Intelligent system for automatic feature detection and selection or identification

• US 5,664,066 A
• Filed: 09/09/1994
• Issued: 09/02/1997
• Est. Priority Date: 11/09/1992
• Status: Expired due to Fees

• Current Assignee: United States Department of Energy
• Original Assignee: United States Department of Energy
• Inventors: Jang, Jyh-Shing, Sun, Chuen-Tsai, Fu, Chi-Yung
• Primary Examiner(s): Downs, Robert W.
• Assistant Examiner(s): SHAH, SANJIV
• Application Number:
  US08/304,660
• Time in Patent Office: 1,089 Days
• Field of Search: 395/23, 395/22, 395/11, 395/900
• US Class Current: 706/25
• CPC Class Codes: G06F 2218/12 Classification; Matching
• CPC Class Codes: G06N 3/043 based on fuzzy logic, fuzzy membership or fuzzy inference, e.g. adaptive neuro-fuzzy inference systems [ANFIS]
• CPC Class Codes: H01J 37/32935 Monitoring and controlling tubes by information coming from the object and/or discharge

Abstract

A neural network uses a fuzzy membership function, the parameters of which are adaptive during the training process, to parameterize the interconnection weights between an (n-1)'"'"'th layer and an n'"'"'th layer of the network. Each j'"'"'th node in each k'"'"'th layer of the network except the input layer produces its output value y_k,j according to the function ##EQU1## where N_k-1 is the number of nodes in layer k-1, i indexes the nodes of layer k-1 and all the w_k,i,j are interconnection weights. The interconnection weights to all nodes j in the n'"'"'th layer are given by w_n,i,j =w_n,j (i, p_n,j,1, . . . , p_n,j,p.sbsb.n).

The apparatus is trained by setting values for at least one of the parameters p_n,j,1, . . . , p_n,j,Pn. Preferably the number of parameters P_n is less than the number of nodes N_n-1 in layer n-1. w_n,j (i,p_n,j,1, . . . , p_n,j,Pn) can be convex in i, and it can be bell-shaped. Sample functions for w_n,j (i, p_n,j,1, . . . , p_n,j,Pn) include ##EQU2##

Claims

1. A neural network having a plurality of nodes each having an output carrying a respective output value y, said nodes being grouped into a plurality of layers including an input layer and an n'"'"'th layer different from said input layer, each k'"'"'th layer having N_k nodes, and each j'"'"'th node in each k'"'"'th layer except said input layer producing its output value y_k,j according to the node function ##EQU13## where i indexes the nodes of layer k-1 and all the w_k,i,j are connection weights,

wherein for all nodes j in said n'"'"'th layer,

View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19)

2. A network according to claim 1, wherein each node in said input layer produces its output value in response to exactly one input value.

3. A network according to claim 1, wherein all of said layers in said plurality of layers are distinct from each other.

4. A network according to claim 1, wherein none of the node output values y_k1,j in a layer k1 of said plurality of layers influences any output value y_k0,j in a layer k0 of said plurality of layers, where k0<

k1.

5. A network according to claim 1, wherein said plurality of nodes includes all of the nodes in said apparatus.

6. A network according to claim 1, wherein said plurality of layers collectively includes all of the nodes in said plurality of nodes.

7. A network according to claim 1, wherein said teaching means comprises back-propagation apparatus.

8. A network according to claim 1, wherein said teaching means comprises means for setting p_n,j,1, . . . , p_n,j,P.sbsb.n,j to predetermined values in said network for each node j in layer n.

9. A network according to claim 1, wherein said plurality of layers further includes an output layer different from said input layer and said n'"'"'th layer.

10. A network according to claim 9, wherein f_n is a linear function and the node functions for all of said layers except said input layer and said n'"'"'th layer are sigmoid functions.

