Multimodal fusion decision logic system using copula model

1. A method of deciding whether a data set is acceptable for making a decision, the data set being comprised of information pieces about objects, each object having a number of modalities, the number being at least two, the method being executed by a computer processor, comprising:

provide a first probability partition array (“Pm(i,j)”), the Pm(i,j) being comprised of probability values for information pieces in the data set, each probability value in the Pm(i,j) corresponding to the probability of an authentic match;

provide a second probability partition array (“Pfm(i,j)”), the Pfm(i,j) being comprised of probability values for information pieces in the data set, each probability value in the Pfm(i,j) corresponding to the probability of a false match;

identify a first index set (“A”), the indices in set A being the (i,j) indices that have values in both Pfm(i,j) and Pm(i,j);

identify a second index set (“Z∞”), the indices of Z∞ being the (i,j) indices in set A where both Pfm(i,j) is larger than zero and Pm(i,j) is equal to zero;

determine FAR Z∞ , where FAR Z∞ =1−Σ (i,j)∈Z∞ P fm (i,j);

compare FAR Z∞ to a desired false-acceptance-rate (“FAR”);

if FAR Z∞ is greater than the desired false-acceptance-rate, then reject the data set.

2. The method of claim 1 , wherein Pfm(i,j) is a Copula model.

3. The method of claim 1 , wherein Pm(i,j) is a Copula model.

4. A method of deciding whether a data set is acceptable for making a decision, the data set being comprised of information pieces about objects, each object having a number of modalities, the number being at least two, the method being executed by a computer processor, comprising:

provide a first probability partition array (“Pm(i,j)”), the Pm(i,j) being comprised of probability values for information pieces in the data set, each probability value in the Pm(i,j) corresponding to the probability of an authentic match;

provide a second probability partition array (“Pfm(i,j)”), the Pfm(i,j) being comprised of probability values for information pieces in the data set, each probability value in the Pfm(i,j) corresponding to the probability of a false match;

identify a first index set (“A”), the indices in A being the (i,j) indices that have values in both Pfm(i,j) and Pm(i,j);

identify a second index set (“Z∞”), the indices of Z∞ being the (i,j) indices of A where Pm(i,j) is equal to zero;

identify a third index set (“C”), the indices of C being the (i,j) indices that are in A but not Z∞,

arrange the (i,j) indices of C such that

P

fm

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(

i

,

j

)

k

P

m

⁡

(

i

,

j

)

k

>=

P

fm

⁡

(

i

,

j

)

k

+

1

P

m

⁡

(

i

,

j

)

k

+

1

to provide an arranged C index;

identify a fourth index set (“Cn”), the indices of Cn being the first N (i,j) indices of the arranged C index, where N is a number for which the following is true:

FAR

Z

∞

⋃

C

N

=

1

-

∑

(

i

,

j

)

∈

Z

∞

⁢

⁢

P

fm

⁡

(

i

,

j

)

-

∑

(

i

,

j

)

∈

C

N

⁢

P

fm

⁡

(

i

,

j

)

≤

FAR

;

determine

⁢

⁢

FRR

,

where

⁢

⁢

FRR

=

∑

(

i

,

j

)

∈

C

N

⁢

⁢

P

m

⁡

(

i

,

j

)

;

compare FRR to a desired false-rejection-rate;

if FRR is greater than the desired false-rejection-rate, then reject the data set.

5. The method of claim 4 , wherein Pfm(i,j) is a Copula model.

6. The method of claim 4 , wherein Pm(i,j) is a Copula model.

7. A computer readable memory device having stored thereon instructions that are executable by a computer to decide whether a data set is acceptable for making a decision, the data set being comprised of information pieces about objects, each object having a number of modalities, the number being at least two, the instructions causing a computer to:

(a) identify a first index set (“A”), the indices in set A being the (i,j) indices that have values in both Pm(i,j) and Pfm(i,j), Pm(i,j) being a probability partition array comprised of probability values for information pieces in the data set, each probability value in the Pm(i,j) corresponding to the probability of an authentic match, and Pfm(i,j) being a probability partition array comprised of probability values for information pieces in the data set, each probability value in the Pfm(i,j) corresponding to the probability of a false match;

