Method and system for interactive parameter optimization using multi-dimensional scaling

• US 20060173874A1
• Filed: 01/27/2006
• Published: 08/03/2006
• Est. Priority Date: 02/03/2005
• Status: Abandoned Application

• Current Assignee: Siemens Medical Solutions USA Incorporated (Siemens AG)
• Original Assignee: Siemens Medical Solutions USA Incorporated (Siemens AG)
• Inventors: Chen, Yunqiang, Tyan, Jason Jenn-Kwei
• Application Number:
  US11/342,150
• Publication Number:
  US 20060173874A1
• Time in Patent Office: Days
• US Class Current: 1/1
• CPC Class Codes: G06F 17/11 for solving equations , e.g. nonlinear equations, general mathematical optimization problems optimization specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06F 18/2137 based on criteria of topology preservation, e.g. multidimensional scaling or self-organising maps
• CPC Class Codes: G06T 5/20 using local operators

Abstract

A method for interactively optimizing a system comprises interactively adjusting controlling parameters in a parameter set, by deriving successive pluralities of parameter sets in a parameter space, each of whose respective member parameter sets are respectively ranked in order, utilizing a ranking input based on respective system performance associated with each parameter set and from each of which plurality of parameter sets an optimal parameter set is selected and used as a point of departure for deriving the next following plurality of parameter sets in the parameter space, in accordance with the preceding ranking, in conjunction with a step size and a step direction derived from the ranking, in accordance with multidimensional scaling (MDS).

Claims

1. A method for interactively optimizing parameters in a parameter set, comprising:

deriving successive pluralities of parameter sets in a parameter space, each of whose respective member parameter sets are respectively ranked in order based on a ranking input, and from each of which an optimal parameter set is selected and used as a point of departure for deriving in a next iteration, the next following plurality of parameter sets in said parameter space, in accordance with said ranking input in the preceding iteration, in conjunction with a step size and a step direction derived from said ranking input, in accordance with multidimensional scaling (MDS).

2. A method for interactively optimizing a system comprising:

interactively adjusting controlling parameters in a parameter set, by deriving successive pluralities of parameter sets in a parameter space, each of whose respective member parameter sets are respectively ranked in order, utilizing a ranking input based on respective system performance associated with each parameter set and from each of which plurality of parameter sets an optimal parameter set is selected and used as a point of departure for deriving the next following plurality of parameter sets in said parameter space, in accordance with said preceding ranking, in conjunction with a step size and a step direction derived from said ranking, in accordance with multidimensional scaling (MDS).

3. A method for optimizing a system, comprising:

interactively adjusting controlling parameters in a parameter set comprising respective member parameter sets, said adjustment comprising;

deriving successive pluralities of parameter sets in a parameter space;

ranking each of said respective member parameter sets in order, utilizing a ranking input based on respective system performance associated with each parameter set;

selecting an optimal parameter set from said plurality of parameter sets; and

using said optimal parameter set as a point of departure for deriving a next following plurality of parameter sets in said parameter space, in accordance with the preceding ranking, in conjunction with a step size and a step direction derived from the ranking, in accordance with multidimensional scaling (MDS).

4. A method as recited in claim 3, comprising deriving said successive pluralities of parameter sets by utilizing reconstruction of data sets of said plurality of parameter sets in a lower-dimensional space, while optimally preserving ranking and mutual distances, considered in a least-squares sense.

5. A method as recited in claim 4, comprising utilizing user input as said ranking input.

6. A method as recited in claim 5, comprising using comparisons with a desired standard as said ranking input.

7. A method for optimizing a system, comprising:

interactively adjusting controlling parameters in a parameter set comprising respective member parameter sets, said adjusting comprising;

deriving a first plurality of parameter sets in a parameter space from a given parameter set for controlling said system;

ranking each of said respective parameter sets in order, utilizing a ranking input based on respective system performance associated with each parameter set, wherein a topmost ranked parameter set is selected as a first optimal parameter set; and

using said optimal parameter set as a point of departure for deriving a next following plurality of parameter sets in said parameter space, in accordance with the preceding ranking, in conjunction with a step size and a step direction derived from the ranking, in accordance with multidimensional scaling (MDS).

8. A method in accordance with claim 7, including in a first iteration:

deriving a second plurality of parameter sets from said first plurality of parameter sets beginning with the said first optimal parameter set as a first starting parameter set in said parameter space, wherein other parameter sets of said second plurality are placed in said parameter space, using information from said ranking, said ranking being weighted for placement of parameter sets of said second plurality in accordance with multi-dimensional scaling so as to increase a likelihood of said other parameter sets of said second plurality including a parameter representing an optimal parameter in a next iteration of ranking and selection; and

ranking performance with said second plurality of parameter sets in descending order of optimality, whereof the topmost parameter set is selected as a second optimal parameter set.

9. A method in accordance with claim 8, including in a second iteration:

deriving a third plurality of parameter sets from said second plurality of parameter sets beginning with said second optimal parameter set as a second starting parameter set in said parameter space, and continuing in an analogous manner to selection of said second optimal parameter set to select a third optimal parameter set.

10. A method in accordance with claim 9, wherein a fourth, and optionally, further iterations are performed in accordance with the steps, mutatis mutandis, performed in the foregoing iteration.

11. A method in accordance with claim 8, wherein said parameter space is a multi-dimensional space.

12. A method in accordance with claim 9, wherein said parameter space is a multi-dimensional space.

13. A method in accordance with claim 8, wherein said step of deriving a second plurality of parameter sets comprises utilizing a multi-dimensional scaling algorithm designed to find an optimal search direction in said parameter space, which best preserves relative ranking between said parameter sets.

14. A method in accordance with claim 14, wherein said step of deriving a second plurality of parameter sets comprises computing from said ranking, a center point, a direction for placement of parameter sets and a step size for proceeding in said direction, computed from said ranking.

15. A method in accordance with claim 14, wherein said step of computing from said ranking, a center point, a direction for placement of parameter sets and a step size for proceeding in said direction is performed in each iteration.

16. A method in accordance with claim 15, wherein said step of computing a direction comprises a computing a direction for placement of said parameter sets such that ranking of parameter sets onto the direction vector is preserved, and mutual distances are preserved in an optimal manner.

17. A method in accordance with claim 16, wherein said parameter space is a multi-dimensional space.

18. A method in accordance with claim 17 comprising:

computing said step size, defined as s;

computing said center point, defined as C; and

computing said direction {right arrow over (d)}, all computations using feedback from said rankings.

19. A method in accordance with claim 18, wherein said center point is always set to a point with the best rating, whereby said point with the best rating is thus always shown, permitting comparison between different iterations.

20. A method in accordance with claim 19, comprising:

updating said step size in accordance with the following;

if said center point corresponds to an optimal ranking, then dividing said step size by 2, or

if a different point yields the best rating and the best point in the previous iteration was not the center point, multiplying said step size by 1.25 so as to tend to recover from any excessive amount of shrinking in a previous step, or

otherwise, said step size remains unchanged.

