Method for training of supervised prototype neural gas networks and their use in mass spectrometry
View Patent ↗A Neural Gas network used for pattern recognition, sequence and image processing is extended to a supervised classifier with labeled prototypes by extending a cost function of the Neural Gas network with additive terms, each of which increases with a difference between elements of the class labels of a prototype and a training data point and decreases with their distance. The extended cost function is then iteratively minimized by adapting weight vectors of the prototypes. The trained network can then be used to classify mass spectrometric data, especially mass spectrometric data derived from biological samples.
1. A method for training a Neural Gas network having a cost function on mass spectrometric data, comprising:
(a) initializing a set of prototypes, each prototype including a weight vector and a class label vector;
(b) receiving a set of training mass spectrometric data points, each training data point including a data vector and a class label vector;
(c) extending the cost function of the Neural Gas network by additive terms, wherein each of the terms increases with an increase in a difference between elements of class label vectors of a prototype and a training data point and decreases with an increase in the distance between the data vector of the training data point and the weight vector of the prototype; and
(d) iteratively adapting the weight vectors of the prototypes such that the extended cost function is minimized.
2. The method of claim 1 , wherein class labels of the class label vectors are fuzzy.
3. The method of claim 1 , wherein class labels of the class label vectors are crisp.
4. The method of claim 1 , wherein step (c) comprises extending the cost function by a sum of integrals denoted as
∑
wi
∫
P
(
v
)
·
exp
(
-
d
(
v
,
w
i
)
σ
2
)
·
(
c
v
-
c
wi
)
2
ⅆ
v
,
wherein w i and c wi are respectively, the weight vectors and the class label vectors of the prototypes, v and c(v) are respectively the data vectors and the class label vectors of the training data points, d(v, w i ) is a distance measure between the prototypes and the training data points and P(v) is a density distribution of the training data points.
5. The method of claim 1 , wherein step (c) comprises extending the cost function by an sum of integrals
∑
wi
∫
P
(
v
)
·
exp
(
-
∑
wl
ζ
(
d
(
v
,
w
i
)
-
d
(
v
,
w
i
)
)
σ
)
·
(
c
v
-
c
wi
)
2
ⅆ
v
,
wherein ξ is the sigmoid function, w i and c wi are respectively the weight vectors and the class label vectors of the prototypes, v and c(v) are respectively the data vectors and the class label vectors of the training data points, d(w i ,v) is a distance measure between the prototypes and the training data points and P(v) is a density distribution of training data points.
6. The method of claim 1 , wherein step (c) comprises extending the cost function by a sum over the additive terms
∑
vj
∑
wi
h
(
v
j
,
w
i
)
·
(
c
wi
-
c
vj
)
2
,
wherein w i and c wi are respectively the weight vectors and the class label vectors of the prototypes, v j and c vj are respectively the data vectors and the class label vectors of the training data points and h(v j , w i ) is a neighborhood function between the prototypes and the training data points.
7. The method of claim 1 , further comprising iteratively adapting the class label vectors of the prototypes such that the extended cost function is minimized.
8. The method of claim 1 , wherein a distance measure is applied in the extended cost function and wherein the distance measure depends on a plurality of relevance parameters, such that there is a relevance parameter for each data space dimension.
9. The method of claim 8 , further comprising iteratively adapting each of the plurality of relevance parameters such that the extended cost function is minimized.
10. The method of claim 1 , further comprising initializing and iteratively adapting a second set of unlabeled prototypes.
11. A method for classifying unlabeled biological data generated by mass spectrometry or unlabeled mass spectrometric data, comprising:
(a) training a Neural Gas network having a cost function on mass spectrometric data by,
(i) initializing a set of prototypes, each prototype including a weight vector and a class label vector,
(ii) receiving a set of training mass spectrometric data points, each training data point including a data vector and a class label vector,
(iii) extending the cost function of the Neural Gas network by additive terms, wherein each of the terms increases with an increase in a difference between elements of class label vectors of a prototype and a training data point and decreases with an increase in the distance between the data vector of the training data point and the weight vector of the prototype, and
(iv) iteratively adapting the weight vectors of the prototypes such that the extended cost function is minimized; and
(b) comparing a distance of weight vectors of the prototypes adapted in step
(a)(iv) with data vectors of the unlabeled data.
