by way of
example, a view of overlapping, non-circular clusters generated by
the clustered display system of FIG. 1.
DETAILED DESCRIPTION
[0030] FIG. 1 is a block diagram 10 showing a system for generating
a visualized data representation preserving independent variable
geometric relationships, in accordance with the present invention.
The system consists of a cluster display system 11, such as
implemented on a general-purpose programmed digital computer. The
cluster display system 11 is coupled to input devices, including a
keyboard 12 and a pointing device 13, such as a mouse, and display
14, including a CRT, LCD display, and the like. As well, a printer
(not shown) could function as an alternate display device. The
cluster display system 11 includes a processor, memory and
persistent storage, such as provided by a storage device 16, within
which are stored clusters 17 representing visualized
multi-dimensional data. The cluster display system 11 can be
interconnected to other computer systems, including clients and
servers, over a network 15, such as an intranetwork or
internetwork, including the Internet, or various combinations and
topologies thereof.
[0031] Each cluster 17 represents a grouping of one or more points
in a virtualized concept space, as further described below
beginning with reference to FIG. 2. Preferably, the clusters 17 are
stored as structured data sorted into an ordered list in ascending
(preferred) or descending order. In the described embodiment, each
cluster represents individual concepts and themes categorized based
on, for example, Euclidean distances calculated between each pair
of concepts and themes and defined within a pre-specified range of
variance, such as described in common-assigned U.S. Pat. No.
6,778,995, issued Aug. 17, 2004, to Gallivan, the disclosure of
which is incorporated by reference.
[0032] The cluster display system 11 includes four modules: sort
18, reorient 19, display and visualize 20, and, optionally, overlap
check 21. The sort module 18 sorts a raw list of clusters 17 into
either ascending (preferred) or descending order based on the
relative distance of the center of each cluster from a common
origin. The reorient module 19, as further described below with
reference to FIG. 10, reorients the data representation display of
the clusters 17 to preserve the orientation of independent variable
relationships. The reorient module 19 logically includes a
comparison submodule for measuring and comparing pair-wise spans
between the radii of clusters 17, a distance determining submodule
for calculating a perspective-corrected distance from a common
origin for select clusters 17, and a coefficient submodule taking a
ratio of perspective-corrected distances to original distances. The
display and visualize module 20 performs the actual display of the
clusters 17 via the display 14 responsive to commands from the
input devices, including keyboard 12 and pointing device 13.
Finally, the overlap check module 21, as further described below
with reference to FIG. 12, is optional and, as a further
embodiment, provides an optimization whereby clusters 17 having
overlapping bounding regions are skipped and not reoriented.
[0033] The individual computer systems, including cluster display
system 11, are general purpose, programmed digital computing
devices consisting of a central processing unit (CPU), random
access memory (RAM), non-volatile secondary storage, such as a hard
drive or CD ROM drive, network interfaces, and peripheral devices,
including user interfacing means, such as a keyboard and display.
Program code, including software programs, and data are loaded into
the RAM for execution and processing by the CPU and results are
generated for display, output, transmittal, or storage.
[0034] Each module is a computer program, procedure or module
written as source code in a conventional programming language, such
as the C++ programming language, and is presented for execution by
the CPU as object or byte code, as is known in the art. The various
implementations of the source code and object and byte codes can be
held on a computer-readable storage medium or embodied on a
transmission medium in a carrier wave. The cluster display system
11 operates in accordance with a sequence of process steps, as
further described below with reference to FIG. 9.
[0035] FIG. 2 is a data representation diagram 30 showing, by way
of example, a view 31 of overlapping clusters 33-36 generated by
the cluster display system 11 of FIG. 1. Each cluster 33-36 has a
center c 37-40 and radius r 41-44, respectively, and is oriented
around a common origin 32. The center c of each cluster 33-36 is
located at a fixed distance (magnitude) d 45-48 from the common
origin 32. Cluster 34 overlays cluster 33 and clusters 33, 35 and
36 overlap.
[0036] Each cluster 33-36 represents multi-dimensional data modeled
in a three-dimensional display space. The data could be visualized
data for a virtual semantic concept space, including semantic
content extracted from a collection of documents represented by
weighted clusters of concepts, such as described in
commonly-assigned U.S. Pat. No. 6,978,274, issued Dec. 20, 2005, to
Gallivan, the disclosure of which is incorporated by reference.
[0037] FIG. 3 is a graph 50 showing, by way of example, the polar
coordinates of the overlapping clusters 33-36 of FIG. 2. Each
cluster 33-36 is oriented at a fixed angle .theta. 52-55 along a
common axis x 51 drawn through the common origin 32. The angles
.theta. 52-55 and radii r 41-44 (shown in FIG. 2) of each cluster
33-36, respectively, are independent variables. The distances d
56-59 represent dependent variables.