21. A method in accordance with claim 20, wherein said computing said direction {right arrow over (d)}, in accordance with multidimensional scaling (MDS), is performed as follows:

points in said parameter space be are given as P⁽ⁱ⁾ with coordinates P_j⁽ⁱ⁾ and ratings r⁽ⁱ⁾, with 0≦

i<

p and 0≦

j<

n;

differences between the ratings of the parameter sets are interpreted as distances between the respective points in said parameter space;

computing a p×

p distance matrix D, being a Euclidian Distance, as follows;

D_kl=(r^(k)−

r^(l))²;

computing an auxiliary matrix M with the elements

$M_{\mathrm{ab}}=-\frac{1}{2}<br><br>\left(D_{\mathrm{ab}}-\frac{1}{p}<br><br>\underset{a}{\sum <br><br>}<br><br>D_{\mathrm{ab}}+\frac{1}{p^2}<br><br>\underset{a,b}{\sum <br><br>}<br><br>D_{\mathrm{ab}}-\frac{1}{p}<br><br>\underset{b}{\sum <br><br>}<br><br>D_{\mathrm{ab}}\right);<br><br>$

making a singular value decomposition of M, yielding the eigenvalues λ

⁽ⁱ⁾ and the corresponding eigenvectors {right arrow over (e⁽ⁱ⁾)};

selecting, in a given setting, only the dimension with the largest eigenvalue and a new direction based on multidimensional scaling is

{right arrow over (d)}={right arrow over (e⁽¹⁾)}

where {right arrow over (d)} is a unit vector (i.e. |{right arrow over (d)}|=1); and

setting a minimum criterion to ensures a non-zero step size in every direction, absent user input setting a step size.

22. A method in accordance with claim 21, wherein;

said number of points, p is taken as six (6) and said number of dimensions, n, is taken as five (5).

23. A method in accordance with claim 22, wherein placement of said points on a hyper-sphere is as follows:

computing six parameter sets for a next iteration, given a step size s, a center C and a direction {right arrow over (d)};

as a first step, said computing is performed is done in an isotropic space, wherein a length unit is the same for all dimensions;

said points are set on a sphere with center C_s=(0,0,0,0,0) and radius 1, said placement depending only on {right arrow over (d)} and the previous direction;

indexing all points in said isotropic space with ^iso;

the first point is the center of the sphere;

^isoP⁽⁰⁾=(0;

0;

0;

0;

0),

the second point is given by the direction {right arrow over (d)};

^isoP⁽¹⁾=^isoP⁽⁰⁾+{right arrow over (d)}=(d₁;

d₂;

d₃;

d₄;

d₅), and

the third point is given by a combination of the last direction and the current one;

${\text{\hspace{1em}<br><br>}}^{\mathrm{iso}}<br><br>P^{\left(2\right)}<br><br>{=}^{\mathrm{iso}}<br><br>P^{\left(0\right)}+\stackrel{\to <br><br>}{k},\mathrm{with}<br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{\to <br><br>}{k}=\frac{\frac{\stackrel{\to <br><br>}{d}}{4}+\stackrel{\to <br><br>}{d_{\mathrm{prev}}}}{<br><br>\frac{\stackrel{\to <br><br>}{d}}{4}+\stackrel{\to <br><br>}{d_{\mathrm{prev}}}<br><br>};<br><br>$

for the rest of said points, randomly selecting three unit vectors {right arrow over (r₁)}, {right arrow over (r₂)}, {right arrow over (r₃)}, observing a minimal angle of 72°

, corresponding to a division of 360°

by 5 or, in the alternative, a corresponding division by another number of points, between every pair of them as well as between any of them and {right arrow over (d)} and {right arrow over (k)}, which conditions are formulated as follows;

|{right arrow over (r₁)}|=|{right arrow over (r₂)}|=|{right arrow over (r₃)}|=1
{right arrow over (r_i)}·

{right arrow over (k)}≦

cos (72°

), i=1, 2, 3
{right arrow over (r_i)}·

{right arrow over (d)}≦

cos (72°

), i=1, 2, 3
{right arrow over (r_i)}·

{right arrow over (r_j)}≦

cos (72°

), i, j=1, 2, 3 and i≠

j,

 

said minimal angles ensuring a sufficient difference of said parameter points and the corresponding parameter sets; and

defining the remaining three points;

^isoP⁽³⁾=^isoP⁽⁰⁾+{right arrow over (r₁)}, ^isoP⁽⁴⁾=^isoP⁽⁰⁾+{right arrow over (r₂)} and ^isoP⁽⁵⁾=^isoP⁽⁰⁾+{right arrow over (r₃)} by these vectors.

24. A method in accordance with claim 23, wherein:

generating the points in said isotropic space in the case of decreased dimensionality is performed alternatively as follows;

in the case where a user has set the direction in two or more directions to 0, the first point, ^isoP⁽⁰⁾, is set to the center;

^isoP⁽⁰⁾=(0;

0;

0;

0;

0);

placing the other points, depending on the number of dimensions with non-zero step size, as follows;

where no dimension has a non-zero step size;

f, all parameters have zero step size, nothing further is done, as the direction vector is identical to the zero-vector and all points are set to the center;

^isoP⁽ⁱ⁾=^isoP⁽⁰⁾, i=1 . . . p−

1;

in the case of one dimension with non-zero step size;

if one parameter has non-zero step size, the five points, or another number where the number of points selected is different, in are computed in an adaptation of Brent'"'"'s Golden Section Search.

25. A method in accordance with claim 24, wherein:

new points in accordance with said adaptation Brent'"'"'s Golden Section Search are the following;

^isoP⁽¹⁾=^isoP⁽⁰⁾+φ

·

{right arrow over (d)}
^isoP⁽²⁾=^isoP⁽⁰⁾−

φ

·

{right arrow over (d)}
^isoP⁽³⁾=^isoP⁽⁰⁾+{right arrow over (d)}
^isoP⁽⁴⁾=^isoP⁽⁰⁾−

{right arrow over (d)}
^isoP⁽⁵⁾=^isoP⁽⁰⁾+(1+φ

)·

{right arrow over (d)}

wherein φ

denotes the golden section;

$\mathrm{\phi <br><br>}=\frac{\sqrt{5}-1}{2}\approx <br><br>0.618034.$

26. A method in accordance with claim 25 wherein:

in the case of two dimensions with non-zero step size;

in the case of two varying parameters, wherein a circle is defined by its center and the direction, computing said first point ^isoP⁽¹⁾ on said circle as ^isoP⁽¹⁾=^isoP⁽⁰⁾−

{right arrow over (d)}; and

the other four being rotations of ^isoP⁽¹⁾ of 72°

around said center.

