초록 ▼

A recursively partitioned/nested geometric structure is employed to graphically present and/or facilitate analysis of multi-variate data, including functions of multi-dimensional variables. Visual attributes are associated with appropriate ones of the regions within the geometric structure, in accor

A recursively partitioned/nested geometric structure is employed to graphically present and/or facilitate analysis of multi-variate data, including functions of multi-dimensional variables. Visual attributes are associated with appropriate ones of the regions within the geometric structure, in accordance with determined graphing values. In one embodiment, the data are normalized, comprising relative coordinate values, and encoded into polynary strings. Processing is advantageously performed using the polynary strings.

대표청구항 ▼

What is claimed is: 1. A processor implemented data processing method comprising: identifying a first plurality of areas defined by a first corresponding plurality of geometric primitives disposed within a first innermost nested level of a first recursively partitioned/nested geometric structure ha

What is claimed is: 1. A processor implemented data processing method comprising: identifying a first plurality of areas defined by a first corresponding plurality of geometric primitives disposed within a first innermost nested level of a first recursively partitioned/nested geometric structure having at least the first plurality of geometric primitives and a first other geometric primitive disposed in a first immediately preceding outer nesting level of the first innermost nested level, with the first plurality of areas defined by the first plurality of geometric primitives nested within a first other area defined by the first other geometric primitive, the first plurality of areas corresponding to a first plurality of normalized multi-dimensional data of a first normalized multi-dimensional data space, and the first recursively partitioned/nested geometric structure corresponding to the first normalized multi-dimensional data space; determining corresponding first graphing values for said first corresponding areas within said first recursively partitioned/nested geometric structure determined for said first normalized multi-dimensional data of said first normalized multi-dimensional data space; associating corresponding first visual attributes with said first corresponding areas within said first recursively partitioned/nested geometric structure, based at least in part on corresponding ones of said determined first graphing values; and displaying said first recursively partitioned/nested geometric structure, visually differentiating said first corresponding areas based at least in part on corresponding ones of said associated first visual attributes. 2. The method of claim 1, wherein each of said first normalized multi-dimensional data of said first normalized multi-dimensional data space comprises a plurality of relative coordinate values, and the method further comprises constructing a polynary string to represent each of said first normalized multi-dimensional data and its corresponding one of said first areas within said first recursively partitioned/nested geometric structure in accordance with the relative coordinate values. 3. The method of claim 2, wherein said constructing of a polynary string to represent each of said first normalized multi-dimensional data and its corresponding one of said first areas within said first recursively partitioned/nested geometric structure in accordance with the relative coordinate values comprises selecting a symbol as the next symbolic member of the polynary string based on which of the relative coordinate values is the current highest relative coordinate value. 4. The method of claim 3, wherein said constructing of a polynary string to represent each of said first normalized multi-dimensional data and its corresponding one of said first areas within said first recursively partitioned/nested geometric structure in accordance with the relative coordinate values further comprises reducing the highest relative coordinate value in by an amount (G), upon each selection, and reducing the amount (G) after each reduction. 5. The method of claim 4, wherein the amount (G) initially equals 1-F, and thereafter reduced each time by G*(1-F), where F equals (n-1)/n, and n equals the number of relative coordinate values. 6. The method of claim 2, wherein said determining of corresponding first graphic values comprises determining frequencies of occurrence of the various polynary strings of said first normalized multi-dimensional data, and assigning the determined frequencies of occurrence to the corresponding first areas within the first recursively partitioned/nested geometric structure as the determined first graphing values of the corresponding first areas. 7. The method of claim 2, wherein the method further comprises receiving a first zooming specification comprising one or more of said polynary string constituting symbols; excluding a first subset of said first areas based at least in part on said received first zooming specification; and repeating said displaying for the remaining ones of said first areas in an expanded manner. 8. The method of claim 7, wherein the method further comprises receiving a second zooming specification comprising one or more additional ones of said polynary string constituting symbols; excluding a second subset of said remaining ones of said first areas based at least in part on said received second zooming specification; and repeating said displaying for the remaining ones of said first areas. 9. The method of claim 8, wherein the method further comprises receiving an unzoom specification; restoring the remaining ones of said first areas to re-include said excluded second subset of said first areas; and repeating said displaying for the remaining ones of said first areas. 10. The method of claim 7, wherein the method further comprises receiving an unzoom specification; restoring the remaining ones of said first areas to re-include said excluded first subset of said first areas; and repeating said displaying for said first areas. 11. The method of claim 1, wherein said determining of corresponding first graphic values comprises assigning first output values corresponding to the first normalized multi-dimensional data as the determined first graphing values of the corresponding first areas within the first recursively partitioned/nested geometric structure. 