# Fusion rule estimation using vector space methods [electronic resource].

- Published:
- Washington, D.C. : United States. Dept. of Energy. Office of Energy Research, 1997.

Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy. - Physical Description:
- 8 pages : digital, PDF file
- Additional Creators:
- Oak Ridge National Laboratory, United States. Department of Energy. Office of Energy Research, and United States. Department of Energy. Office of Scientific and Technical Information

##### Access Online

- Restrictions on Access:
- Free-to-read Unrestricted online access
- Summary:
- In a system of N sensors, the sensor S{sub j}, j = 1, 2 .... N, outputs Y{sup (j)} ∈ ℜ, according to an unknown probability distribution P{sub (Y(j) /X)}, corresponding to input X ∈ [0, 1]. A training n-sample (X₁, Y₁), (X₂, Y₂), ..., (X{sub n}, Y{sub n}) is given where Y{sub i} = (Y{sub i}{sup (1)}, Y{sub i}{sup (2)}, . . . , Y{sub i}{sup N}) such that Y{sub i}{sup (j)} is the output of S{sub j} in response to input X{sub i}. The problem is to estimate a fusion rule f : ℜ{sup N} → [0, 1], based on the sample, such that the expected square error is minimized over a family of functions Y that constitute a vector space. The function f* that minimizes the expected error cannot be computed since the underlying densities are unknown, and only an approximation f to f* is feasible. We estimate the sample size sufficient to ensure that f provides a close approximation to f* with a high probability. The advantages of vector space methods are two-fold: (a) the sample size estimate is a simple function of the dimensionality of F, and (b) the estimate f can be easily computed by well-known least square methods in polynomial time. The results are applicable to the classical potential function methods and also (to a recently proposed) special class of sigmoidal feedforward neural networks.
- Report Numbers:
- E 1.99:conf-970465--18

conf-970465--18 - Subject(s):
- Other Subject(s):
- Note:
- Published through SciTech Connect.

05/01/1997.

"conf-970465--18"

"DE97006006"

SPIE international conference, Orlando, FL (United States), 21-25 Apr 1997.

Rao, N.S.V. - Funding Information:
- AC05-96OR22464

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