27. A method in accordance with claim 26, wherein:

in the case of three dimensions with non-zero step size;

if three parameters have non-zero variation, utilizing an equilateral tetrahedron wherein said first point ^isoP⁽¹⁾=^isoP⁽⁰⁾−

{right arrow over (d)} being the apex;

the other four points lying on a plane corresponding to the ground plane of a tetrahedron, whereof the middle point is herein called M, is M=C+⅓

·

{right arrow over (d)}, and from said middle point M of said ground plane, four vectors orthogonal to {right arrow over (d)} lead to the remaining points;

selecting a first vector to P₂ such that the two components with the biggest step sizes are parallel to the direction of the last step;

determining said vector by the following the length condition ({right arrow over (^isoP^{(0) iso}P⁽²⁾)} has the same length as {right arrow over (d)}) and the condition of the perpendicularity between {right arrow over (M^isoP⁽²⁾)} and {right arrow over (d)}, and thus ^isoP⁽²⁾. ^isoP⁽⁴⁾ is ^isoP⁽²⁾ reflected on M; and

for the two remaining points, choosing the vectors to be orthogonal to the previously generated vectors, that is, {right arrow over (M^isoP⁽³⁾)} is rectangular to {right arrow over (M^isoP⁽²⁾)}, and, wherein, subject to the two other conditions ({right arrow over (M^isoP⁽³⁾)} rectangular to {right arrow over (d)}, {right arrow over (^isoP^{(0) iso}P⁽³⁾)} has the same length as {right arrow over (d)}) determine {right arrow over (M ^isoP⁽³⁾)} and ^isoP⁽³⁾. ^isoP⁽⁵⁾ is thus the reflection of ^isoP⁽³⁾ on M.

28. A method in accordance with claim 26, including:

mapping said points in an isotropic parameter space into an anisotropic parameter space by;

deforming said hyper-sphere into a five-dimensional ellipsoid, taking into account said center C;

utilizing said step size s to determine the size of said sphere; and

initial parameter directions determine the anisotropy of said anisotropic parameter space.

29. A method in accordance with claim 28, wherein said mapping said points in an isotropic parameter space into an anisotropic parameter comprises:

mapping in accordance with the following formula;

P_j⁽ⁱ⁾=C+s·

({right arrow over (d_init)})_j·

^isoP_j⁽ⁱ⁾

wherein ({right arrow over (d_init)})_j denotes the j-th component of said initial direction.

30. A method in accordance with claim 29, including performing a permutation of the point numbering.

31. A method for interactively optimizing parameters in a parameter set for controlling an image filtering algorithm, comprising deriving successive pluralities of parameter sets in a parameter space, each of whose respective member parameter sets are respectively ranked in order based on a ranking input, utilizing respective filtered images, and from each of which an optimal parameter set is selected, based on a selection input, and used as a point of departure for deriving the next following plurality of parameter sets in said parameter space, in accordance with the preceding ranking, in conjunction with a step size and a step direction derived from said ranking, in accordance with multidimensional scaling (MDS).

32. A method as recited in claim 31, comprising deriving said successive pluralities of parameter sets by utilizing reconstruction of data sets of said plurality of parameter sets in a lower-dimensional space, while optimally preserving ranking and mutual distances, considered in a least-squares sense.

33. A method as recited in claim 31, comprising utilizing user input as said ranking input.

34. A method as recited in claim 31, comprising using comparisons with a desired standard as said ranking input.

35. A method for interactively optimizing parameters in a parameter set for controlling an image filtering algorithm, comprising:

inputting an original image to said image filtering algorithm;

deriving successive pluralities of parameter sets in a parameter space;

deriving a plurality of filtered images from said original image, corresponding respectively to each parameter set;

ranking said plurality of images in descending order based on a ranking input and designating a first top-ranking image;

starting with a parameter set corresponding to said first top-ranking image, as a point of departure for deriving a next succeeding plurality of parameter sets in said parameter space, in accordance with said ranking, in conjunction with a step size and a step direction derived from said ranking, in accordance with multidimensional scaling (MDS);

deriving a second plurality of filtered images from said original image, corresponding respectively to each parameter set of said succeeding plurality;

ranking said second plurality of images in descending order based on a ranking input and designating a second top-ranking image; and

starting with a parameter set corresponding to said second top-ranking image, proceeding analogously, mutatis mutandis, as follows starting with said first top-ranking image until sufficient iterations are made to determine a best one of said top-ranking images.

36. A method as recited in claim 35, comprising utilizing user input as said ranking input.

37. A method as recited in claim 35, comprising using comparisons with a desired standard as said ranking input.

38. A method as recited in claim 37, comprising deriving said plurality of parameter sets by utilizing MDS.

39. A method as recited in claim 38, comprising deriving said plurality of parameter sets by utilizing reconstruction of data sets of said plurality of parameter sets in a lower-dimensional space, while optimally preserving ranking and mutual distances, considered in a least-squares sense.

40. A method for interactively optimizing parameters in a parameter set for controlling an image filtering algorithm, comprising

deriving a first plurality of parameter sets in a parameter space from a given parameter set for controlling said image filtering algorithm;

inputting an initial image for filtering by said image filtering algorithm for deriving a first plurality of filtered images from said initial image, each corresponding to a respective parameter set of said first plurality of parameter sets;

ranking images of said first plurality of filtered images in descending order of optimality, whereof the topmost image is selected as a first optimal image; and

including in a first iteration;

deriving a second plurality of parameter sets from said first plurality of parameter sets beginning with the parameter set corresponding to said first optimal image as a first starting parameter set in a parameter space, wherein other parameter sets of said second plurality are placed in said parameter space, using information from said ranking images of said first plurality of filtered images, said ranking being weighted such that placement of parameter sets of said second plurality in accordance with multi-dimensional scaling so as to increase a likelihood of said other parameter sets of said second plurality including a parameter representing an optimal image in a next iteration of ranking and selection;

deriving a second plurality of filtered images from said second plurality of parameter sets, each corresponding to a respective parameter set of said second plurality of parameter sets, and

ranking images of said second plurality of filtered images in descending order of optimality, whereof the topmost image is selected as a second optimal image.

41. A method in accordance with claim 40, including in a second iteration:

deriving a third plurality of parameter sets from said second plurality of parameter sets beginning with the parameter set corresponding to said second optimal image as a first starting parameter set in said parameter space, and continuing in an analogous manner to selection of said second optimal image to select a third optimal image.

42. A method in accordance with claim 41, wherein a fourth, and optionally, further iterations are performed in accordance with the steps, mutatis mutandis, performed in the foregoing iteration.

43. A method in accordance with claim 42, wherein said parameter space is a multi-dimensional space.

44. A method in accordance with claim 40, wherein said parameter space is a multi-dimensional space.

45. A method in accordance with claim 43, wherein said step of deriving a second plurality of parameter sets comprises utilizing a multi-dimensional scaling algorithm designed to find the optimal search direction in the parameter space, which best preserves relative ranking between said parameter sets.

46. A method in accordance with claim 41, wherein said step of deriving a second plurality of parameter sets comprises computing from said ranking, a center point, a direction for placement of parameter sets and a step size for proceeding in said direction, computed from said ranking.