12. The method of claim 11, wherein said determining of corresponding first graphic values further comprises computing said first output values. 13. The method of claim 12, wherein each of said first normalized multi-dimensional data of said first normalized multi-dimensional data space comprises a polynary string having a plurality of symbols, encoding a plurality of relative coordinate values, and said computing of the first output values comprises for each constituting symbols of a polynary string, summing one or more appearance values corresponding to one or more appearances of the particular symbol in the polynary string, and adding the sum to an average residual relative coordinate value. 14. The method of claim 13, wherein each appearance value corresponding to an appearance of a particular symbol is dependent on the position of the particular appearance of the particular symbol in the polynary string. 15. The method of claim 14, wherein each appearance value corresponding to an appearance of a particular symbol is equal to a positional value associated with the position of the particular appearance in the polynary string. 16. The method of claim 15, wherein each positional value equals to (1-F)횞F**(k-1), and the average residual relative coordinate value equals (1-F) 횞F**K, where F equals (n-1)/n, k denotes a position in a polynary string, n equals the number of relative coordinate values, and K equals the length of the polynary string. 17. The method of claim 1, wherein said associating comprises for each of said first areas, associating a selected one of a plurality of symbols with the area based at least in part on the determined graphing value of the area. 18. The method of claim 1, wherein said associating comprises for each of said first areas, associating a selected one of a plurality of color attributes with the area based at least in part on the determined graphing value of the area. 19. The method of claim 1, wherein said associating comprises for each of said first areas, associating a selected blending of a plurality of colors with the area based at least in part on contributions to the determined graphing value of the area. 20. The method of claim 1, wherein said first areas correspond to all constituting areas of the first recursively partitioned/nested geometric structure, said first normalized multi-dimensional data are values of independent variables of a function, and said first graphing values are corresponding values of a dependent variable of the function. 21. The method of claim 1, wherein the method further comprises identifying a second plurality of areas defined by a second plurality of geometric primitives disposed within a second innermost nested level of a second recursively partitioned/nested geometric structure having at least the second plurality of geometric primitives and a second other geometric primitive disposed in a second immediately preceding outer nesting level of the second innermost nested level, with the second plurality of areas defined by the second plurality of geometric primitives nested within a second other area defined by the second other geometric primitive, the second plurality of areas corresponding to a second plurality of normalized multi-dimensional data of a second normalized multi-dimensional data space, and the second recursively partitioned/nested geometric structure corresponding to the second normalized multi-dimensional data space; determining corresponding second graphing values for said second corresponding areas within said second recursively partitioned/nested geometric structure determined for said second normalized multi-dimensional data of said second normalized multi-dimensional data space; associating corresponding second visual attributes with said second corresponding areas within said second recursively partitioned/nested geometric structure, based at least in part on corresponding ones of said determined second graphing values; and displaying said second recursively partitioned/nested geometric structure, visually differentiating said second corresponding areas based at least in part on corresponding ones of said associated second visual attributes. 22. The method of claim 21, wherein said first and second recursively partitioned/nested geometric structures are displayed in a manner such that both recursively partitioned/nested geometric structures are visible concurrently. 23. The method of claim 22, wherein each of said first and second normalized multi-dimensional data of said first and second normalized multi-dimensional data spaces comprises a polynary string having a plurality of symbols, encoding a plurality of relative coordinate values, the method further comprises receiving a first zooming specification comprising one or more of said polynary string constituting symbols; excluding a first subset of said first areas based at least in part on said received first zooming specification; excluding a second subset of said second areas based at least part on the removed ones of said first areas; and repeating said displaying for the remaining ones of said first and second areas. 24. The method of claim 21, wherein said first and second normalized multi-dimensional data are values of first and second input variables. 25. The method of claim 21, wherein said first normalized multi-dimensional data are values of input variables, and said second normalized multi-dimensional data are values of corresponding output variables. 26. The method of claim 1, wherein the method further comprises computing a location for a centroid for each of a plurality primitive elements of the geometric structure. 27. The method of claim 26, wherein coordinates (xp, yp) of the location of each centroid is computed as follows: where: (Xc, Yc) are coordinate values of the geometric structure's centroid; R is a radius extending from the geometric structure's centroid to an outermost vertex of the geometric structure; V(N, k) is w*(1-w)**(k-1) where w=1/(1+sine(π/N)); m[Lk] is outer vertex number (1, 2, . . . , N) assigned to the kth symbol appearing in a corresponding polynary string; C(N, m[Lk])=cosine(a*π); and S(N, m[Lk])=sine(a*π) [where a=(5*N-4*m[L k])/(2*N)]. 28. The method of claim 27, wherein the K values of V(N, k) are computed once responsive to a specification of N. 29. The method of claim 27, wherein at least the N values of C(N, m[Lk]) or the N values of S(N, m[Lk]) are computed once responsive to a specification of N. 30. The method of claim 1, wherein the method further comprises selecting the geometric primitives. 