Patent US5704013A successfully refreshed from Google Patents.
US5704013A
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Map determination method and apparatus
Assignee: Sony Corp
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Filing: 1994-12-28
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Granted: 1997-12-30
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Expires: 2014-12-28
Abstract
Abstract A map determination method and apparatus for calculating the coefficients to give a minimum evaluation function quickly and reliably where a map is expressed as the linear sum of a function gi(X) and a coefficient ci while a map for transforming a N-dimensional vector (x0, x1, x2, x3) to a M-dimensional vector y is being decided. The coefficient ci for the map is obtained by giving a learning sample and a teaching sample, obtaining an evaluation function and solving a simultaneous linear equation for which the partial differential is zero.
Inventors
- 👤 Masao Watari
- 👤 Kazuo Ishii
- 👤 Yasuhiko Kato
- 👤 Hiroaki Ogawa
- 👤 Masanori Omote
- 👤 Kazuo Watanabe
- 👤 Katsuki Minamino
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-09 17:49
CPC Classifications
G; G06; G06N; G06N3/00; G06N3/02; G06N3/08; G06F; G06F18/00; G06F18/20; G06F18/21; G06F18/213; G06F18/2135; G06F18/21355; G06N3/09
Claims Analysis
Total Claims: 39
Claim 1
Independent Claim
207 words
In a data processing system which generates output vectors, representing output data, of a predetermined number of dimensions with respect to input vectors, representing input data, of a prescribed number of dimensions, a map determination method for building a map F from N-dimensional weighted vector space Ω N to M-dimensional weighted vector space Ω M comprising: a first step of computing in a processor L complete component functions g lm (X) determined from the distribution of samples grouped into Q categories in the N-dimensional weighted vector space Ω N ; a second step of computing in a processor the function f m (X) for the mth component of the map F as the linear sum of the function g lm (X) and the Lm coefficients c lm ; a third step of computing in a processor a prescribed evaluation function J based on Q teaching vectors (t a0 , t a1 , t a2 , . . . t a (m-)) relative to the Q categories over M-dimensional weighted vector space Ω M , and computing the coefficient c lm which makes the evaluation function J a minimum; and a fourth step of storing the coefficient c lm obtained in the third step in a digital memory.
Claim 2
Dependent Claim
207 words
In a data processing system which generates output vectors, representing output data, of a predetermined number of dimensions with respect to input vectors, representing input data, of a prescribed number of dimensions, a map determination method for building a map F from N-dimensional weighted vector space Ω N to M-dimensional weighted vector space Ω M comprising: a first step of computing in a processor L complete component functions g lm (X) determined from the distribution of samples grouped into Q categories in the N-dimensional weighted vector space Ω N ; a second step of computing in a processor the function f m (X) for the mth component of the map F as the linear sum of the function g lm (X) and the Lm coefficients c lm ; a third step of computing in a processor a prescribed evaluation function J based on Q teaching vectors (t a0 , t a1 , t a2 , . . . t a (m-)) relative to the Q categories over M-dimensional weighted vector space Ω M , and computing the coefficient c lm which makes the evaluation function J a minimum; and a fourth step of storing the coefficient c lm obtained in the third step in a digital memory.
Claim 3
Dependent Claim
48 words
A map determination method for use in a data processing system according to claim 1, wherein the evaluation function J is expressed by: ##EQU38## when E{XεS q }·{f(X)} is computed across all elements of the teaming samples S q to obtain the desired value for the function f(X).
Claim 4
Dependent Claim
60 words
A map determination method for use in a data processing system according to claim 2, wherein in the third step, the partial differential is found for the evaluation function J using the coefficient c lm , and the coefficient c lm is then found by making the partial differential zero in order to make the evaluation function J a minimum.
Claim 5
Dependent Claim
25 words
A map determination method for use in a data processing system according to claim 3, wherein the function g lm (X) is a variable monomial.
Claim 6
Dependent Claim
41 words
A map determination method for use in a data processing system according to claim 3, the third step comprising: a step of computing ##EQU39## a step of computing ##EQU40## and a step of computing ##EQU41## to the coefficient c jm .