47. A method in accordance with claim 41, wherein said step of computing from said ranking, a center point, a direction for placement of parameter sets and a step size for proceeding in said direction is performed in each iteration.

48. A method in accordance with claim 47, wherein said step of computing a direction comprises a computing a direction for placement of said parameter sets such that ranking of parameter sets onto the direction vector is preserved, and mutual distances are preserved in an optimal manner.

49. A method in accordance with claim 48, wherein said parameter space is a multi-dimensional space.

50. A method in accordance with claim 49, comprising:

computing said step size, defined as s;

computing said center, defined as C; and

computing said direction {right arrow over (d)}, all computations using feedback from said rankings of images of said filtered images.

51. A method in accordance with claim 50, wherein said center point is always set to point with the best rating, whereby said point with the best rating is thus always shown, permitting comparison between different iterations.

52. A method in accordance with claim 51, comprising:

updating said step size in accordance with the following;

if said center point corresponds to an optimal ranking, then dividing said step size by 2, or

if a different point yields the best rating and the best point in the previous iteration was not the center point, multiplying said step size by 1.25 so as to tend to recover from any excessive amount of shrinking in a previous step, or

otherwise, said step size remains unchanged.

53. A method in accordance with claim 52, wherein said computing said direction {right arrow over (d)}, in accordance with multidimensional scaling (MDS), is performed as follows:

points in said parameter space be are given as P⁽ⁱ⁾ with coordinates P_j⁽ⁱ⁾ and ratings r⁽ⁱ⁾, with 0≦

i<

p and 0≦

j<

n;

differences between the ratings of the image are interpreted as distances between the respective points in said parameter space;

computing a p×

p distance matrix D, being a Euclidian Distance, as follows;

D_kl=(r^(k)−

r^(l))²;

computing an auxiliary matrix M with the elements

$M_{\mathrm{ab}}=-\frac{1}{2}<br><br>\left(D_{\mathrm{ab}}-\frac{1}{p}<br><br>\underset{a}{\sum <br><br>}<br><br>D_{\mathrm{ab}}+\frac{1}{p^2}<br><br>\underset{a,b}{\sum <br><br>}<br><br>D_{\mathrm{ab}}-\frac{1}{p}<br><br>\underset{b}{\sum <br><br>}<br><br>D_{\mathrm{ab}}\right);<br><br>$

making a singular value decomposition of M, yielding the eigenvalues λ

⁽ⁱ⁾ and the corresponding eigenvectors {right arrow over (e⁽ⁱ⁾)};

selecting, in a given setting, only the dimension with the largest eigenvalue and a new direction based on multidimensional scaling is

{right arrow over (d)}={right arrow over (e⁽¹⁾)}

where {right arrow over (d)} is a unit vector (i.e. |{right arrow over (d)}|=1); and

setting a minimum criterion to ensures a non-zero step size in every direction, absent user input setting a step size.

54. A method in accordance with claim 53, wherein;

said number of points, p is taken as not more than six (6) and said number of dimensions, n, is taken as no more than five (5).

55. A method in accordance with claim 54, wherein placement of said points hyper-sphere is as follows:

computing six parameter sets for a next iteration, given a step size s, a center C and a direction {right arrow over (d)};

as a first step, said computing is performed is done in an isotropic space, wherein a length unit is the same for all dimensions;

said points are set on a sphere with center C_s=(0,0,0,0,0) and radius 1, said placement depending only on {right arrow over (d)} and the previous direction;

indexing all points in said isotropic space with ^iso;

the first point is the center of the sphere;

^isoP⁽⁰⁾=(0;

0;

0;

0;

0),

the second point is given by the direction {right arrow over (d)};

^isoP⁽¹⁾=^isoP⁽⁰⁾+{right arrow over (d)}=(d₁;

d₂;

d₃;

d₄;

d₅), and

the third point is given by a combination of the last direction and the current one;

${\text{\hspace{1em}<br><br>}}^{\mathrm{iso}}<br><br>P^{\left(2\right)}<br><br>{=}^{\mathrm{iso}}<br><br>P^{\left(0\right)}+\stackrel{\to <br><br>}{k},\mathrm{with}<br><br>\text{\hspace{1em}<br><br>}<br><br>\stackrel{\to <br><br>}{k}=\frac{\frac{\stackrel{\to <br><br>}{d}}{4}+\stackrel{\to <br><br>}{d_{\mathrm{prev}}}}{<br><br>\frac{\stackrel{\to <br><br>}{d}}{4}+\stackrel{\to <br><br>}{d_{\mathrm{prev}}}<br><br>};<br><br>$

for the rest of said points, randomly selecting three unit vectors {right arrow over (r₁)}, {right arrow over (r₂)}, {right arrow over (r₃)}, observing a minimal angle of 72°

, corresponding to a division of 360°

by 5 or, in the alternative, a corresponding division by another number of points, between every pair of them as well as between any of them and {right arrow over (d)} and {right arrow over (k)}, which conditions are formulated as follows;

|{right arrow over (r₁)}|=|{right arrow over (r₂)}|=|{right arrow over (r₃)}|=1
{right arrow over (r_i)}·

{right arrow over (k)}≦

cos (72°

), i=1, 2, 3
{right arrow over (r_i)}·

{right arrow over (d)}≦

cos (72°

), i=1, 2, 3
{right arrow over (r_i)}·

{right arrow over (r_j)}≦

cos (72°

), i, j=1, 2, 3 and i≠

j,

 

said minimal angles ensuring a sufficient difference of said parameter points and the corresponding images; and

defining the remaining three points;

^isoP⁽³⁾=^isoP⁽⁰⁾+{right arrow over (r₁)}, ^isoP⁽⁴⁾=^isoP⁽⁰⁾+{right arrow over (r₂)} and ^isoP⁽⁵⁾=^isoP⁽⁰⁾+{right arrow over (r₃)} by these vectors.

56. A method in accordance with claim 55, wherein:

generating the points in said isotropic space in the case of decreased dimensionality is performed alternatively as follows;

in the case where a user has set the direction in two or more directions to 0, the first point, ^isoP⁽⁰⁾, is set to the center;

^isoP⁽⁰⁾=(0;

0;

0;

0;

0);

placing the other points, depending on the number of dimensions with non-zero step size, as follows;

where no dimension has a non-zero step size;

f, all parameters have zero step size, nothing further is done, as the direction vector is identical to the zero-vector and all points are set to the center;

^isoP⁽ⁱ⁾=^isoP⁽⁰⁾, i=1 . . . p−

1;

in the case of one dimension with non-zero step size;

if one parameter has non-zero step size, the five points, or another number where the number of points selected is different, in are computed in an adaptation of Brent'"'"'s Golden Section Search.