[0038] Referring back to FIG. 2, the radius r 41-44 (shown in FIG.
2) of each cluster 33-36 signifies the number of documents
attracted to the cluster. The distance d 56-59 increases as the
similarity of concepts represented by each cluster 33-36 decreases.
However, based on appearance alone, a viewer can be misled into
interpreting cluster 34 as being dependent on cluster 33 due to the
overlay of data representations. Similarly, a viewer could be
misled to interpret dependent relationships between clusters 33, 35
and 36 due to the overlap between these clusters.
[0039] FIG. 4 is a data representation diagram 60 showing, by way
of example, the pair-wise spans between the centers of the clusters
of FIG. 2. Centers c 37-40 of the clusters 33-36 (shown in FIG. 2)
are separated respectively by pair-wise spans s 61-66. Each span s
61-66 is also dependent on the independent variables radii r 41-44
(shown in FIG. 2) and angles .theta. 52-55.
[0040] For each cluster 33-36 (shown in FIG. 2), the radii r is an
independent variable. The distances d 56-59 (shown in FIG. 3) and
angles .theta. 52-55 (shown in FIG. 3) are also independent
variables. However, the distances d 56-59 and angles .theta. 52-55
are correlated, but there is no correlation between different
distances d 56-59. As well, the relative angles .theta. 52-55 are
correlated relative to the common axis x, but are not correlated
relative to other angles .theta. 52-55. However, the distances d
56-59 cause the clusters 33-36 to appear to either overlay or
overlap and these visual artifacts erroneously imply dependencies
between the neighboring clusters based on distances d 56-59.
[0041] FIG. 5 is a data representation diagram 70 showing, by way
of example, an exploded view 71 of the clusters 33-36 of FIG. 2. To
preserve the relationships between the dependent variables distance
d and span s, the individual distances d 56-59 (shown in FIG. 3)
are multiplied by a fixed coefficient to provide a proportionate
extension e 71-75, respectively, to each of the distances d 56-59.
The resulting data visualization view 71 "explodes" clusters 33-36
while preserving the independent relationships of the radii r 41-44
(shown in FIG. 2) and angles .theta. 52-55 (shown in FIG. 3).
[0042] Although the "exploded" data visualization view 71 preserves
the relative pair-wise spans s 61-66 between each of the clusters
33-36, multiplying each distance d 56-59 by the same coefficient
can result in a potentially distributed data representation
requiring a large display space.
[0043] FIG. 6 is a data representation diagram 80 showing, by way
of example, a minimized view 81 of the clusters 33-36 of FIG. 2. As
in the exploded view 71 (shown in FIG. 5), the radii r 41-44 (shown
in FIG. 2) and angles .theta. 52-55 (shown in FIG. 3) of each
cluster 33-36 are preserved as independent variables. The distances
d 56-59 are independent variables, but are adjusted to correct to
visualization. The "minimized" data representation view 81
multiplies distances d 45 and 48 (shown in FIG. 2) by a variable
coefficient k. Distances d 46 and 47 remain unchanged, as the
clusters 34 and 35, respectively, need not be reoriented.
Accordingly, the distances d 45 and 48 are increased by extensions
e' 82 and 83, respectively, to new distances d'.
[0044] FIG. 7 is a graph 90 showing, by way of example, the polar
coordinates of the minimized clusters 33-36 of FIG. 5. Although the
clusters 33-36 have been shifted to distances d' 106-109 from the
common origin 32, the radii r 41-44 (shown in FIG. 2) and angles
.theta. 102-105 relative to the shared axis x 101 are preserved.
The new distances d' 106-109 also approximate the proportionate
pair-wise spans s' 110-115 between the centers c 37-40.
[0045] FIG. 8 is a data representation diagram 110 showing, by way
of example, the pair-wise spans between the centers of the clusters
of FIG. 2. Centers c 37-40 (shown in FIG. 2) of the clusters 33-36
are separated respectively by pair-wise spans s 111-116. Each span
s 111-116 is dependent on the independent variables radii r 41-44
and the angles .theta. 52-55 (shown in FIG. 3). The length of each
pair-wise span s 111-116 is proportionately increased relative to
the increase in distance d 56-69 of the centers c 37-40 of the
clusters 33-36 from the origin 32.
[0046] FIG. 9 is a flow diagram showing a method 120 for generating
a visualized data representation preserving independent variable
geometric relationships, in accordance with the present invention.
As a preliminary step, the origin 32 (shown in FIG. 2) and x-axis
51 (shown in FIG. 3) are selected (block 121). Although described
herein with reference to polar coordinates, any other coordinate
system could also be used, including Cartesian, Logarithmic, and
others, as would be recognized by one skilled in the art.
