US2007005538A1PendingUtilityA1
Lagrangian support vector machine
Est. expiryJun 18, 2021(expired)· nominal 20-yr term from priority
G06F 18/2411
37
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Claims
Abstract
A Lagrangian support vector machine solves problems having massive data sets (e.g., millions of sample points) by defining an input matrix representing a set of data having an input space with a dimension of n that corresponds to a number of features associated with the data set, generating a support vector machine to solve a system of linear equations corresponding to the input matrix with the system of linear equations defined by a positive definite matrix, and calculating a separating surface with the support vector machine to divide the set of data into two subsets of data
Claims
exact text as granted — not AI-modified1 . A method of classifying numerical data sets comprising the steps of:
defining an input matrix representing a set of numerical data having an input space with a dimension of n, wherein n corresponds to a number of features associated with the data set; generating a support vector machine to solve a system of linear equations corresponding to the input matrix, wherein the system of linear equations is defined by a positive definite matrix; and calculating a separating surface with the support vector machine to divide the set of numerical data into at least two subsets of data.
2 . A method according to claim 1 , wherein a dimension of the positive definite matrix is equal to the dimension of (n+1).
3 . A method according to claim 2 , wherein the separating surface is a linear surface.
4 . A method according to claim 2 , wherein the separating surface is a nonlinear surface.
5 . A method according to claim 3 , wherein the separating surface is midway between a pair of parallel bounding planes.
6 . A method according to claim 5 , wherein the positive definite matrix is defined as:
Q
=
I
v
+
H
H
′
wherein
H
=
D
[
A
-
e
]
.
and v is a parameter associated with the distance between the pair of parallel bounding planes, A is a matrix representing the set of data, e is a vector of ones, and D is a diagonal matrix wherein a value on a diagonal of the D matrix is equal to a value of the corresponding row of the A matrix.
7 . A method according to claim 6 , further comprising the step of minimizing a function defined by:
min
0
≤
u
∈
R
m
f
(
u
)
:
=
1
2
u
′
Q
u
-
e
′
u
.
8 . A method according to claim 7 , wherein the separating plane is generated by iteratively calculating a value u defined by:
u i+1 =Q −1 ( e +(( Qu i −e )−α u i ) + ), i= 0,1, . . . ,.
9 . A method according to claim 8 , wherein global linear convergence is achieved by satisfying a condition defined by:
0
〈
α
〈
2
v
.
10 . A method according to claim 9 , wherein the separating surface is defined by a vector that is orthogonal to the pair of parallel bounding planes, and a coordinate that represents the location of the separating surface relative to an origin.
11 . A method according to claim 10 , wherein the vector is represented by:
w=A′Du.
12 . A method according to claim 10 , wherein the coordinate is represented by:
γ=−e′Du.
13 . A method according to claim 4 , wherein the positive definite matrix is defined as:
Q
=
I
v
+
D
K
(
G
,
G
′
)
D
,
wherein
G
=
[
A
-
e
]
and v is a parameter, I is an identity matrix, A is a matrix representing the set of data, e is a vector of ones, D is a matrix wherein a value on a diagonal of the D matrix is equal to the classification of the corresponding row of the A matrix, and K is a mathematical kernel.
14 . A method according to claim 13 , wherein the kernel K is a positive semidefinite kernel function.
15 . A method according to claim 14 , wherein the kernel K(A,B) maps R m×n ×R n×l into R m×l for AεR m×n and BεR n×l .
16 . A method according to claim 15 , wherein the kernel K(A,B) is a Gaussian kernel.
17 . A method according to claim 16 , further comprising the step of minimizing a function defined by:
min
0
≤
u
∈
R
m
f
(
u
)
:
=
1
2
u
′
Q
u
-
e
′
u
.
18 . A method according to claim 17 , wherein the nonlinear separating surface is generated by iteratively calculating a value u defined by:
u i+1 =Q −1 ( e +(( Qu i −e )−α u i ) + ), i= 0,1, . . . ,
19 . A method according to claim 18 , wherein the nonlinear separating surface is defined by:
K
(
[
x
′
-
1
]
,
[
A
′
-
e
′
]
)
D
u
=
0.
20 - 41 . (canceled)
42 . A support vector computing machine to classify numerical data sets comprising:
an input module that generates an input matrix representing a set of numerical data having an input space with a dimension of n, wherein n corresponds to a number of features associated with the numerical data set; a processor that receives an input signal from the input module representing the numerical data, wherein the processor calculates an output signal representing a solution to a system of linear equations corresponding to the input signal, and the system of linear equations is defined by a positive definite matrix; and an output module that divides the set of numerical data into a plurality of subsets of numerical data based on the output signal from the processor that corresponds to a separating surface between the plurality of subsets of data.
43 . A machine according to claim 42 , wherein a dimension of the positive definite matrix is equal to the dimension of (n+1).
44 . A machine according to claim 42 , wherein the separating surface is a nonlinear surface.
45 . A method of classifying patients comprising the steps of:
defining an input matrix representing a set of patient data having an input space with a dimension of n, wherein n corresponds to a number of features associated with each patient in the set of patient data; generating a support vector machine to solve a system of linear equations corresponding to the input matrix, wherein the system of linear equations is defined by a positive definite matrix; and calculating a separating surface with the support vector machine to divide the set of patient data into a plurality of subsets of data.
46 . A method according to claim 45 , wherein a dimension of the positive definite matrix is equal to the dimension of (n+1).
47 . A method according to claim 45 , wherein the separating surface is a linear surface.
48 . A method according to claim 45 , wherein the separating surface is a nonlinear surface.
49 . (canceled)
50 . (canceled)
51 . A machine according to claim 42 , wherein the separating surface is a linear surface.
52 . A method according to claim 1 , wherein the at least two subsets of data include a node-positive set of data and a node-negative set of data.
53 . A method according to claim 1 , wherein the at least two subsets of data include a good prognostic set of data and a poor prognostic set of data.
54 . A method according to claim 1 , wherein the set of numerical data comprises a set of data indicating presence of metastasized lymph nodes.
55 . A method according to claim 45 , wherein the plurality of subsets of data include a node-positive set of data and a node-negative set of data.
56 . A method according to claim 45 , wherein the plurality of subsets of data include a good prognostic set of data, an intermediate prognostic set of data, and a poor prognostic set of data.
57 . A method according to claim 45 , wherein the set of patient data comprises a set of data indicating presence of metastasized lymph nodes.Join the waitlist — get patent alerts
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