57. A method in accordance with claim 56, wherein:

new points in accordance with said adaptation Brent'"'"'s Golden Section Search are the following;

^isoP⁽¹⁾=^isoP⁽⁰⁾+φ

·

{right arrow over (d)}
^isoP⁽²⁾=^isoP⁽⁰⁾−

φ

·

{right arrow over (d)}
^isoP⁽³⁾=^isoP⁽⁰⁾+{right arrow over (d)}
^isoP⁽⁴⁾=^isoP⁽⁰⁾−

{right arrow over (d)}
^isoP⁽⁵⁾=^isoP⁽⁰⁾+(1+φ

)·

{right arrow over (d)}

 

wherein φ

denotes the golden section;

$\mathrm{\phi <br><br>}=\frac{\sqrt{5}-1}{2}\approx <br><br>0.618034.$

58. A method in accordance with claim 57, wherein:

in the case of two dimensions with non-zero step size;

in the case of two varying parameters, wherein a circle is defined by its center and the direction, computing said first point ^isoP⁽¹⁾ on said circle as ^isoP⁽¹⁾=^isoP⁽⁰⁾−

{right arrow over (d)}; and

the other four being rotations of ^isoP⁽¹⁾ of 72°

around said center.

59. A method in accordance with claim 58, wherein:

in the case of three dimensions with non-zero step size;

if three parameters have non-zero variation, utilizing an equilateral tetrahedron wherein said first point ^isoP⁽¹⁾=^isoP⁽⁰⁾−

{right arrow over (d)} being the apex;

the other four points lying on a plane corresponding to the ground plane of a tetrahedron, whereof the middle point is herein called M, is M=C+⅓

·

{right arrow over (d)}, and from said middle point M of said ground plane, four vectors orthogonal to {right arrow over (d)} lead to the remaining points;

selecting a first vector to P₂ such that the two components with the biggest step sizes are parallel to the direction of the last step;

determining said vector by the following the length condition ({right arrow over (^isoP^{(0) iso}P⁽²⁾)} has the same length as {right arrow over (d)}) and the condition of the perpendicularity between {right arrow over (M^isoP⁽²⁾)} and {right arrow over (d)}, and thus ^isoP⁽²⁾. ^isoP⁽⁴⁾ is ^isoP⁽²⁾ reflected on M;

for the two remaining points, choosing the vectors to be orthogonal to the previously generated vectors, that is, {right arrow over (M^isoP⁽³⁾)} is rectangular to {right arrow over (M^isoP⁽²⁾)}, and, wherein, subject to the two other conditions ({right arrow over (M^isoP⁽³⁾)} rectangular to {right arrow over (d)}, {right arrow over (^isoP^{(0) iso}P⁽³⁾)} has the same length as {right arrow over (d)}) determine {right arrow over (M^isoP⁽³⁾)} and ^isoP⁽³⁾. ^isoP⁽⁵⁾ is thus the reflection of ^isoP⁽³⁾ on M.

60. A method in accordance with claim 59, including:

mapping said points in an isotropic parameter space into an anisotropic parameter space by;

deforming said hyper-sphere into a five-dimensional ellipsoid, taking into account said center C;

utilizing said step size s to determine the size of said sphere; and

initial parameter directions determine the anisotropy of said anisotropic parameter space.

61. A method in accordance with claim 60, wherein said mapping said points in an isotropic parameter space into an anisotropic parameter comprises:

mapping in accordance with the following formula;

P_j⁽ⁱ⁾=C+s·

({right arrow over (d_init)})_j·

^isoP_j⁽ⁱ⁾

wherein ({right arrow over (d_init)})_j denotes the j-th component of said initial direction.

62. A method in accordance with claim 60, including performing a permutation of the point numbering.

63. A method for interactively optimizing parameters for controlling an image filtering algorithm, comprising:

inputting an image to said image filtering algorithm;

deriving a plurality of parameter sets from a given parameter set in accordance with multi-dimensional scaling (MDS);

deriving a plurality of filtered images from said image filtering algorithm under control of said plurality of parameter sets, each filtered image being associated with a respective parameter set of said plurality of parameter sets;

selecting an optimal filtered image from said plurality of filtered images; and

ranking the remainder of the filtered images of said plurality in descending order of optimality.

64. A method as recited in claim 63, comprising:

deriving a second plurality of parameter sets from an optimal parameter set associated with said optimal filtered image;

deriving a second plurality of filtered images from said image filtering algorithm under control of said second plurality of parameter sets, each filtered image of said second plurality being associated with a respective parameter set of said second plurality of parameter sets; and

selecting a second optimal filtered image from said second plurality of filtered images and ranking the remainder of the filtered images of said second plurality in descending order of optimality.

65. A method as recited in claim 64, wherein said step of deriving a second plurality of parameter sets comprises including said optimal parameter set in said second plurality of parameter sets.

66. A method as recited in claim 65, wherein said step of deriving a second plurality of filtered images comprises including said optimal filtered image in said second plurality of filtered images.

67. A method as recited in claim 65, comprising:

iteratively performing the following steps, with m=2, m=3, m=4, and so on, until an m^th iteration includes an optimal filtered image meeting a required criterion;

deriving an m^th plurality of parameter sets from a parameter set associated with the (m−

1)^th optimal filtered image;

deriving an m^th plurality of filtered images from said image filter under control of said m^th plurality of parameter sets, each filtered image of said m^th plurality being associated with a respective parameter set of said m^th plurality of parameter sets; and

selecting said m^th optimal filtered image from said m^th plurality of filtered images and ranking the remainder of the filtered images of said m^th plurality according to distance from said m^th optimal filtered image.

68. A method as recited in claim 67, wherein said step of deriving an m^th plurality of parameter sets comprises including said parameter set associated with the (m−

1)^th optimal filtered image.

69. A method as recited in claim 68, wherein deriving a plurality of parameter sets from a given parameter set comprises:

designating by p the number of parameter sets in a plurality of parameter sets;

designating by n the number of dimensions in each parameter;

representing in a multi-dimensional parameter space said p parameter sets;

utilizing information from a step of selecting an optimal filtered image from a plurality of filtered images and ranking the remainder of the filtered images of said plurality according to variation from said optimal image, then

determining a search step size s;

determining a center C for a search; and

determining a search direction {right arrow over (d)}.

updating step size s in accordance with the following criteria;

if said center C is associated with an optimal image, then updating step size s by dividing step size s by a first given number,

if a different point from C is associated with said optimal image and said optimal image in the previous iteration was not associated with said center point, step size s is multiplied by a second given number,

otherwise, step size s stays unchanged;

setting center point C to a point associated with an optimal rating; and

determining a search direction {right arrow over (d)}, as follows;

wherein said step of representing in a multi-dimensional parameter space said p parameter sets comprises representing in a multi-dimensional parameter space said p parameter sets as;

P⁽ⁱ⁾ with coordinates P_j⁽ⁱ⁾ and ratings r⁽ⁱ⁾, with 0≦

i<

p and 0≦

j<

n,

computing a p×

p Euclidian Distance matrix D as D_kl=(r^(k)−

r^(l))²,

calculating an auxiliary matrix M with elements

$M_{\mathrm{ab}}=-\frac{1}{2}<br><br>\left(D_{\mathrm{ab}}-\frac{1}{p}<br><br>\underset{a}{\sum <br><br>}<br><br>D_{\mathrm{ab}}+\frac{1}{p^2}<br><br>\underset{a,b}{\sum <br><br>}<br><br>D_{\mathrm{ab}}-\frac{1}{p}<br><br>\underset{b}{\sum <br><br>}<br><br>D_{\mathrm{ab}}\right),$

performing a singular value decomposition of M to yield eigenvalues λ

⁽ⁱ⁾ and the corresponding eigenvectors {right arrow over (e⁽ⁱ⁾)},

selecting that dimension with the largest eigenvalue,

determining a new direction based on multidimensional scaling as {right arrow over (d)}={right arrow over (e⁽¹⁾)} where {right arrow over (d)} is a unit vector (i.e. |{right arrow over (d)}|=1), and

establishing a minimum criterion to ensure a non-zero step size in every direction, absent a contrary user input.