31. An apparatus comprising: storage medium having stored therein programming instructions designed to enable the apparatus to identify a first plurality of areas defined by a first plurality of geometric primitives disposed within a first innermost nested level of a first recursively partitioned/nested geometric structure having the first plurality of geometric primitives and a first other geometric primitive disposed in a first immediately preceding outer nesting level of the first innermost nested level, with the first plurality of areas of the first plurality of geometric primitives nested within a first other area defined by the first other geometric primitive, the first plurality of areas corresponding to a first plurality of normalized multi-dimensional data of a first normalized multi-dimensional data space, and the first recursively partitioned/nested geometric structure being-corresponding to the first normalized multi-dimensional data space, determine corresponding first graphing values for said first corresponding areas within said first recursively partitioned/nested geometric structure determined for said first normalized multi-dimensional data of said first normalized multi-dimensional data space; associate corresponding first visual attributes with said first corresponding areas within said first recursively partitioned/nested geometric structure, based at least in part on corresponding ones of said determined first graphing values, and display said first recursively partitioned/nested geometric structure, visually differentiating said first corresponding areas based at least in part on corresponding ones of said associated first visual attributes; and at least one processor coupled to the storage medium to execute the programming instructions. 32. The apparatus of claim 31, wherein each of said first normalized multi-dimensional data of said first normalized multi-dimensional data space comprises a plurality of relative coordinate values, and the programming instructions are further designed to enable the apparatus to construct a polynary string to represent each of said first normalized multi-dimensional data and its corresponding one of said first areas within said first recursively partitioned/nested geometric structure in accordance with the relative coordinate values. 33. The apparatus of claim 32, wherein said programming instructions are designed to enable the apparatus to perform said constructing of a polynary string by selecting a symbol as the next symbolic member of the polynary string based on which of the relative coordinate values is the current highest relative coordinate value. 34. The apparatus of claim 33, wherein said programming instructions are further designed to enable the apparatus to perform said constructing of a polynary string by reducing the highest relative coordinate value in by an amount (G), upon each selection, and reducing the amount (G) after each reduction. 35. The apparatus of claim 34, wherein said programming instructions are designed to enable the apparatus to set the amount (G) initially to 1-F, and thereafter reduced each time by G*(1-F), where F equals (n-1)/n, and n equals the number of relative coordinate values. 36. The apparatus of claim 32, wherein said programming instructions are designed to enable the apparatus to perform said determining by determining frequencies of occurrence of the various polynary strings of said first normalized multi-dimensional data, and assigning the determined frequencies of occurrence to the corresponding first areas within the first recursively partitioned/nested geometric structure as the determined first graphing values of the corresponding first areas. 37. The apparatus of claim 32, wherein said programming instructions are further designed to enable the apparatus to receive a first zooming specification comprising one or more of said polynary string constituting symbols; exclude a first subset of said first areas based at least in part on said received first zooming specification; and repeat said displaying for the remaining ones of said first areas in an expanded manner. 38. The apparatus of claim 37, wherein said programming instructions are further designed to enable the apparatus to receive a second zooming specification comprising one or more additional ones of said polynary string constituting symbols; exclude a second subset of said remaining ones of said first areas based at least in part on said received second zooming specification; and repeat said displaying for the remaining ones of said first areas. 39. The apparatus of claim 38, wherein said programming instructions are designed to enable the apparatus to receive an unzoom specification; restore the remaining ones of said first areas to re-include said excluded second subset of said first areas; and repeat said displaying for the remaining ones of said first areas. 40. The apparatus of claim 37, wherein said programming instructions are further designed to enable the apparatus to receive an unzoom specification; restore the remaining ones of said first areas to re-include said excluded first subset of said first areas; and repeat said displaying for said first areas. 41. The apparatus of claim 31, wherein said programming are designed to enable the apparatus to perform said determining by first output values corresponding to the first normalized multi-dimensional data as the determined first graphing values of the corresponding first areas within the first recursively partitioned/nested geometric structure. 42. The apparatus of claim 41, wherein said programming instructions are further designed to enable the apparatus to perform said determining by computing said first output values. 43. The apparatus of claim 42, wherein each of said first normalized multi-dimensional data of said first normalized multi-dimensional data space comprises a polynary string having a plurality of symbols, encoding a plurality of relative coordinate values, and said programming instructions are designed to enable the apparatus to perform said computing by summing one or more appearance values corresponding to one or more appearances of the particular symbol in a polynary string, and adding the sum to an average residual relative coordinate value, and repeating said summing and adding for each constituting symbols of the polynary string. 44. The apparatus of claim 43, wherein each appearance value corresponding to an appearance of a particular symbol is dependent on the position of the particular appearance of the particular symbol in the polynary string. 