12. The method of claim 11 , wherein class labels of the class label vectors are fuzzy.
13. The method of claim 11 , wherein class labels of the class label vectors are crisp.
14. The method of claim 11 , wherein step (a)(iii) comprises extending the cost function by a sum of integrals denoted as
∑
wi
∫
P
(
v
)
·
exp
(
-
d
(
v
,
w
i
)
σ
2
)
·
(
c
v
-
c
wi
)
2
ⅆ
v
,
wherein w i and c wi are respectively, the weight vectors and the class label vectors of the prototypes, v and c(v) are respectively the data vectors and the class label vectors of the training data points, d(v, w i ) is a distance measure between the prototypes and the training data points and P(v) is a density distribution of the training data points.
15. The method of claim 11 , wherein step (a)(iii) comprises extending the cost function by an sum of integrals
∑
wi
∫
P
(
v
)
·
exp
(
-
∑
wl
ζ
(
d
(
v
,
w
i
)
-
d
(
v
,
w
l
)
)
σ
)
·
(
c
v
-
c
wi
)
2
ⅆ
v
,
wherein ξ is the sigmoid function, w i and c wi are respectively the weight vectors and the class label vectors of the prototypes, v and c(v) are respectively the data vectors and the class label vectors of the training data points, d(w i ,v) is a distance measure between the prototypes and the training data points and P(v) is a density distribution of training data points.
16. The method of claim 11 , wherein step (a)(iii) comprises extending the cost function by a sum over the additive terms
∑
vj
∑
wi
h
(
v
j
,
w
i
)
·
(
c
wi
-
c
vj
)
2
,
wherein w i and c wi are respectively the weight vectors and the class label vectors of the prototypes, v j and c vj are respectively the data vectors and the class label vectors of the training data points and h(v j , w i ) is a neighborhood function between the prototypes and the training data points.
17. The method of claim 11 , wherein step (a) further comprises iteratively adapting the class label vectors of the prototypes such that the extended cost function is minimized.
18. The method of claim 11 , wherein a distance measure is applied in the extended cost function and wherein the distance measure depends on a plurality of relevance parameters, such that there is a relevance parameter for each data space dimension.
19. The method of claim 18 , wherein step (a) further comprises iteratively adapting each of the plurality of relevance parameters such that the extended cost function is minimized.
20. The method of claim 11 , wherein step (a) further comprises initializing and iteratively adapting a second set of unlabeled prototypes.
21. A method for estimating the number and size of different classes of biological data generated by mass spectrometry or mass spectrometric data comprising:
(a) training a Neural Gas network having a cost function on mass spectrometric data, by
(i) initializing a set of prototypes, each prototype including a weight vector and a class label vector,
(ii) receiving a set of training mass spectrometric data points, each training data point including a data vector and a class label vector,
(iii) extending the cost function of the Neural Gas network by additive terms, wherein each of the terms increases with an increase in a difference between elements of class label vectors of a prototype and a training data point and decreases with an increase in the distance between the data vector of the training data point and the weight vector of the prototype,
(iv) iteratively adapting the weight vectors of the prototypes such that the extended cost function is minimized, and
(v) iteratively adapting the class label vectors of the prototypes such that the extended cost function is minimized; and
(b) comparing the class label vectors of the prototypes adapted in step (a)(v) before and after the training in step (a).
22. A method for estimating the relevance of data dimensions of biological data generated by mass spectrometry or mass spectrometric data comprising:
(a) training a Neural Gas network on mass spectrometric data, the Neural Gas network having a cost function and a distance measure that depends on a plurality of relevance parameters wherein there is a relevance parameter for each data space dimension, by
(i) initializing a set of prototypes, each prototype including a weight vector and a class label vector,
(ii) receiving a set of training mass spectrometric data points, each training data point including a data vector and a class label vector,
(iii) extending the cost function of the Neural Gas network by additive terms, wherein each of the terms increases with an increase in a difference between elements of class label vectors of a prototype and a training data point and decreases with an increase in the distance between the data vector of the training data point and the weight vector of the prototype,
(iv) iteratively adapting the weight vectors of the prototypes such that the extended cost function is minimized, and
(v) iteratively adapting each of the plurality of relevance parameters such that the extended cost function is minimized; and
(b) comparing the relevance parameters adapted in step (a)(v) before and after the training in step (a).