70. A method as recited in claim 69 including:

designating by p the number of parameter sets in a plurality of parameter sets;

designating by n the number of dimensions in each parameter;

representing in a multi-dimensional parameter space said p parameter sets as P⁽ⁱ⁾ with coordinates P_j⁽ⁱ⁾ and ratings r⁽ⁱ⁾, with 0≦

i<

p and 0≦

j<

n;

computing a p×

p Euclidian Distance matrix D as D_kl=(r^(k)−

r^(l))²;

calculating an auxiliary matrix M with elements

$M_{\mathrm{ab}}=-\frac{1}{2}<br><br>\left(D_{\mathrm{ab}}-\frac{1}{p}<br><br>\underset{a}{\sum <br><br>}<br><br>D_{\mathrm{ab}}+\frac{1}{p^2}<br><br>\underset{a,b}{\sum <br><br>}<br><br>D_{\mathrm{ab}}-\frac{1}{p}<br><br>\underset{b}{\sum <br><br>}<br><br>D_{\mathrm{ab}}\right);<br><br>$

performing a singular value decomposition of M to yield eigenvalues λ

⁽ⁱ⁾ and the corresponding eigenvectors {right arrow over (e⁽ⁱ⁾)};

selecting that dimension with the largest eigenvalue;

determining a new direction based on multidimensional scaling as {right arrow over (d)}={right arrow over (e⁽¹⁾)} where {right arrow over (d)} is a unit vector (i.e. |{right arrow over (d)}|=1);

establishing a minimum criterion to ensure a non-zero step size in every direction, absent a contrary user input; and

deriving an m^th plurality of parameter sets from a parameter set associated with the (n−

1)^th optimal filtered image.

71. A method for interactively optimizing parameters in a parameter set for controlling an image filtering algorithm, said method comprising:

(a) generating a plurality of parameter sets by varying parameters in a parameter set in accordance with multi-dimensional scaling (MDS);

(b) generating a plurality of filtered images corresponding respectively to parameter sets of said plurality of parameter sets;

(c) selecting an optimal image from said plurality of filtered images, said optimal image corresponding to an optimal parameter set;

(d) ending with said optimal image if a given criterion is met, and if not, then going to step (e);

(e) deriving a further plurality of parameter sets by varying parameters of said optimal parameter set;

(f) generating a further plurality of filtered images corresponding respectively to parameter sets of said further plurality of parameter sets;

(g) selecting a further optimal image from said further plurality of filtered images, said further optimal image corresponding to a further optimal parameter set; and

(h) ending with said further optimal image if said criterion is met; and

, if not, then

(i) repeatedly performing, mutatis mutandis, the steps (e), (f), (g), and (h), with a yet further plurality of parameter sets in place of said further plurality of parameter sets, a yet further plurality of filtered images in place of said plurality of filtered images, and a yet further optimal image corresponding to a yet further optimal parameter set, until ending with a last further optimal image when said criterion is met.

72. A method as recited in claim 71, wherein step (c) comprises including said optimal parameter set in said second plurality of parameter sets.

73. A method as recited in claim 71, including applying a qualitative image criterion.

74. A method as recited in claim 71, including applying a comparative criterion by comparing with a reference model image.

75. A method as recited in claim 71, including applying said comparative criterion by comparing respective parameter sets of an optimal image and of a reference model image.

76. A method for interactively optimizing parameters for an image filter, comprising:

applying a first parameter set to an image filter;

inputting an image to said image filter;

deriving a first filtered image from said image filter, corresponding to said first parameter set;

modifying parameters of said first parameter set in accordance with multi-dimensional scaling (MDS) for providing a first plurality of modified parameter sets to said image filter;

deriving a first plurality of filtered images from said image filter corresponding to respective modified parameter sets of said first plurality;

selecting a first optimal image out of said first filtered image and said first plurality of filtered images, said first optimal image corresponding to a respective parameter set, hereinafter referred to as a first optimal parameter set;

modifying parameters of said first optimal parameter set for providing a second plurality of modified parameter sets to said image filter;

deriving a second plurality of filtered images from said image filter corresponding to respective modified parameter sets of said second plurality; and

selecting a second optimal image out of said second plurality of filtered images, said optimal image corresponding to a respective parameter set, hereinafter referred to as a second optimal parameter set.

77. A method for interactively optimizing parameters for controlling an image filter, comprising:

deriving parameters from a first parameter set in accordance with multi-dimensional scaling (MDS) for providing a first plurality of parameter sets to said image filter;

deriving a first plurality of filtered images from said image filter corresponding to respective parameter sets of said first plurality;

selecting a first optimal image out of said filtered images, said first optimal image corresponding to a respective parameter set, hereinafter referred to as a first optimal parameter set;

deriving parameters from said first optimal parameter set for providing a second plurality of parameter sets to said image filter; and

deriving a second plurality of filtered images from said image filter corresponding to respective parameter sets of said second plurality.

78. A method in accordance with claim 77, wherein said method comprises:

applying a plurality of parameter sets successively to said image filter for successively deriving a plurality of filtered images each corresponding respectively a parameter set.

79. A method in accordance with claim 77, wherein said method comprises:

said step of deriving parameters from a first parameter set for providing a first plurality of parameter sets includes;

80. A method for interactively optimizing parameters for controlling an image filter, comprising:

providing a first plurality of parameter sets to said image filter;

deriving a first plurality of filtered images from said image filter each corresponding to a respective parameter set of said first plurality of parameter sets;

selecting a first optimal image out of said first plurality of filtered images, said first optimal image corresponding to a respective parameter set, hereinafter referred to as a first optimal parameter set;

providing a second plurality of parameter sets to said image filter by deriving parameters from said first optimal parameter set by using multi-dimensional scaling (MDS), said second plurality of parameter sets in including said optimal parameter set; and

deriving a second plurality of filtered images from said image filter corresponding to respective parameter sets of said second plurality.