[0047] Next, the clusters 17 (shown in FIG. 1) are sorted in order
of relative distance d from the origin 32 (block 122). Preferably,
the clusters 17 are ordered in ascending order, although descending
order could also be used. The clusters 17 are reoriented (block
123), as further described below with reference to FIG. 10.
Finally, the reoriented clusters 17 are displayed (block 124),
after which the routine terminates.
[0048] FIG. 10 is a flow diagram showing a routine 130 for
reorienting clusters 17 for use in the method 120 of FIG. 9. The
purpose of this routine is to generate a minimized data
representation, such as described above with reference to FIG. 5,
preserving the orientation of the independent variables for radii r
and angles .theta. relative to a common x-axis.
[0049] Initially, a coefficient k is set to equal 1 (block 131).
During cluster reorientation, the relative distances d of the
centers c of each cluster 17 from the origin 32 is multiplied by
the coefficient k. The clusters 17 are then processed in a pair of
iterative loops as follows. During each iteration of an outer
processing loop (blocks 132-146), beginning with the innermost
cluster, each cluster 17, except for the first cluster, is selected
and processed. During each iteration of the inner processing loop
(blocks 135-145), each remaining cluster 17 is selected and
reoriented, if necessary.
[0050] Thus, during the outer iterative loop (blocks 132-146), an
initial Cluster.sub.i is selected (block 133) and the radius
r.sub.i, center c.sub.i, angle .theta..sub.i, and distance d.sub.i
for the selected Cluster.sub.i are obtained (block 134). Next,
during the inner iterative loop (blocks 135-145), another
Cluster.sub.j (block 136) is selected and the radius r.sub.j,
center c.sub.j, angle .theta..sub.j, and distance d.sub.j are
obtained (block 137).
[0051] In a further embodiment, bounding regions are determined for
Cluster.sub.i and Cluster.sub.j and the bounding regions are
checked for overlap (block 138), as further described below with
reference to FIG. 14.
[0052] Next, the distance d.sub.i of the cluster being compared,
Cluster.sub.i, is multiplied by the coefficient k (block 139) to
establish an initial new distance d'.sub.i, for Cluster.sub.i. A
new center c.sub.i is determined (block 140). The span s.sub.ij
between the two clusters, Cluster.sub.i and Cluster.sub.j, is set
to equal the absolute distance between center c.sub.i plus center
c.sub.j. If the pair-wise span s.sub.ij is less than the sum of
radius r.sub.i and radius r.sub.j for Cluster.sub.i and
Cluster.sub.j, respectively (block 143), a new distance d.sub.i for
Cluster.sub.i is calculated (block 144), as further described below
with reference to FIG. 11. Processing of each additional
Cluster.sub.i continues (block 145) until all additional clusters
have been processed (blocks 135-145). Similarly, processing of each
Cluster.sub.j (block 146) continues until all clusters have been
processed (blocks 132-146), after which the routine returns.
[0053] FIG. 11 is a flow diagram showing a routine 170 for
calculating a new distance for use in the routine 130 of FIG. 10.
The purpose of this routine is to determine a new distance d'.sub.i
for the center c.sub.i of a selected cluster.sub.i from a common
origin. In the described embodiment, the new distance d'.sub.i is
determined by solving the quadratic equation formed by the
distances d.sub.i and d.sub.j and adjacent angle.
[0054] Thus, the sum of the radii (r.sub.i+r.sub.j).sup.2 is set to
equal the square of the distance d.sub.j plus the square of the
distance d.sub.i minus the product of the 2 times the distance
d.sub.j times the distance d.sub.i times cos .theta. (block 171),
as expressed by equation (1):
(r.sub.i+r.sub.j).sup.2=d.sub.i.sup.2+d.sub.j.sup.2-2d.sub.id.sub.j
cos .theta. (1)
The distance d.sub.i can be calculated by solving a quadratic
equation (5) (block 172), derived from equation (1) as follows:
1 d i 2 + ( 2 d j cos .theta. ) d i = ( d j 2 - [ r i + r j ] 2 ) (
2 ) 1 d i 2 + ( 2 d j cos .theta. ) d i - ( d j 2 - [ r i + r j ] 2
) = 0 ( 3 ) d i = ( 2 d j cos .theta. ) .+-. ( 2 d j cos .theta. )
2 - 4 1 ( d j 2 - [ r i + r j ] 2 ) 2 1 ( 4 ) d i = ( 2 d j cos
.theta. ) .+-. ( 2 d j cos .theta. ) 2 - 4 ( d j 2 - [ r i + r j ]
2 ) 2 ( 5 ) ##EQU00001##
In the described embodiment, the `.+-.` operation is simplified to
a `+` operation, as the distance d.sub.i is always increased.
