System and method for multiple-instance learning for computer aided diagnosis
A method for training a classifier for classifying candidate regions in computer aided diagnosis of digital medical images includes providing a training set of images, each image including one or more candidate regions that have been identified as suspicious by a computer aided diagnosis system. Each image has been manually annotated to identify malignant regions. Multiple instance learning is applied to train a classifier to classify suspicious regions in a new image as malignant or benign by identifying those candidate regions that overlap a same identified malignant region, grouping each candidate region that overlaps the same identified malignant region into a same bag, and maximizing a probability P = ∏ i = 1 N p i y i ( 1 - p i ) 1 - y i , wherein N is a number of bags, p i is a probability of bag i containing a candidate region that overlaps with an identified malignant region, and y i is a label where a value of 1 indicates malignancy and 0 otherwise.
1. A method for training a classifier for classifying candidate regions in computer aided diagnosis of digital medical images, said method comprising the steps of:
providing a training set of images, each said image including one or more candidate regions that have been identified as suspicious by a candidate generation step of a computer aided diagnosis system, and wherein each said image has been manually annotated to identify malignant regions; and
using information about the number of candidate regions that overlap a same identified malignant region to train a classifier, wherein said classifier is adapted to classifying a suspicious region in a new image as malignant or benign.
2. The method of claim 1 , wherein training said classifier comprises: identifying those candidate regions that overlap a same identified malignant region;
grouping each candidate region that overlaps the same identified malignant region into a same bag;
grouping each candidate region that does not overlap any identified malignant region into its own bag;
associating a probability to each bag as being malignant or benign; and
maximizing this probability over all images of the training set.
3. The method of claim 2 , further comprising deriving a set of d-dimensional descriptive feature vectors x from a feature computation step of a computer aided diagnosis system, wherein each candidate region is associated with a feature vector x, and wherein a probability that a bag is malignant is
p
(
y
=
1
❘
x
)
=
1
-
∏
j
=
1
K
[
1
-
p
(
y
=
1
❘
x
j
)
]
,
wherein yε{0,1} is a label where a value of 1 indicates malignancy and 0 otherwise, bag x={x j } j=1 K contains K feature vectors x j , and a probability that a bag is benign is
p
(
y
=
0
❘
x
)
=
∏
j
=
1
K
p
(
y
=
0
❘
x
j
)
,
and the probability to be maximized is
log
∏
i
=
1
N
p
i
y
i
(
1
-
p
i
)
1
-
y
i
=
∑
i
=
1
N
[
y
i
log
p
i
+
(
1
-
y
i
)
log
(
1
-
p
i
)
]
,
wherein N is a number of bags.
4. The method of claim 3 , wherein maximizing said probability comprises:
modeling said probability p i as a logistic sigmoid σ(w i T x i )=1/(1+exp(−w i T x i )) wherein w is a weight vector that weights the contribution of each component of x, wherein w has a zero-mean Gaussian prior N(w|0, A −1 ) with an inverse covariance matrix A=diag(α 1 . . . α d ); and
finding a w that minimizes
L
(
w
)
=
[
∑
i
=
1
N
(
y
i
log
p
i
+
(
1
-
y
i
)
log
(
1
-
p
i
)
)
]
-
w
T
Aw
2
.
5. The method of claim 4 , wherein minimizing L(w) comprises performing a Newton-Raphson update w←w−ηH −1 g, wherein g is a gradient of L(w), H is a Hessian matrix of L(w), and η is a step size, wherein w is updated until a ratio ∥g∥/d is less than a predetermined constant.
6. The method of claim 4 , further comprising
finding α i that maximizes a marginal likelihood p(D|A) of A over said training bags D defined as
p
(
D
❘
A
)
=
∫
(
∏
i
=
1
N
p
i
y
i
(
1
-
p
i
)
1
-
y
i
)
(
N
(
w
❘
0
,
A
-
1
)
)
ⅆ
w
;
and
removing a feature weight vector w i if an associated α i is greater than a predetermined threshold value, wherein a remaining set of features weight vectors w is a weight vector for a linear classifier ƒ w (x)=w T x.