81. A method in accordance with claim 80, wherein said step of providing a first plurality of parameter sets comprises deriving said plurality of parameter sets from an initial parameter set.

82. A method in accordance with claim 81 including:

providing said first plurality of parameter sets to include said initial parameter set;

83. A method in accordance with claim 80 including:

selecting a second optimal image out of said second plurality of filtered images, said second optimal image corresponding to a respective parameter set, hereinafter referred to as a second optimal parameter set;

providing a third plurality of parameter sets to said image filter by deriving parameters from said second optimal parameter set in accordance with multi-dimensional scaling (MDS); and

deriving a third plurality of filtered images from said image filter corresponding to respective parameter sets of said third plurality.

selecting a third optimal image out of said third plurality of filtered images, said third optimal image corresponding to a respective parameter set, hereinafter referred to as a third optimal parameter set.

84. A method in accordance with-claim 83 including:

providing said second plurality of parameter sets to include said first optimal parameter set.

85. A method in accordance with claim 80, wherein said method comprises:

applying a plurality of parameter sets successively to said image filter for successively deriving a plurality of filtered images each corresponding respectively a parameter set.

86. A method in accordance with claim 85 including repetitively:

selecting a further optimal image out of said second plurality of filtered images, said further optimal image corresponding to a respective parameter set, hereinafter referred to as a further optimal parameter set;

providing a still further plurality of parameter sets in accordance with multi-dimensional scaling (MDS) to said image filter by deriving parameters from said further optimal parameter set;

deriving a still further plurality of filtered images from said image filter corresponding to respective parameter sets of said still further plurality;

selecting a still further optimal image out of said still further plurality of filtered images, said still further optimal image corresponding to a respective parameter set, hereinafter referred to as a still further optimal parameter set.

87. A method in accordance with claim 86, comprising:

repetitively performing the steps of claim D6 by providing successive parameter sets to said image filter, wherein said parameter sets are derived from the foregoing optimal parameter set for providing successive pluralities of filtered images, whereof a respective optimal image is selected corresponding to a respective optimal parameter set; and

continuing said repetitively performing until at least one of;

(a) a satisfactory degree of optimization has been reached, and

(b) a defined criterion has been reached.

88. A method in accordance with claim 87 comprising:

providing a further plurality of parameter sets to said image filter by deriving parameters from said the previous optimal parameter set; and

deriving a further plurality of filtered images from said image filter corresponding to respective parameter sets of said further plurality of parameter sets.

89. A method for interactively optimizing parameters for controlling an image filtering algorithm, comprising:

inputting an image to said image filtering algorithm;

designating a number of parameter sets in a plurality of parameter sets;

designating a number of dimensions in each parameter;

representing in a multi-dimensional parameter space said number of parameter sets;

deriving a plurality of parameter sets from a given parameter set in accordance with multi-dimensional scaling (MDS);

deriving a plurality of filtered images from said image filtering algorithm under control of said plurality of parameter sets, each filtered image being associated with a respective parameter set of said plurality of parameter sets;

selecting an optimal filtered image from said plurality of filtered images, said optimal filtered image being associated with a parameter set hereinafter referred to as an optimal parameter set;

ranking the remainder of the filtered images of said plurality in descending order of optimality;

utilizing information from said step of selecting an optimal filtered image from a plurality of filtered images and ranking the remainder of the filtered images of said plurality according to variation from said optimal image, to

determine a search step size,

determine a center for a search, and

determine a search direction;

deriving a second plurality of parameter sets from said optimal parameter set, by using said search step size, said center for a search, and said search direction;

deriving a second plurality of filtered images from said image filtering algorithm under control of said second plurality of parameter sets, each filtered image of said second plurality being associated with a respective parameter set of said second plurality of parameter sets;

selecting a second optimal filtered image from said second plurality of filtered images and ranking the remainder of the filtered images of said second plurality in descending order of optimality, said second optimal filtered image being associated with a parameter set hereinafter referred to as an optimal parameter set;

utilizing information from said step of selecting a second optimal filtered image from said plurality of filtered images and and ranking the remainder of said second plurality of filtered images according to variation from said optimal image, to

determine a second search step size,

determine a second center for a search, and

determine a second search direction; and

deriving a third plurality of parameter sets from said second optimal parameter set, by using said second search step size, said second center for a search, and said second search direction.

90. A method as recited in claim 89, wherein said step of deriving a second plurality of parameter sets comprises including said optimal parameter set in said second plurality of parameter sets.

91. A method as recited in claim 90, wherein said step of deriving a third plurality of parameter sets comprises including said second optimal parameter set in said third plurality of parameter sets.

92. A method as recited in claim 89, comprising:

iteratively performing the following steps, with m=4, m=5, m=6, and so on, until an m^th iteration includes an optimal filtered image meeting a required criterion;

deriving an m^th plurality of parameter sets from a parameter set associated with the (m−

1)^th optimal filtered image;

deriving an m^th plurality of filtered images from said image filter under control of said m^th plurality of parameter sets, each filtered image of said m^th plurality being associated with a respective parameter set of said m^th plurality of parameter sets; and

selecting said m^th optimal filtered image from said m^th plurality of filtered images and ranking the remainder of the filtered images of said m^th plurality according to distance from said m^th optimal filtered image.

93. A method as recited in claim 92 wherein said step of determining a search direction {right arrow over (d)} comprises updating step size s in accordance with the following criteria:

if said center C is associated with an optimal image, then updating step size s by dividing step size s by a first given number,

if a different point from C is associated with said optimal image and said optimal image in the previous iteration was not associated with said center point, step size s is multiplied by a second given number,

otherwise, step size s stays unchanged;

setting center point C to a point associated with an optimal rating; and

determining a search direction {right arrow over (d)}, as follows;

wherein said step of representing in a multi-dimensional parameter space said p parameter sets comprises representing in a multi-dimensional parameter space said p parameter sets as;

P⁽ⁱ⁾ with coordinates P_j⁽ⁱ⁾ and ratings r⁽ⁱ⁾, with 0≦

i<

p and 0≦

j<

n;

computing a p×

p Euclidian Distance matrix D as D_kl=(r^(k)−

r^(l))²;

calculating an auxiliary matrix M with elements

$M_{\mathrm{ab}}=-\frac{1}{2}<br><br>\left(D_{\mathrm{ab}}-\frac{1}{p}<br><br>\underset{a}{\sum <br><br>}<br><br>D_{\mathrm{ab}}+\frac{1}{p^2}<br><br>\underset{a,b}{\sum <br><br>}<br><br>D_{\mathrm{ab}}-\frac{1}{p}<br><br>\underset{b}{\sum <br><br>}<br><br>D_{\mathrm{ab}}\right);<br><br>$

performing a singular value decomposition of M to yield eigenvalues λ

⁽ⁱ⁾ and the corresponding eigenvectors {right arrow over (e⁽ⁱ⁾)};

selecting that dimension with the largest eigenvalue;

determining a new direction based on multidimensional scaling as {right arrow over (d)}={right arrow over (e⁽¹⁾)} where {right arrow over (d)} is a unit vector (i.e. |{right arrow over (d)}|=1); and

establishing a minimum criterion to ensure a non-zero step size in every direction, absent a contrary user input.

