Fusion rule estimation using vector space methods
Conference
·
OSTI ID:471398
In a system of N sensors, the sensor S{sub j}, j = 1, 2 .... N, outputs Y{sup (j)} {element_of} {Re}, according to an unknown probability distribution P{sub (Y(j) /X)}, corresponding to input X {element_of} [0, 1]. A training n-sample (X{sub 1}, Y{sub 1}), (X{sub 2}, Y{sub 2}), ..., (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 : {Re}{sup N} {r_arrow} [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.
- Research Organization:
- Oak Ridge National Lab., TN (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States)
- DOE Contract Number:
- AC05-96OR22464
- OSTI ID:
- 471398
- Report Number(s):
- CONF-970465--18; ON: DE97006006
- Country of Publication:
- United States
- Language:
- English
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