Claim 7
Dependent Claim
35 words
A map determination method for use in a data processing system according to claim 2, wherein the coefficient c lm suitable for use in the steepest descent method for the evaluation function J is obtained.
Claim 8
Dependent Claim
47 words
A map determination method for use in a data processing system according to claim 2, further comprising a step giving the Sigmoid function with respect to the map output for the function f m (X) obtained as a result of having obtained the coefficient c lm .
Claim 9
Dependent Claim
215 words
In a data processing system which generates output vectors, representing output data, of a predetermined number of dimensions with respect to input vectors, representing input data, of a prescribed number of dimensions, a map determination method for building a map F from N-dimensional weighted vector space Ω N to M-dimensional weighted vector space Ω M comprising: a first step of computing in a processor L complete component functions g lm (X) determined from the distribution of samples grouped into Q categories in the N-dimensional weighted vector space Ω N ; a second step of computing in a processor the function f m (I, X) for the mth component of the map F updated at the ith time from the linear sum of the function g lm (X) and the Lm coefficients c lm (I); a third step of computing in a processor a prescribed evaluation function J based on Q teaching vectors (t a0 , t a1 , t a2 , . . . t a (m-1)) relative to the Q categories over M-dimensional weighted vector space Ω M , and computing the coefficient c lm (I) which makes the evaluation function J a minimum; and a fourth step of storing the coefficient c lm (I) obtained in the third step in a digital memory.
Claim 10
Dependent Claim
215 words
In a data processing system which generates output vectors, representing output data, of a predetermined number of dimensions with respect to input vectors, representing input data, of a prescribed number of dimensions, a map determination method for building a map F from N-dimensional weighted vector space Ω N to M-dimensional weighted vector space Ω M comprising: a first step of computing in a processor L complete component functions g lm (X) determined from the distribution of samples grouped into Q categories in the N-dimensional weighted vector space Ω N ; a second step of computing in a processor the function f m (I, X) for the mth component of the map F updated at the ith time from the linear sum of the function g lm (X) and the Lm coefficients c lm (I); a third step of computing in a processor a prescribed evaluation function J based on Q teaching vectors (t a0 , t a1 , t a2 , . . . t a (m-1)) relative to the Q categories over M-dimensional weighted vector space Ω M , and computing the coefficient c lm (I) which makes the evaluation function J a minimum; and a fourth step of storing the coefficient c lm (I) obtained in the third step in a digital memory.
Claim 11
Dependent Claim
97 words
A map determination method for use in a data processing system according to claim 8, the third step comprising: a step of computing the error between the map f m (I, X) for every learning data category and the teaching vector t am using D.sub.qm (I, X)=f.sub.m (I, X)-t.sub.qm ; and a step of successively updating the coefficient c lm (I) using c.sub.lm (I+1)=c.sub.im (I)-ε·D.sub.qm (I, X)·g.sub.lm (X) taking the (I+1)th item of learning data as X, the: (I+1)th item for the coefficient c lm (I) as c lm (I+1) and ε as a prescribed updating constant.
Claim 12
Dependent Claim
146 words
A map determination method for use in a data processing system according to claim 8, the first step comprising: a step of obtaining each component coordinate correlation coefficient with respect to the learning data belonging to each of the categories Q using a prescribed operational equation; a step of deciding a monomial taken as a normalized function from a combination of the coordinate components for which the correlation coefficient becomes large; a step of making a combination from the monomial taken as the normalized function for choosing a high order normalized function; a step of repeating the process of choosing the high order normalized function a prescribed number of times; and a step of arranging the combinations obtained in the repeated processes in order of largeness of correlation coefficient and in order of the smallness of the monomial and then selecting a prescribed number of items.
Claim 13
Dependent Claim
37 words
A map determination method for use in a data processing system according to claim 10 wherein the operational equation for obtaining the correlation coefficient is expressed by the equation ##EQU42## where k is the average component value.