94. A method for interactively optimizing parameters in a parameter set, comprising:

deriving a plurality of parameter sets in a parameter space, from an initial parameter set;

selecting an optimal parameter set of said plurality;

ranking the remaining parameter sets in descending order from said optimal parameter set;

starting with said optimal parameter set as a center in said parameter space, deriving a step size and a step direction from said ranking, in accordance with multidimensional scaling (MDS);

deriving a further plurality of parameter sets in said parameter space, in accordance with said center, said step size, and said direction while preserving said ranking;

selecting a further optimal parameter set of said further plurality;

ranking the remaining parameter sets of said further plurality in descending order from said optimal parameter set; and

starting from said further optimal parameter set as a center in place of said optimal parameter set, iterating the subsequent steps until a best one of said optimal parameter sets is reached.

95. A method as recited in claim 94, comprising utilizing user input as said ranking input.

96. A method as recited in claim 95, comprising using comparisons with a desired standard as said ranking input.

97. A method as recited in claim 96, comprising optimizing parameters controlling an image filtering algorithm.

98. A method as recited in claim 97, comprising deriving said plurality of parameter sets by utilizing MDS.

99. A method as recited in claim 98, comprising deriving said plurality of parameter sets by utilizing reconstruction of data sets of said plurality of parameter sets in a lower-dimensional space, while optimally preserving ranking and mutual distances, considered in a least-squares sense.

100. A system for interactively optimizing performance of a system comprising:

means for interactively adjusting controlling parameters in a parameter set, by deriving successive pluralities of parameter sets in a parameter space, each of whose respective member parameter sets are respectively ranked in order, means for utilizing a ranking input based on respective system performance associated with each parameter set and means for selecting from each of which plurality of parameter sets an optimal parameter set and using said optimal parameter set as a point of departure for deriving the next following plurality of parameter sets in said parameter space, in accordance with said preceding ranking, in conjunction with a step size and a step direction derived from said ranking, in accordance with multidimensional scaling (MDS).

101. A system for optimizing performance of a system, comprising:

means for interactively adjusting controlling parameters in a parameter set comprising respective member parameter sets, said means comprising;

means for deriving successive pluralities of parameter sets in a parameter space;

means for ranking each of said respective member parameter sets in order, utilizing a ranking input based on respective system performance associated with each parameter set;

means for selecting an optimal parameter set from said plurality of parameter sets; and

means for using said optimal parameter set as a point of departure for deriving a next following plurality of parameter sets in said parameter space, in accordance with the preceding ranking, in conjunction with a step size and a step direction derived from the ranking, in accordance with multidimensional scaling (MDS).

102. A system as recited in claim 101, comprising:

means for deriving said successive pluralities of parameter sets by utilizing reconstruction of data sets of said plurality of parameter sets in a lower-dimensional space, while optimally preserving ranking and mutual distances, considered in a least-squares sense.

103. A system as recited in claim 102, comprising:

means for utilizing user input as said ranking input.

104. A system as recited in claim 103, comprising:

means for using comparisons with a desired standard as said ranking input.

105. A system for optimizing performance of a system, comprising:

means for interactively adjusting controlling parameters in a parameter set comprising respective member parameter sets, said adjusting comprising;

means for deriving a first plurality of parameter sets in a parameter space from a given parameter set for controlling said system;

means for ranking each of said respective parameter sets in order, utilizing a ranking input based on respective system performance associated with each parameter set, wherein a topmost ranked parameter set is selected as a first optimal parameter set; and

means for using said optimal parameter set as a point of departure for deriving a next following plurality of parameter sets in said parameter space, in accordance with the preceding ranking, in conjunction with a step size and a step direction derived from the ranking, in accordance with multidimensional scaling (MDS).

106. A system in accordance with claim 105, including means for:

in a first iteration;

deriving a second plurality of parameter sets from said first plurality of parameter sets beginning with the said first optimal parameter set as a first starting parameter set in said parameter space, wherein other parameter sets of said second plurality are placed in said parameter space, using information from said ranking, said ranking being weighted for placement of parameter sets of said second plurality in accordance with multi-dimensional scaling so as to increase a likelihood of said other parameter sets of said second plurality including a parameter representing an optimal parameter in a next iteration of ranking and selection; and

ranking performance with said second plurality of parameter sets in descending order of optimality, whereof the topmost parameter set is selected as a second optimal parameter set.

107. A system in accordance with claim 106, including means for, in a second iteration:

deriving a third plurality of parameter sets from said second plurality of parameter sets beginning with said second optimal parameter set as a second starting parameter set in said parameter space, and continuing in an analogous manner to selection of said second optimal parameter set to select a third optimal parameter set.

108. A system in accordance with claim 107, including means for performing a fourth, and optionally, further iterations are performed, mutatis mutandis, in accordance with the foregoing iteration.

109. A system in accordance with claim 106, wherein said parameter space is a multi-dimensional space.

110. A system in accordance with claim 108, wherein said parameter space is a multi-dimensional space.

111. A system in accordance with claim 106, wherein said means for deriving a second plurality of parameter sets comprises means utilizing a multi-dimensional scaling algorithm designed to find an optimal search direction in said parameter space, which best preserves relative ranking between said parameter sets.

112. A system in accordance with claim 111, wherein said means for deriving a second plurality of parameter sets comprises means for computing from said ranking, a center point, a direction for placement of parameter sets and a step size for proceeding in said direction, computed from said ranking.

113. A system in accordance with claim 112, wherein said means for computing from said ranking, a center point, a direction for placement of parameter sets and a step size for proceeding in said direction comprises means for performing said computing in each iteration.

114. A system in accordance with claim 113, wherein said means for computing a direction comprises means for computing a direction for placement of said parameter sets such that ranking of parameter sets onto the direction vector is preserved, and mutual distances are preserved in an optimal manner.

115. A system in accordance with claim 114, wherein said parameter space is a multi-dimensional space.

116. A system in accordance with claim 115, comprising means for:

computing said step size, defined as s;

computing said center, defined as C; and

computing said direction {right arrow over (d)}, all computations using feedback from said rankings.

117. A computer program product comprising a computer useable medium having computer program logic recorded thereon for program code for optimizing a system, comprising:

interactively adjusting controlling parameters in a parameter set comprising respective member parameter sets, said adjustment comprising;

deriving successive pluralities of parameter sets in a parameter space;

ranking each of said respective member parameter sets in order, utilizing a ranking input based on respective system performance associated with each parameter set;

selecting an optimal parameter set from said plurality of parameter sets; and

using said optimal parameter set as a point of departure for deriving a next following plurality of parameter sets in said parameter space, in accordance with the preceding ranking, in conjunction with a step size and a step direction derived from the ranking, in accordance with multidimensional scaling (MDS).