Multimodal fusion decision logic system
The present invention includes a method of deciding whether a data set is acceptable for making a decision. A first probability partition array and a second probability partition array may be provided. A no-match zone may be established and used to calculate a false-acceptance-rate (“FAR”) and/or a false-rejection-rate (“FRR”) for the data set. The FAR and/or the FAR may be compared to desired rates. Based on the comparison, the data set may be either accepted or rejected. The invention may also be embodied as a computer readable memory device for executing the methods.
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, 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 if FAR Z∞ is less than or equal to the desired false-acceptance-rate, then accept the data set if false-rejection-rate is not important.
3. The method of claim 1 , wherein Pfm(i,j) is similar to a Neyman-Pearson Lemma probability partition array.
4. The method of claim 1 , wherein Pm(i,j) is similar to a Neyman-Pearson Lemma probability partition array.
5. The method of claim 1 , further comprising:
identify a third index set ZM∞, the indices of ZM∞ being the (i,j) indices in Z∞ plus those indices where both Pfm(i,j) and Pm(i,j) are equal to zero;
identify a fourth index set (“C”), the indices of C being the (i,j) indices that are in A but not ZM∞,
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;
identify a fifth 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)−Σ (i,j)∈C N P fm (i,j)≦FAR;
determine FRR, where FRR=Σ (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.
6. 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, 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
(
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−Σ (i,j)∈Z ∞ P fm (i,j)−Σ (i,j)∈C N P fm (i,j)≦FAR;
determine FRR, where FRR=Σ (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.
7. The method of claim 6 , wherein if FRR is less than or equal to the desired false-rejection-rate, then accept the data set if false-acceptance-rate is not important.
8. The method of claim 6 , further comprising:
determine FAR Z∞ , where FAR Z ∞ =1−Σ (i,j)∈Z ∞ P fm (i,j);
compare FAR Z∞ to a desired false-acceptance-rate;
if FAR Z∞ is greater than the desired false-acceptance-rate, then reject the data set.
9. The method of claim 6 , wherein Pfm(i,j) is similar to a Neyman-Pearson Lemma probability partition array.
10. The method of claim 6 , wherein Pm(i,j) is similar to a Neyman-Pearson Lemma probability partition array.
11. 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.
12. The memory device of claim 11 , wherein the instructions further include instructions causing a computer to accept the data set if FAR Z∞ is less than or equal to the desired false-acceptance-rate and false-rejection-rate is not important.
13. The memory device of claim 11 , wherein the instructions further include instructions causing a computer to:
identify a third index set ZM∞, the indices of ZM∞ being the (i,j) indices in Z∞ plus those indices where both Pfm(i,j) and Pm(i,j) are equal to zero;
identify a fourth index set (“C”), the indices of C being the (i,j) indices that are in A but not ZM∞;
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;
identify a fifth 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)−Σ (i,j)∈C N P fm (i,j)≦FAR;
determine FRR, where FRR=Σ (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.
14. 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;
(e) identify a third index set (“C”), the indices of C being the (i,j) indices that are in A but not Z∞;
(f) 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;
(g) 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−Σ (i,j)∈Z ∞ P fm (i,j)−Σ (i,j)∈C N P fm (i,j)≦FAR;
(h) determine FRR, where FRR=Σ (i,j)∈C N P m (i,j);
(i) compare FRR to a desired false-rejection-rate;
(j) reject the data set if FRR is greater than the desired false-rejection-rate.
15. The memory device of claim 14 , wherein the instructions further include instructions causing a computer to accept the data set if FRR is less than or equal to the desired false-rejection-rate and false-acceptance-rate is not important.
16. The memory device of claim 14 , wherein the instructions further include instructions causing a computer to:
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”);
reject the data set if FAR Z∞ is greater than the desired false-acceptance-rate.
17. 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, 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∞ to 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∞ to 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)−Σ (i,j)∈C N 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.
18. The method of claim 17 , wherein if FAR Z∞ is less than or equal to the desired false-acceptance-rate, and FRR is less than or equal to the desired false-rejection-rate, then accept the data set.
19. The method of claim 17 , wherein Pfm(i,j) is similar to a Neyman-Pearson Lemma probability partition array.
20. The method of claim 17 , wherein Pm(i,j) is similar to a Neyman-Pearson Lemma probability partition array.
21. The method of claim 17 , wherein Z1∞ includes the indices of set A for which Pm(i,j) is equal to zero.