(b) identify a second index set (“Z∞”), the indices of Z∞ being the (i,j) indices in set A where both Pfm(i,j) is larger than zero and Pm(i,j) is equal to zero;

(c) determine FAR Z∞ , where FAR Z ∞ =1−Σ (i,j)∈Z ∞ P fm (i,j);

(d) compare FAR Z∞ to a desired false-acceptance-rate (“FAR”);

(e) if FAR Z∞ is greater than the desired false-acceptance-rate, then reject the data set.

8. The memory device of claim 7 , wherein Pfm(i,j) is a Copula model.

9. The memory device of claim 7 , wherein Pm(i,j) is a Copula model.

10. A computer readable memory device having stored thereon instructions that are executable by a computer to decide whether a data set is acceptable for making a decision, the data set being comprised of information pieces about objects, each object having a number of modalities, the number being at least two, the instructions causing a computer to:

(a) identify a first index set (“A”), the indices in A being the (i,j) indices that have values in both Pm(i,j) and Pfm(i,j), wherein the Pm(i,j) is a probability partition array comprised of probability values for information pieces in the data set, each probability value in the Pm(i,j) corresponding to the probability of an authentic match, and Pfm(i,j) is a probability partition array comprised of probability values for information pieces in the data set, each probability value in the Pfm(i,j) corresponding to the probability of a false match

(b) identify a second index set (“Z∞”), the indices of Z∞ being the (i,j) indices of A where Pm(i,j) is equal to zero;

(c) identify a third index set (“C”), the indices of C being the (i,j) indices that are in A but not Z∞;

(d) arrange the (i,j) indices of C such that

P

fm

⁡

(

i

,

j

)

k

P

m

⁡

(

i

,

j

)

k

>=

P

fm

⁡

(

i

,

j

)

k

+

1

P

m

⁡

(

i

,

j

)

k

+

1

to provide an arranged C index;

(e) identify a fourth index set (“Cn”), the indices of Cn being the first N (i,j) indices of the arranged C index, where N is a number for which the following is true:

FAR

Z

∞

⋃

C

N

=

1

-

∑

(

i

,

j

)

∈

Z

∞

⁢

⁢

P

fm

⁡

(

i

,

j

)

-

∑

(

i

,

j

)

∈

C

N

⁢

P

fm

⁡

(

i

,

j

)

≤

FAR

;

(

f

)

⁢

determine

⁢

⁢

FRR

,

where

⁢

⁢

FRR

=

∑

(

i

,

j

)

∈

C

N

⁢

⁢

P

m

⁡

(

i

,

j

)

;

(g) compare FRR to a desired false-rejection-rate;

(h) reject the data set if FRR is greater than the desired false-rejection-rate.

11. The memory device of claim 10 , wherein Pfm(i,j) is a Copula model.

12. The memory device of claim 10 , wherein Pm(i,j) is a Copula model.

13. A method of deciding whether a data set is acceptable for making a decision, the data set being comprised of information pieces about objects, each object having a number of modalities, the number being at least two, the method being executed by a computer processor, comprising:

provide a first probability partition array (“Pm(i,j)”), the Pm(i,j) being comprised of probability values for information pieces in the data set, each probability value in the Pm(i,j) corresponding to the probability of an authentic match;

provide a second probability partition array (“Pfm(i,j)”), the Pfm(i,j) being comprised of probability values for information pieces in the data set, each probability value in the Pfm(i,j) corresponding to the probability of a false match;

identify a first index set (“A”), the indices in set A being the (i,j) indices that have values in both Pfm(i,j) and Pm(i,j);

execute at least one of the following:

a) identify a first no-match zone (“Z1∞”) that includes at least the indices of set A for which both Pfm(i,j) is larger than zero and Pm(i,j) is equal to zero, and use Z1∞ determine FAR Z∞ , where FAR Z ∞ =1−Σ (i,j)∈Z ∞ P fm (i,j), and compare FAR Z∞ to a desired false-acceptance-rate (“FAR”), and if FAR Z∞ greater than the desired false-acceptance-rate, then reject the data set;

b) identify a second no-match zone (“Z2∞”) that includes the indices of set A for which Pm(i,j) is equal to zero, and use Z2∞ identify a second index set (“C”), the indices of C being the (i,j) indices that are in A but not Z2∞ and arrange the (i,j) indices of C such that

