Apparatus for and method of generating an approximation function
First Claim
1. An apparatus (5) for generating an approximation function based on first pairs ((X1, Y1) to (X6, Y6)) of values associating a dependent variable (Y1 to Y6) with an independent variable (X1 to X6), and for determining second pairs (XA, Y'"'"'A) of values of said variables in accordance with said approximation function, characterized in that the apparatus comprises:
- first means (10);
for iteratively determining at least one current linear regression function by making first errors of alternating sign equal in absolute value, which first errors have been measured between, respectively, first values (Y3, Y4, Y5) of the dependent variable for three pairs (X3, Y3) (X4, Y4) (X5, Y5) of a series of pairs, and second values (Y'"'"'3, Y'"'"'4, Y'"'"'5) of the dependent variable determined, in accordance with said current linear regression function, for the same values (X3, X4, X5) of the independent variable,for selecting that one of the current linear regression functions which produces an approximation of all the pairs of said series with a minimum error, andfor coding the selected linear regression function with the aid of specific codes (p, q), andsecond means (17) for determining said second pairs (XA, Y'"'"'A) with the aid of said specific codes.
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Abstract
An apparatus (5) for generating an approximation function based on first pairs ((X1, Y1) to (X6, Y6)) of values associating a dependent variable (Y1 to Y6) with an independent variable (X1 to X6), and for determining second pairs (XA, Y'"'"'A) of values of said variables in accordance with said approximation function. The apparatus comprises: a) first means (10) for iteratively determining at least one current linear regression function, for selecting that one of the current linear functions which produces the approximation of all the pairs of said series with minimal errors, and for coding the selected linear regression function with the aid of specific codes (p, q), and b) second means (17) for determining said second pairs (XA, Y'"'"'A) with the aid of said specific codes. The apparatus can also be used for calculating approximated values of mathematical functions, for example a in a neural network, or for determining a regression function forming an approximation to experimental measurement results, for example distributed measurements resulting from monitoring an industrial process. The invention also relates to a method of generating an approximation function.
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Citations
20 Claims
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1. An apparatus (5) for generating an approximation function based on first pairs ((X1, Y1) to (X6, Y6)) of values associating a dependent variable (Y1 to Y6) with an independent variable (X1 to X6), and for determining second pairs (XA, Y'"'"'A) of values of said variables in accordance with said approximation function, characterized in that the apparatus comprises:
first means (10); for iteratively determining at least one current linear regression function by making first errors of alternating sign equal in absolute value, which first errors have been measured between, respectively, first values (Y3, Y4, Y5) of the dependent variable for three pairs (X3, Y3) (X4, Y4) (X5, Y5) of a series of pairs, and second values (Y'"'"'3, Y'"'"'4, Y'"'"'5) of the dependent variable determined, in accordance with said current linear regression function, for the same values (X3, X4, X5) of the independent variable, for selecting that one of the current linear regression functions which produces an approximation of all the pairs of said series with a minimum error, and for coding the selected linear regression function with the aid of specific codes (p, q), and second means (17) for determining said second pairs (XA, Y'"'"'A) with the aid of said specific codes. - View Dependent Claims (2, 3, 4, 5)
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6. In an apparatus for generating an approximation function based on first pairs ((X1, Y1) to (X6, Y6)) of values associating a dependent variable (Y1 to Y6) with an independent variable (X1 to X6), a method of generating said approximation function based on first pairs (X1, Y1) (X6, Y6) of values, and for determining second pairs (XA, Y'"'"'A) of values of said variables in accordance with said approximation function, characterized in that the method comprises:
a first phase; for iteratively determining at least one current linear regression function by making first errors (EPD) of alternating sign equal in absolute value, which first errors have been measured between, respectively, first values (Y3, Y4, Y5) of the dependent variable for three pairs (X3, Y3) (X4, Y4) (X5, Y5) of a series of pairs, and second values (Y'"'"'3, Y'"'"'4, Y'"'"'5) of the dependent variable determined, in accordance with said current linear regression function, for the same values (X3, X4 4, X5) of the independent variable, for selecting that one of the current linear regression functions which produces an approximation of all the pairs of said series with a minimum error, and for coding the selected linear regression function with the aid of specific codes, and second means (17) for determining said second pairs (XA, Y'"'"'A) with the aid of said specific codes. - View Dependent Claims (7, 8, 9, 10, 11, 12)
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13. Data processing system comprising, in succession, an input neuron layer, at least one hidden neuron layer, and an output neuron layer, means for calculating neural potentials of the neurons in the output neuron layer by cumulating activities of previous layers connected thereto, means for delivering output neurons states by applying an activation function to the neural potentials, wherein the system comprises:
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a) means for storing pairs of values of the activation function, as values of an independent variable and as values of a dependent variable defining the activation function, b) first calculation means for computing a linear regression function approximating the pairs of values within a predetermined error, and for coding the linear regression function, c) second calculation means addressing the codes for computing the output neuron states by applying the activation function to the neural potentials on the basis of the codes of the linear regression function. - View Dependent Claims (14, 15, 16)
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17. Apparatus for generating an approximation function approximating first pairs of values, a pair comprising one value of an independent variable and one value of a dependent variable, and for computing second pairs of values based on the approximation function for request values of the independent variable, wherein the apparatus comprises:
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a) means for storing the first pairs of values, b) first calculation means for computing the approximation function as a linear regression function approximating the first pairs of values to within a predetermined error, and for delivering codes coding the linear regression function, c) second calculation means for computing the second pairs of values based on the codes of the linear regression function. - View Dependent Claims (18, 19, 20)
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Specification