7. The method of claim 6 , wherein finding α i that maximizes p(D|A) comprises:
calculating a Hessian matrix H(ŵ MAP , A) of p(D|A); and
updating said hyper-parameters from
α
i
new
=
1
w
i
2
+
Σ
ii
,
wherein Σ ii is the i th diagonal element of H −1 (ŵ MAP , A), and wherein Σ ii does not depend on A.
8. The method of claim 6 , further comprising:
providing one or more additional training sets of M j bags {x i j } i=1 M j ;
finding w j that maximizes
[
∑
i
=
1
N
(
y
i
j
log
p
i
j
+
(
1
-
y
i
j
)
log
(
1
-
p
i
j
)
)
]
-
w
j
,
T
Aw
j
2
,
wherein
p
i
j
=
1
-
∏
k
∈
i
⌊
1
-
σ
(
w
j
,
T
x
ik
j
)
⌋
;
and
updating
α
i
new
=
1
∑
task
j
(
(
w
i
j
)
2
+
Σ
ii
j
)
,
wherein w i j is an i th feature weight vector of a j th training set, Σ ii is the i th diagonal element of an inverse Hessian matrix H −1 of p(D|A), and wherein Σ ii does not depend on A.
9. The method of claim 6 , further comprising repeating the finding of w that minimizes L(w) for each α i ε{α 1 , . . . , α d }, and repeating said steps of finding w i for each α i , finding the α i that maximizes said marginal likelihood p(D|A), and removing a feature vector x i until the α i 's have converged in value.
10. A method for training a classifier for classifying candidate regions in computer aided diagnosis of digital medical images, said method comprising the steps of:
providing a training set of images, each said image including one or more candidate regions that have been identified as suspicious by a candidate generation step of a computer aided diagnosis system, and wherein each said image has been manually annotated to identify malignant regions; and
applying multiple instance learning to train a classifier to classify suspicious regions in a new image as malignant or benign by identifying those candidate regions that overlap a same identified malignant region grouping each candidate region that overlaps the same identified malignant region into a same bag, and maximizing a probability
P
=
∏
i
=
1
N
p
i
y
i
(
1
-
p
i
)
1
-
y
i
,
wherein N is a number of bags, p i is a probability of a bag i containing a candidate region that overlaps with an identified malignant region, and y i is a label wherein yε{0,1} wherein a value of 1 indicates malignancy and 0 otherwise.
11. The method of claim 10 , further comprising:
deriving a set of d-dimensional descriptive feature vectors x from a feature computation step of a computer aided diagnosis system, wherein each candidate region is associated with a feature vector x;
grouping each candidate region that does not overlap any identified malignant region into its own bag; and
maximizing said probability P over all images in said training set using information about the number of candidate regions that overlap the same identified malignant region, wherein a probability that a bag is malignant is
p
(
y
=
1
❘
x
)
=
1
-
∏
j
=
1
K
[
1
-
p
(
y
=
1
❘
x
j
)
]
,
wherein bag x={x j } j=1 K contains K feature vectors x j , and a probability that a bag is benign is
p
(
y
=
0
❘
x
)
=
∏
j
=
1
K
p
(
y
=
0
❘
x
j
)
.
12. A program storage device readable by a computer, tangibly embodying a program of instructions executable by the computer to perform the method steps for training a classifier for classifying candidate regions in computer aided diagnosis of digital medical images, said method comprising the steps of:
providing a training set of images, each said image including one or more candidate regions that have been identified as suspicious by a candidate generation step of a computer aided diagnosis system, and wherein each said image has been manually annotated to identify malignant regions; and
using information about the number of candidate regions that overlap a same identified malignant region to train a classifier, wherein said classifier is adapted to classifying a suspicious region in a new image as malignant or benign.
13. The computer readable program storage device of claim 12 , wherein training said classifier comprises:
identifying those candidate regions that overlap a same identified malignant region;
grouping each candidate region that overlaps the same identified malignant region into a same bag;
grouping each candidate region that does not overlap any identified malignant region into its own bag;
associating a probability to each bag as being malignant or benign; and
maximizing this probability over all images of the training set.