45. The apparatus of claim 44, wherein each appearance value corresponding to an appearance of a particular symbol is equal to a positional value associated with the position of the particular appearance in the polynary string. 46. The apparatus of claim 45, wherein each positional value equals to (1-F)횞F**(k-1), and the average residual relative coordinate value equals (1-F) 횞F**K, where F equals (n-1)/n, k denotes a position in a polynary string, n equals the number of relative coordinate values, and K equals the length of the polynary string. 47. The apparatus of claim 31, wherein said programming instructions are designed to enable the apparatus to perform said associating by associating, for each of said first areas, a selected one of a plurality of symbols with the area based at least in part on the determined graphing value of the area. 48. The apparatus of claim 31, wherein said programming instructions are designed to enable the apparatus to perform said associating by associating, for each of said first areas, a selected one of a plurality of color attributes with the area based at least in part on the determined graphing value of the area. 49. The apparatus of claim 31, wherein said programming instructions are designed to enable the apparatus to perform said associating by associating, for each of said first areas, a selected blending of a plurality of colors with the area based at least in part on contributions to the determined graphing value of the area. 50. The apparatus of claim 31, wherein said first areas correspond to all constituting areas of the first recursively partitioned/nested geometric structure, said first normalized multi-dimensional data are values of independent variables of a function, and said first graphing values are corresponding values of a dependent variable of the function. 51. The apparatus of claim 31, wherein said programming instructions are further designed to enable the apparatus to identify a second plurality of areas defined by a second plurality of geometric primitives disposed within a second innermost nested level of a second recursively partitioned/nested geometric structure having at least the second plurality of geometric primitives and a second other geometric primitive disposed in a second immediately preceding outer nesting level of the second innermost nested level, with the second plurality of areas defined by the second plurality of geometric primitives nested within a second other area defined by the second other geometric primitive, the second plurality of areas corresponding to a second plurality of normalized multi-dimensional data of a second normalized multi-dimensional data space, and the second recursively partitioned/nested geometric structure corresponding to the second normalized multi-dimensional data space; determine corresponding second graphing values for said second corresponding areas within said second recursively partitioned/nested geometric structure determined for said second normalized multi-dimensional data of said second normalized multi-dimensional data space; associate corresponding second visual attributes with said second corresponding areas within said second recursively partitioned/nested geometric structure, based at least in part on corresponding ones of said determined second graphing values; and display said second recursively partitioned/nested geometric structure, visually differentiating said second corresponding areas based at least in part on corresponding ones of said associated second visual attributes. 52. The apparatus of claim 51, wherein said first and second partitioned/nested geometric structures are displayed in a manner such both recursively partitioned/nested geometric structures are visible concurrently. 53. The apparatus of claim 52, wherein each of said first and second normalized multi-dimensional data of said first and second normalized multi-dimensional data spaces comprises a polynary string having a plurality of symbols, encoding a plurality of relative coordinate values, said programming instructions are further designed to enable the apparatus to receive a first zooming specification comprising one or more of said polynary string constituting symbols; exclude a first subset of said first areas based at least in part on said received first zooming specification; exclude a second subset of said second areas based at least part on the removed ones of said first areas; and repeat said displaying for the remaining ones of said first and second areas. 54. The apparatus of claim 51, wherein said first and second normalized multi-dimensional data are values of first and second input variables. 55. The apparatus of claim 51, wherein said first normalized multi-dimensional data are values of input variables, and said second normalized multi-dimensional data are values of corresponding output variables. 56. The apparatus of claim 31, wherein said apparatus is a selected one of a palm sized processor based device, a notebook computer, a desktop computer, a set-top box, a single processor server, a multi-processor server, and a collection of coupled servers. 57. The apparatus of claim 31, wherein said programming instructions are further designed to compute a location for a centroid for each of a plurality of primitive elements of the geometric structure. 58. The apparatus of claim 57, wherein said programming instructions are designed to compute coordinates (xp, yp ) of the location of each centroid as follows: where: (Xc, Yc) are coordinate values of the geometric structure's centroid; R is a radius extending from the geometric structure's centroid to an outermost vertex of the geometric structure; V(N, k) is w*(1-w)**(k-1) where w=1/(1+sine(π/N)); m[Lk] is outer vertex number (1, 2, . . . , N) assigned to the kth symbol appearing in a corresponding polynary string; C(N, m[Lk])=cosine(a*π); and S(N, m[Lk])=sine(a*π) [where a=(5*N-4*m[L k])/(2*N)]. 59. The apparatus of claim 58, wherein said programming instructions are designed to compute the K values of V(N, k) once responsive to a specification of N. 60. The method of claim 58, wherein said programming instructions are designed to compute at least the N values of C(N, m[L k]) or the N values of S(N, m[Lk]) once responsive to a specification of N. 61. The apparatus of claim 31, wherein the programming instructions are further designed to enable the apparatus to select the geometric primitives.