[0055] Finally, the coefficient k, used for determining the
relative distances d from the centers c of each cluster 17 (block
139 in FIG. 10), is determined by taking the product of the new
distance d.sub.i divided by the old distance d.sub.i (block 173),
as expressed by equation (6):
k = d i new d i old ( 6 ) ##EQU00002##
The routine then returns.
[0056] In a further embodiment, the coefficient k is set to equal 1
if there is no overlap between any clusters, as expressed by
equation (7):
if d i - 1 + r i - 1 d i - r i > 1 , then k = 1 ( 7 )
##EQU00003##
where d.sub.i and d.sub.i-1 are the distances from the common
origin r.sub.i and r.sub.i-1 and are the radii of clusters i and
i-1, respectively. If the ratio of the sum of the distance plus the
radius of the further cluster i-1 over the difference of the
distance less the radius of the closer cluster i is greater than 1,
the two clusters do not overlap and the distance d.sub.i of the
further cluster need not be adjusted.
[0057] FIG. 12 is a graph showing, by way of example, a pair of
clusters 181-182 with overlapping bounding regions generated by the
cluster display system 11 of FIG. 1. The pair of clusters 181-182
are respectively located at distances d 183-184 from a common
origin 180. A bounding region 187 for cluster 181 is formed by
taking a pair of tangent vectors 185a-b from the common origin 180.
Similarly, a bounding region 188 for cluster 182 is formed by
taking a pair of tangent vectors 186a-b from the common origin 180.
The intersection 189 of the bounding regions 187-188 indicates that
the clusters 181-182 might either overlap or overlay and
reorientation may be required.
[0058] FIG. 13 is a graph showing, by way of example, a pair of
clusters 191-192 with non-overlapping bounding regions generated by
the cluster display system 11 of FIG. 1. The pair of clusters
191-192 are respectively located at distances d 193-194 from a
common origin 190. A bounding region 197 for cluster 191 is formed
by taking a pair of tangent vectors 195a-b from the common origin
190. Similarly, a bounding region 198 for cluster 192 is formed by
taking a pair of tangent vectors 196a-b from the common origin 190.
As the bounding regions 197-198 do not intersect, the clusters
191-192 are non-overlapping and non-overlaid and therefore need not
be reoriented.
[0059] FIG. 14 is a flow diagram showing a routine 200 for checking
for overlap of bounding regions for use in the routine 130 of FIG.
10. As described herein, the terms overlap and overlay are simply
referred to as "overlapping." The purpose of this routine is to
identify clusters 17 (shown in FIG. 1) that need not be reoriented
due to the non-overlap of their respective bounding regions. The
routine 200 is implemented as an overlap submodule in the reorient
module 19 (shown in FIG. 1).
[0060] Thus, the bounding region of a first Cluster.sub.i is
determined (block 201) and the bounding region of a second
Cluster.sub.j is determined (block 202). If the respective bounding
regions do not overlap (block 203), the second Cluster.sub.j is
skipped (block 204) and not reoriented. The routine then
returns.
[0061] FIG. 15 is a data representation diagram 210 showing, by way
of example, a view 211 of overlapping non-circular cluster 213-216
generated by the clustered display system 11 of FIG. 1. Each
cluster 213-216 has a center of mass c.sub.m 217-220 and is
oriented around a common origin 212. The center of mass as c.sub.m
of each cluster 213-216 is located at a fixed distance d 221-224
from the common origin 212. Cluster 218 overlays cluster 213 and
clusters 213, 215 and 216 overlap.
[0062] As described above, with reference to FIG. 2, each cluster
213-216 represents multi-dimensional data modeled in a
three-dimension display space. Furthermore, each of the clusters
213-216 is non-circular and defines a convex volume representing a
data grouping located within the multi-dimensional concept space.
The center of mass c.sub.m at 217-220 for each cluster 213-216, is
logically located within the convex volume. The segment measured
between the point closest to each other cluster along a span drawn
between each pair of clusters is calculable by dimensional
geometric equations, as would be recognized by one skilled in the
art. By way of example, the clusters 213-216 represent non-circular
shapes that are convex and respectively comprise a square,
triangle, octagon, and oval, although any other form of convex
shape could also be used either singly or in combination therewith,
as would be recognized by one skilled in the art.
[0063] Where each cluster 213-216 is not in the shape of a circle,
a segment is measured in lieu of the radius. Each segment is
measured from the center of mass 217-220 to a point along a span
drawn between the centers of mass for each pair of clusters
213-216. The point is the point closest to each other cluster along
the edge of each cluster. Each cluster 213-216 is reoriented along
the vector such that the edges of each cluster 213-216 do not
overlap.
[0064] While the invention has been particularly shown and
described as referenced to the embodiments thereof, those skilled
in the art will understand that the foregoing and other changes in
form and detail may be made therein without departing from the
spirit and scope of the invention.
* * * * *