Claim 14
Dependent Claim
157 words
A map determination apparatus for building a map F from N-dimensional weighted vector space Ω N to M-dimensional weighted vector space Ω M comprising: first means for computing L complete component functions g lm (X) determined from the distribution of samples grouped into Q categories in the N-dimensional weighted vector space Ω N ; second means for computing the function f m (X) for the mth component of the map F from the linear sum of the function g lm (X) and the Lm coefficients c lm ; third means for computing a prescribed evaluation function J based on Q teaching vectors (t a0 , t a1 , t a2 , . . . t a (m-1)) relative to the Q categories over M-dimensional weighted vector space Ω M , and means for computing the coefficient c lm which makes the evaluation function J a minimum; and fourth means for storing the coefficient c lm in memory.
Claim 15
Dependent Claim
157 words
A map determination apparatus for building a map F from N-dimensional weighted vector space Ω N to M-dimensional weighted vector space Ω M comprising: first means for computing L complete component functions g lm (X) determined from the distribution of samples grouped into Q categories in the N-dimensional weighted vector space Ω N ; second means for computing the function f m (X) for the mth component of the map F from the linear sum of the function g lm (X) and the Lm coefficients c lm ; third means for computing a prescribed evaluation function J based on Q teaching vectors (t a0 , t a1 , t a2 , . . . t a (m-1)) relative to the Q categories over M-dimensional weighted vector space Ω M , and means for computing the coefficient c lm which makes the evaluation function J a minimum; and fourth means for storing the coefficient c lm in memory.
Claim 16
Dependent Claim
41 words
A map determination apparatus according to claim 12, wherein the evaluation function J is expressed by: ##EQU43## when E{XεS q }·{f(X)} is computed across all elements of the learning samples S q to obtain the desired value for the function f(X).
Claim 17
Dependent Claim
48 words
A map determination apparatus according to claim 13, wherein the third means finds the partial differential for the evaluation function J using the coefficient c lm , and finds the coefficient clm by making the partial differential zero in order to make the evaluation function J a minimum.
Claim 18
Dependent Claim
18 words
A map determination apparatus according to claim 14, wherein the function g lm (X) is a variable monomial.
Claim 19
Dependent Claim
37 words
A map determination apparatus according to claim 14, the third means comprising: first arithmetic means for calculating ##EQU44## second arithmetic means for calculating ##EQU45## and third arithmetic means for calculating ##EQU46## to the coefficient c jm .
Claim 20
Dependent Claim
30 words
A map determination apparatus according to claim 13, wherein the third means obtains the coefficient c lm suitable for use in the steepest descent method for the evaluation function J.
Claim 21
Dependent Claim
38 words
A map determination apparatus according to claim 13, further comprising means for giving the Sigmoid function with respect to the map output for the function f m (X) obtained as a result of having obtained the coefficient clm.
Claim 22
Dependent Claim
163 words
A map determination apparatus for building a map F from N-dimensional weighted vector space Ω N to M-dimensional weighted vector space Ω M comprising: first means for computing L complete component functions g lm (X) determined from the distribution of samples grouped into Q categories in the N-dimensional weighted vector space Ω N ; second means for computing the function f m (I, X) for the mth component of the map F updated at the ith time from the linear sum of the function g lm (X) and the Lm coefficients c lm (I); third means for computing a prescribed evaluation function J based on Q teaching vectors (t a0 , t a1 , t a2 , . . . t a (m-1)) relative to the Q categories over M-dimensional weighted vector space Ω M , and computing the coefficient c lm (I) which makes the evaluation function J a minimum; and fourth means for storing the coefficient c lm (I) in memory.
Claim 23
Dependent Claim
163 words
A map determination apparatus for building a map F from N-dimensional weighted vector space Ω N to M-dimensional weighted vector space Ω M comprising: first means for computing L complete component functions g lm (X) determined from the distribution of samples grouped into Q categories in the N-dimensional weighted vector space Ω N ; second means for computing the function f m (I, X) for the mth component of the map F updated at the ith time from the linear sum of the function g lm (X) and the Lm coefficients c lm (I); third means for computing a prescribed evaluation function J based on Q teaching vectors (t a0 , t a1 , t a2 , . . . t a (m-1)) relative to the Q categories over M-dimensional weighted vector space Ω M , and computing the coefficient c lm (I) which makes the evaluation function J a minimum; and fourth means for storing the coefficient c lm (I) in memory.