P

fm

⁡

(

i

,

j

)

k

P

m

⁡

(

i

,

j

)

k

>=

P

fm

⁡

(

i

,

j

)

k

+

1

P

m

⁡

(

i

,

j

)

k

+

1

 to provide an arranged C index, and identify a third index set (“Cn”), the indices of Cn being the first N (i,j) indices of the arranged C index, where N is a number for which the following is true:

 FAR Z ∞ ∪C N =1−Σ (i,j)∈Z ∞ P fm (i,j)≦FAR and determine FRR, where FRR=Σ (i,j)∈C N P m (i,j), and compare FRR to a desired false-rejection-rate, and if FRR is greater than the desired false-rejection-rate, then reject the data set.

14. The method of claim 13 , wherein Pfm(i,j) is a Copula model.

15. The method of claim 13 , wherein Pm(i,j) is a Copula model.

16. A computer readable memory device having stored thereon instructions that are executable by a computer to decide whether a data set is acceptable for making a decision, the data set being comprised of information pieces about objects, each object having a number of modalities, the number being at least two, the instructions causing a computer to:

identify a first index set (“A”), the indices in A being the (i,j) indices that have values in both Pm(i,j) and Pfm(i,j), wherein the Pm(i,j) is a probability partition array comprised of probability values for information pieces in the data set, each probability value in the Pm(i,j) corresponding to the probability of an authentic match, and Pfm(i,j) is a probability partition array comprised of probability values for information pieces in the data set, each probability value in the Pfm(i,j) corresponding to the probability of a false match;

execute at least one of the following:

a) identify a first no-match zone (“Z1∞”) that includes at least the indices of set A for which both Pfm(i,j) is larger than zero and Pm(i,j) is equal to zero, and use Z1∞ determine FAR Z∞ , where FAR Z ∞ 1−Σ (i,j)∈Z ∞ P fm (i,j), and compare FAR Z∞ to a desired false-acceptance-rate (“FAR”), and if FAR Z∞ is greater than the desired false-acceptance-rate, then reject the data set;

b) identify a second no-match zone (“Z2∞”) that includes the indices of set A for which Pm(i,j) is equal to zero, and use Z2∞ identify a second index set (“C”), the indices of C being the (i,j) indices that are in A but not Z2∞, and arrange the (i,j) indices of C such that

P

fm

⁡

(

i

,

j

)

k

P

m

⁡

(

i

,

j

)

k

>=

P

fm

⁡

(

i

,

j

)

k

+

1

P

m

⁡

(

i

,

j

)

k

+

1

to provide an arranged C index, and identify a third index set (“Cn”), the indices of Cn being the first N (i,j) indices of the arranged C index, where N is a number for which the following is true:

FAR

Z

∞

⋃

C

N

=

1

-

∑

(

i

,

j

)

∈

Z

∞

⁢

⁢

P

fm

⁡

(

i

,

j

)

-

∑

(

i

,

j

)

∈

C

N

⁢

P

fm

⁡

(

i

,

j

)

≤

FAR

⁢

⁢

and

⁢

⁢

determine

⁢

⁢

FRR

,

where

⁢

⁢

FRR

=

∑

(

i

,

j

)

∈

C

N

⁢

⁢

P

m

⁡

(

i

,

j

)

;

and compare FRR to a desired false-rejection-rate, and if FRR is greater than the desired false-rejection-rate, then reject the data set.

17. The memory device of claim 16 , wherein Pfm(i,j) is a Copula model.

18. The memory device of claim 16 , wherein Pm(i,j) is a Copula model.