Method for reliable classification of samples in clinical diagnostics using an improved method of classification
A system for classification of a test object using a training set comprising a plurality of objects, each of which is assigned as a member of a class. Collectively, the objects in the training set are members of at least two classes. A computer system is configured as a probabilistic classifier. The classifier estimates the probability of the test object being a member of each of the classes in the training set. The probabilistic classifier estimates the probability with reference to the class assignments of the objects in the training set which are neighbors to the test object within a defined region within the training set. The probabilistic classifier takes into account the situation in which there is an imbalance in the number of objects in the different classes in the training set. Additionally, the probabilistic classifier does not require any knowledge of the probability distribution function of the classes in the training set.
1. A system for classification of a test object, comprising:
a machine-readable storage device storing a training set comprising a plurality of objects, each of the objects being assigned as a member of a class, collectively the objects in the training set comprising members of at least two classes; and
a computer system coupled to the machine-readable storage device configured as a probabilistic classifier, the probabilistic classifier estimating the probability of the test object as being a member of each of the classes in the training set, wherein the probabilistic classifier estimates the probabilities with reference to the class assignments of objects in the training set which are neighbors to the test object within a defined region within the training set; and
wherein the training set comprises objects being members of two classes, class 1 and class 2 , wherein classes 1 and 2 in the training set have N 1 and N 2 numbers of objects respectively, in the training set and wherein the computer system is programmed to determine the probability P(class 1 ) of the object being a member of class 1 according to the relation:
P
(
class
1
)
=
k
1
+
1
k
1
+
k
2
+
2
·
F
1
2
(
1
,
k
2
+
1
;
k
1
+
k
2
+
3
;
1
-
N
1
N
2
)
where 2 F 1 (1, k 2 +1; k 1 +k 2 +3; 1−N1/N2) is a calculation of the hypergeometric function 2 F 1 and where k 1 represents the number of neighbors of class 1 within the defined region and k 2 represents the number of neighbors in class 2 within the defined region.
2. The system of claim 1 , wherein the defined region within the training set comprises a sphere ω centered about the test instance, and wherein there are k 1 neighbors of class 1 within ω and there are k 2 neighbors in class 2 within ω.
3. The system of claim 2 , wherein the size of sphere ω is selected such that probability density for classes 1 and 2 are approximately constant within sphere ω.
4. The system of claim 1 , where the computer system is further configured to compare the estimated probabilities for each of the classes to determine if the difference in estimated probability between the class having the highest probability estimate and the class having the next highest probability estimate is greater than a user-supplied parameter.
5. The system of claim 4 , wherein the user-supplied parameter is 0.1.
6. The system of claim 1 , wherein the probabilistic classifier comprises a probabilistic k nearest neighbor classifier.
7. The system of claim 1 , wherein the defined region comprises a set of k objects within the training set which are the k closest objects to the test object.
8. The system of claim 1 , wherein the objects comprise the intensities of one or more features and/or one or more peaks in mass spectrometry data.
9. The system of claim 8 , wherein the objects in the training set comprise test data obtained from two classes of patients: 1) a first class of patients exhibiting an adverse health condition and 2) a second class of patients that do not exhibit the adverse health condition, and wherein the classes assigned to the objects correspond to the two classes of patients.
10. The system of claim 8 , wherein the objects in the training set comprise the data obtained from two classes of patients: 1) a first class of patients that derive benefit from a particular therapy for treatment of a health condition and 2) a second class of patients that either do not derive benefit, or suffer adverse effects from the particular therapy for treatment of the medical condition, and wherein the classes assigned to the objects correspond to the two classes of patients.
11. The system of claim 10 , wherein the health condition comprises cancer.
12. The system of claim 11 , wherein the cancer comprises non-small cell lung cancer.
13. A method for classifying a test object, comprising the steps of:
accessing a machine-readable storage device storing a training set comprising a number of objects, each of the objects being assigned as a member of a class, collectively the objects in the training set comprising members of at least two classes; and
estimating the probability of an object as being a member of each class in the training set, the estimating being performed with reference to the class assignments of the objects in the training set which are neighbors to the test object within a defined region within the training set, and
classifying the test object as belonging to the class with the highest estimated probability;
wherein the training set comprises objects being members of two classes, class 1 and class 2 , wherein classes 1 and 2 have numbers of objects N 1 and N 2 , respectively, in the training set, and wherein the probability P(class 1 ) of the test instance being a member of Class 1 is estimated according to the relation:
P
(
class
1
)
=
k
1
+
1
k
1
+
k
2
+
2
·
F
1
2
(
1
,
k
2
+
1
;
k
1
+
k
2
+
3
;
1
-
N
1
N
2
)
where 2 F 1 (1, k 2 +1; k 1 +k 2 +3; 1−N1/N2) is a calculation of the hypergeometric function 2 F 1 and where k 1 represents the number of neighbors of class 1 within the defined region and k 2 represents the number of neighbors in class 2 within the defined region.
14. The method of claim 13 , further comprising the step of comparing the estimates of probabilities for each of the classes to determine if the difference of estimated probability between the class having the highest probability estimate and the class having the next highest probability estimate is greater than a user-supplied parameter.
15. The method of claim 14 , wherein the user-supplied parameter is 0.1.
16. The method of claim 13 , wherein the defined region within the training set comprises a sphere ω centered about the test object, and wherein there are k 1 neighbors of class 1 within ω and there are k 2 neighbors in class 2 within ω.