Claim 24
Dependent Claim
90 words
A map determination apparatus according to claim 19, the third means comprising: computing means for computing the error between the map f m (I, X) for every teaming data category and the teaching vector t am using D.sub.qm (I, X)=f.sub.m (I, X)-t.sub.qm ; and updating means for successively updating the coefficient c lm (I) using c.sub.lm (I+1)=c.sub.lm (I)-ε·D.sub.qm (I, X)·g.sub.lm (X) taking the (I+1)th item of learning data as X, the (I+1)th item for the coefficient c lm (I) as c lm (I+1) and ε as a prescribed updating constant.
Claim 25
Dependent Claim
134 words
A map determination apparatus according to claim 19, the first means comprising: means for obtaining each component coordinate correlation coefficient with respect to the learning data belonging to each of the categories Q using a prescribed operational equation; means for deciding a monomial taken as a normalized function from a combination of the coordinate components for which the correlation coefficient becomes large; means for making a combination from the monomial taken as the normalized function for choosing a high order normalized function; means for repeating the process of choosing the high order normalized function a prescribed number of times; and means for arranging the combinations obtained in the repeated processes in order of largeness of correlation coefficient and in order of the smallness of the monomial and then selecting a prescribed number of items.
Claim 26
Dependent Claim
30 words
A map determination apparatus according to claim 21, wherein the operational equation for obtaining the correlation coefficient is expressed by the equation ##EQU47## where k is the average component value.
Claim 27
Dependent Claim
174 words
A data processing apparatus comprising: means for receiving N-dimensional input data to be processed; and means for converting the N-dimensional input data by using a map F, the map F being determined by a map determination apparatus, the map determination apparatus comprising: first means for computing L complete component functions g lm (X) determined from the distribution of samples grouped into Q categories in a N-dimensional weighted input vector space Ω N ; second means for computing the function f m (X) for the mth component of the map F from the linear sum of the function g lm (X) and the Lm coefficients c lm ; third means for computing a prescribed evaluation function J based on Q teaching vectors (t a0 , t a1 , t a2 , . . . t a (m-1)) relative to the Q categories over M-dimensional weighted vector space Ω M , and computing the coefficient c lm which makes the evaluation function J a minimum; and means for storing the coefficient c lm in a memory.
Claim 28
Dependent Claim
174 words
A data processing apparatus comprising: means for receiving N-dimensional input data to be processed; and means for converting the N-dimensional input data by using a map F, the map F being determined by a map determination apparatus, the map determination apparatus comprising: first means for computing L complete component functions g lm (X) determined from the distribution of samples grouped into Q categories in a N-dimensional weighted input vector space Ω N ; second means for computing the function f m (X) for the mth component of the map F from the linear sum of the function g lm (X) and the Lm coefficients c lm ; third means for computing a prescribed evaluation function J based on Q teaching vectors (t a0 , t a1 , t a2 , . . . t a (m-1)) relative to the Q categories over M-dimensional weighted vector space Ω M , and computing the coefficient c lm which makes the evaluation function J a minimum; and means for storing the coefficient c lm in a memory.
Claim 29
Dependent Claim
45 words
The data processing apparatus of claim 23 wherein the evaluation function J of the map determination method is expressed by: ##EQU48## when E{XεS q }·{f(X)} is computed across all elements of the teaming samples S q to obtain the desired value for the function f(X).
Claim 30
Dependent Claim
50 words
The data processing apparatus of claim 24, wherein in the third means computes the partial differential for the evaluation function J using the coefficient c lm , and then finds the coefficient c lm by making the partial differential zero in order to make the evaluation function J a minimum.
Claim 31
Dependent Claim
22 words
The data processing apparatus of claim 25, wherein the function g lm (X) of the map determination method is a viable monomial.