14. The computer readable program storage device of claim 13 , the method further comprising deriving a set of d-dimensional descriptive feature vectors x from a feature computation step of a computer aided diagnosis system, wherein each candidate region is associated with a feature vector x, and wherein a probability that a bag is malignant is
p
(
y
=
1
❘
x
)
=
1
-
∏
j
=
1
K
[
1
-
p
(
y
=
1
❘
x
j
)
]
,
wherein yε{0,1} is a label where a value of 1 indicates malignancy and 0 otherwise, bag x={x j } j=1 K contains K feature vectors x j , and a probability that a bag is benign is
p
(
y
=
0
❘
x
)
=
∏
j
=
1
K
p
(
y
=
0
❘
x
j
)
,
and the probability to be maximized is
log
∏
i
=
1
N
p
i
y
i
(
1
-
p
i
)
1
-
y
i
=
∑
i
=
1
N
[
y
i
log
p
i
+
(
1
-
y
i
)
log
(
1
-
p
i
)
]
,
wherein N is a number of bags.
15. The computer readable program storage device of claim 14 , wherein maximizing said probability comprises:
modeling said probability p i as a logistic sigmoid σ(w i T x i )=1/(1+exp(−w i T x i )) wherein w is a weight vector that weights the contribution of each component of x, wherein w has a zero-mean Gaussian prior N(w|0, A −1 ) with an inverse covariance matrix A=diag(α 1 . . . α d ); and
finding a w that minimizes
L
(
w
)
=
[
∑
i
=
1
N
(
y
i
log
p
i
+
(
1
-
y
i
)
log
(
1
-
p
i
)
)
]
-
w
T
Aw
2
.
16. The computer readable program storage device of claim 15 , wherein minimizing L(w) comprises performing a Newton-Raphson update w←w−ηH −1 g, wherein g is a gradient of L(w), H is a Hessian matrix of L(w), and η is a step size, wherein w is updated until a ratio ∥g∥/d is less than a predetermined constant.
17. The computer readable program storage device of claim 15 , the method further comprising
finding α i that maximizes a marginal likelihood p(D|A) of A over said training bags D defined as
p
(
D
❘
A
)
=
∫
(
∏
i
=
1
N
p
i
y
i
(
1
-
p
i
)
1
-
y
i
)
(
N
(
w
❘
0
,
A
-
1
)
)
ⅆ
w
;
and
removing a feature weight vector w i if an associated α i is greater than a predetermined threshold value, wherein a remaining set of features weight vectors w is a weight vector for a linear classifier ƒ w (x)=w T x.
18. The computer readable program storage device of claim 17 , wherein finding α i that maximizes p(D|A) comprises:
calculating a Hessian matrix H(ŵ MAP , A) of p(D|A); and
updating said hyper-parameters from
α
i
new
=
1
w
i
2
+
Σ
ii
,
wherein Σ ii is the i th diagonal element of H −1 (ŵ MAP , A), and wherein Σ ii does not depend on A.
19. The computer readable program storage device of claim 17 , the method further comprising:
providing one or more additional training sets of M j bags {x i j } i=1 M j ;
finding that maximizes
[
∑
i
=
1
N
(
y
i
j
log
p
i
j
+
(
1
-
y
i
j
)
log
(
1
-
p
i
j
)
)
]
-
w
j
,
T
Aw
j
2
,
wherein
p
i
j
=
1
-
∏
k
∈
i
⌊
1
-
σ
(
w
j
,
T
x
ik
j
)
⌋
;
and
updating
α
i
new
=
1
∑
task
j
(
(
w
i
j
)
2
+
Σ
ii
j
)
,
wherein w i j is an i th feature weight vector of a j th training set, Σ ii is the i th diagonal element of an inverse Hessian matrix H −1 of p(D|A), and wherein Σ ii does not depend on A.
20. The computer readable program storage device of claim 17 , the method further comprising repeating the finding of w that minimizes L(w) for each α i ε{α 1 , . . . , α d }, and repeating said steps of finding w i for each α i , finding the α i that maximizes said marginal likelihood p(D|A), and removing a feature vector x i until the α i 's have converged in value.