17. The method of claim 16 , wherein the size of sphere ω is selected such that probability density for classes 1 and 2 are approximately constant within sphere ω.
18. The method of claim 13 , wherein the defined region comprises a set of k objects within the training set which are the k closest objects to the test instance.
19. The method of claim 13 , wherein the objects comprise the intensities of one or more features and/or one or more peaks in mass spectrometry data.
20. The method of claim 19 , wherein the objects in the training set comprise test data obtained from two classes of patients: 1) a first class of patients exhibiting an adverse health condition and 2) a second class of patients that do not share the adverse health condition, and wherein the classes assigned to the objects correspond to the two classes of patients.
21. The method of claim 19 , wherein the objects in the training set comprise the data obtained from two classes of patients: 1) a first class of patients that derive benefit from a particular therapy for treatment of a health condition and 2) a second class of patients that either do not derive benefit, or suffer adverse effects from the particular therapy for treatment of the health condition, and wherein the classes assigned to the objects correspond to the two classes of patients.
22. The method of claim 21 wherein the health condition comprises cancer.
23. The method of claim 22 , wherein the cancer comprises non-small cell lung cancer.
24. A method of classification of a test instance comprising the steps of:
creating and storing in a machine-readable memory a training set comprising a plurality of objects, the objects being assigned a class label, the objects being members of either class 1 or a class 2 ;
obtaining a test instance to be classified;
classifying the test instance with a computer system configured as a probabilistic classifier by estimating the probability that the test instance is a member of classes 1 and 2 ,
wherein the probability P(class 1 ) of the test instance being a member of Class 1 is estimated according to the relation:
P
(
class
1
)
=
k
1
+
1
k
1
+
k
2
+
2
·
F
1
2
(
1
,
k
2
+
1
;
k
1
+
k
2
+
3
;
1
-
N
1
N
2
)
where 2 F 1 ( 1 , k 2 +1; k 1 +k 2 +3; 1−N1/N2) is a calculation of the hypergeometric function 2 F 1 and where k 1 represents the number of neighbors of class 1 within a defined region in the training set and k 2 represents the number of neighbors in class 2 within the defined region, N 1 is the number of objects in class 1 in the training set, and N 2 is the number of objects in class 2 in the training set.
25. The method of claim 24 , further comprising the steps of
conducting mass spectroscopy on a test sample, wherein the test instance comprises a data set representing a spectrum obtained from the mass spectroscopy.
26. The method of claim 25 , wherein the test sample comprises a sample obtained from a human subject.
27. The method of claim 24 , further comprising the steps of estimating the probability that the test instance is a member of classes 1 and 2 , and comparing the estimates of probabilities for each of the classes to determine if the difference of estimated probability between the class having the highest probability estimate and the class having the next highest probability estimate is greater than a user-supplied parameter.
28. A system for classification of a test object, comprising:
a machine-readable storage device storing a training set comprising a plurality of objects, each of the objects being assigned as a member of a class, collectively the objects in the training set comprising members of at least two classes, including class 1 and class 2 ; and
a computer system coupled to the machine-readable storage device configured as a probabilistic classifier, the probabilistic classifier estimating the probability of the test object as being a member of a class in the training set, wherein the probabilistic classifier estimates the probability with reference to the class assignments of objects in the training set which are neighbors to the test object within a defined region within the training set;
wherein classes 1 and 2 have N 1 and N 2 objects, respectively, in the training set, wherein N 1 and N 2 are not the same; and
wherein there are only two classes of objects in the training set, classes 1 and 2 , and wherein the probability P(class 1 ) of the test instance being a member of Class 1 is estimated according to the relation:
P
(
class
1
)
=
k
1
+
1
k
1
+
k
2
+
2
·
F
1
2
(
1
,
k
2
+
1
;
k
1
+
k
2
+
3
;
1
-
N
1
N
2
)
where 2 F 1 (1, k 2 +1; k 1 +k 2 +3; 1− N1 / N2 ) is a calculation of the hypergeometric function 2 F 1 and where k 1 represents the number of neighbors of class 1 within a defined region in the training set and k 2 represents the number of neighbors in class 2 within the defined region, N 1 is the number of objects in class 1 in the training set, and N 2 is the number of objects in class 2 in the training set.
29. The system of claim 28 , wherein the probabilistic classifier estimates the probability of the test object as being a member of each of the classes in the training set and classifies the test object as belonging to the class with the highest estimated probability.
30. The system of claim 28 , wherein the objects in the training set comprise the intensities of one or more features and/or one or more peaks in mass spectrometry data.
31. The system of claim 30 , wherein the objects in the training set comprise test data obtained from two classes of patients: 1) a first class of patients exhibiting an adverse health condition and 2) a second class of patients that do not exhibit the adverse health condition, and wherein the classes assigned to the objects correspond to the two classes of patients.
32. The system of claim 30 , wherein the objects in the training set comprise the data obtained from two classes of patients: 1) a first class of patients that derive benefit from a particular therapy for treatment of a health condition and 2) a second class of patients that either do not derive benefit, or suffer adverse effects from the particular therapy for treatment of the medical condition, and wherein the classes assigned to the objects correspond to the two classes of patients.
33. The system of claim 32 , wherein the health condition comprises cancer.
34. The system of claim 33 , wherein the cancer comprises non-small cell lung cancer.