Claim 32
Dependent Claim
34 words
The data processing apparatus of claim 25, wherein the third means comprises: fourth means for computing ##EQU49## fifth means for computing ##EQU50## and sixth means for computing ##EQU51## to the coefficient c jm .
Claim 33
Dependent Claim
27 words
The data processing apparatus of claim 24, wherein the coefficient c lm suitable for use in the steepest descent method for the evaluation function J is obtained.
Claim 34
Dependent Claim
37 words
The data processing apparatus of claim 24, means for computing a Sigmoid function with respect to the map output for the function f m (X) obtained as a result of having obtained the coefficient c lm .
Claim 35
Dependent Claim
194 words
A data processing apparatus comprising: means for receiving N-dimensional input dam to be processed; and means for converting the N-dimensional input dam by using a map F, the map F being determined by a map determination apparatus, the map determination apparatus comprising: a first means for computing in a processor L complete component functions g lm (X) determined from the distribution of samples grouped into Q categories in a N-dimensional weighted input vector space Ω N ; a second means for computing in a processor the function f m (I, X) for the mth component of the map F updated at the ith time from the linear sum of the function g lm (X) and the Lm coefficients c lm (I); a third means for computing in a processor a prescribed evaluation function J based on Q teaching vectors (t a0 , t a1 , t a2 , . . . t a (m-1)) relative to the Q categories over M-dimensional weighted vector space Ω M , and computing the coefficient c lm (I) which makes the evaluation function J a minimum; and means for storing the coefficient c lm (I) in a memory.
Claim 36
Dependent Claim
194 words
A data processing apparatus comprising: means for receiving N-dimensional input dam to be processed; and means for converting the N-dimensional input dam by using a map F, the map F being determined by a map determination apparatus, the map determination apparatus comprising: a first means for computing in a processor L complete component functions g lm (X) determined from the distribution of samples grouped into Q categories in a N-dimensional weighted input vector space Ω N ; a second means for computing in a processor the function f m (I, X) for the mth component of the map F updated at the ith time from the linear sum of the function g lm (X) and the Lm coefficients c lm (I); a third means for computing in a processor a prescribed evaluation function J based on Q teaching vectors (t a0 , t a1 , t a2 , . . . t a (m-1)) relative to the Q categories over M-dimensional weighted vector space Ω M , and computing the coefficient c lm (I) which makes the evaluation function J a minimum; and means for storing the coefficient c lm (I) in a memory.
Claim 37
Dependent Claim
90 words
The data processing apparatus of claim 30, wherein the third means comprises: a means for computing the error between the map f m (I, X) for every learning data category and the teaching vector t am using D.sub.qm (I, X)=f.sub.m (I, X)-t.sub.am ; and a means for successively updating the coefficient c lm (I) using c.sub.lm (I+1)=c.sub.l (I)-ε·D.sub.qm (I, X)·g.sub.lm (X) taking the (I+1)th item of learning data as X, the (I+1)th item for the coefficient c lm (I) as c lm (I+1) and ε as a prescribed updating constant.
Claim 38
Dependent Claim
139 words
The data processing apparatus of claim 30 wherein the first means comprises: a means for obtaining each component coordinate correlation coefficient with respect to the learning data belonging to each of the categories Q using a prescribed operational equation; a means for deciding a monomial taken as a normalized function from a combination of the coordinate components for which the correlation coefficient becomes large; a means for making a combination from the monomial taken as the normalized function for choosing a high order normalized function; a means for repeating the process of choosing the high order normalized function a prescribed number of times; and a means for arranging the combinations obtained in the repeated processes in order of largeness of correlation coefficient and in order of the smallness of the monomial and then selecting a prescribed number of items.
Claim 39
Dependent Claim
34 words
The data processing apparatus of claim 32 wherein the operational equation for obtaining the correlation coefficient of the map determination method is expressed by the equations ##EQU52## where k is the average component value.
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| 3.5 Years (Year 4) | 2000-12-29 | 2001-06-30 | 2001-12-30 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 2004-12-29 | 2005-06-30 | 2005-12-30 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2008-12-29 | 2009-06-30 | 2009-12-30 | $7700.00 | Window Closed / Lapsed |