Orthogonal functional basis method for function approximation
First Claim
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1. A method for choosing a set of orthogonal basis functions for a function approximation from empirical data described as comprising the steps of:
- (a) constructing a heterogeneous regressor set
from a set of randomly selected basis functions;
(b) defining Ψ
as Ψ
≡
[φ
1, φ
2, . . . , φ
N]=rearrangement (F) by at a first step k=1, denoting a first column of the Ψ
matrix, φ
1≡
ft(1), selected from fi(1) where
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Abstract
An orthogonal functional basis method for function approximation is disclosed. Starting with the orthogonal least squares method, a new subset selection method for selecting a set of appropriate basis functions is explained where, instead of picking a subset from a given functional basis, the subset is selected from a combination of functional basis evolved from a set of heterogeneous basis functions. The method results in a more efficient neural network.
10 Citations
2 Claims
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1. A method for choosing a set of orthogonal basis functions for a function approximation from empirical data described as
comprising the steps of: -
(a) constructing a heterogeneous regressor set from a set of randomly selected basis functions; (b) defining Ψ
as Ψ
≡
[φ
1, φ
2, . . . , φ
N]=rearrangement (F) by at a first step k=1, denoting a first column of the Ψ
matrix, φ
1≡
ft(1), selected from fi(1) where
-
-
2. A method for controlling a physical process, comprising the steps of:
-
(a) obtaining a set of empirical data from the physical process;
(b) determining a function approximation of the physical process from the empirical data, the determination including the steps of;
(i) choosing a set of orthogonal basis functions for a function approximation from empirical data obtained from a physical process, the empirical data described as comprising the steps of; (ii) constructing a heterogeneous regressor set from a set of randomly selected basis functions; (iii) defining Ψ
as Ψ
≡
[φ
1, φ
2, . . . , φ
N]=rearrangement (F) by at a first step k=1, denoting a first column of the Ψ
matrix, φ
1≡
ft(1), selected from fi(1) where
-
Specification
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Current AssigneeAir Force Government of The United States of America As Represented By The Secretary
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Original AssigneeUnited States Of America As Represented By The Secretary Of The Air Force
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InventorsChen, Chun-Lung Philip, Cao, Yang, LeClair, Steven R.
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Primary Examiner(s)Gordon, Paul P.
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Application NumberUS09/326,441Time in Patent Office1,222 DaysField of Search700/47, 700/48, 706/17, 706/29US Class Current700/48CPC Class CodesG06N 3/08 Learning methods