11. A network according to claim 9, wherein layer n-1 is said input layer.

12. A network according to claim 1, wherein for each node j in layer n, w_n,j (i, p_n,j,1, . . . ,p_n,j,P.sbsb.n,j)≠

0 for at least one value of i between i1_j and i2_j, inclusive, where 1≦

i1_j ≦

N_n-1, 1≦

i2_j ≦

N_n-1, and i1_j <

i2_j, i1_j and i2_j being such that at least one value of i exists within 1≦

i≦

N_n-1, but not within i1_j ≦

i≦

i2_j ;

and wherein w_n,j (p_n,j,1, . . . , p_n,j,P.sbsb.n,j)=0 for all values of i within 1≦

i≦

N_n-1 but not within i1_j ≦

i≦

i2_j.

13. A network according to claim 12, wherein for each node j in layer n, w_n,j (i, p_n,j,1, . . . , p_n,j,P.sbsb.n,j)≠

0for all values of i between i1_j and i2_j inclusive.

14. A network according to claim 1, wherein for all nodes j in layer n, w_n,j (i, p_n,j,1, . . . , p_n,j,P.sbsb.n,j) is convex in i.

15. A network according to claim 14, wherein for all nodes j in layer n, w_n,j (i, p_n,j,1, . . . ,p_n,j,P.sbsb.n,j) is bell-shaped in i.

16. A network according to claim 1, wherein for all nodes j in layer n, P_n,j =3 and ##EQU14##

17. A network according to claim 16, wherein f_n is linear.

18. A network according to claim 1, wherein for all nodes j in layer n, P_n,j =3 and ##EQU15##

19. A network according to claim 18, wherein for all nodes j in layer n, p_n,j,3 =2.

20. A neural network having a plurality of nodes each having an output carrying a respective output value y, said nodes being grouped into a plurality of layers including an input layer and an n'"'"'th layer different from said input layer, each k'"'"'th layer having N_k nodes, the (n-1)'"'"'th layer having more than one node, and each j'"'"'th node in each k'"'"'th layer except said input layer producing its output value y_k,j according to the node function ##EQU16## indexes the nodes of layer k-1 and all the w_k,i,j are connection weights,

wherein for all nodes j in said n'"'"'th layer,

21. A computational network having a plurality of nodes each having an output carrying a respective output value y, for use with N input signals each having a respective value x_i, N>

1, each j'"'"'th one of said nodes producing its output value y_j according to the node function ##EQU17##

22. A network according to claim 21, wherein f is linear.

23. A network according to claim 21, further comprising teaching means for setting values for a_j, b_j and c_j, for each j'"'"'th one of said nodes.

24. A computational network having a plurality of nodes each having an output carrying a respective output value y, for use with N input signal each having a respective value x_i, N>

1, each j'"'"'th one of said nodes producing its output value y_j according to the node function ##EQU18##

25. A method for analyzing a plurality of input signals, comprising the steps of:

providing adaptive learning apparatus having a plurality of nodes each having an output carrying a respective output value y, said nodes being grouped into a plurality of layers including an input layer and an n'"'"'th layer different from said input layer, each node in said input layer receiving a respective one of said input signals, each k'"'"'th layer having N_k nodes, and each j'"'"'th node in each k'"'"'th layer except said input layer producing its output value y_k,j according to the node function ##EQU19## where i indexes the nodes of layer k-1 and all the w_k,i,j are connection weights, wherein for all nodes j in said n'"'"'th layer,

space="preserve" listing-type="equation">w.sub.n,i,j =w.sub.n,j (i, p.sub.n,j, i, . . . P.sub.n,j,P.sbsb.n,j),

p_n,j being an integer greater than zero and less than the number of nodes N_n-1 in layer n-1, N_n-1 >

1; and

training said apparatus by setting values for at least one of p_n,j,1, . . . , p_n,j,P.sbsb.n,j.

26. A method according to claim 25, wherein none of the node output values y_k1,j in a layer k1 of said plurality of layers influences any output value y_k0,j in a layer k0 of said plurality of layers, where k0<

k1.

27. A method according to claim 25, wherein said training step comprises the step of training said apparatus using back-propagation.

28. A method according to claim 25, wherein said training step comprises the step setting p_n,j,1, . . . , and p_n,j,P.sbsb.n,j to predetermined values in said apparatus for each node j in layer n.

29. A method according to claim 28, wherein said training step further comprises the step of predetermining said predetermined values for p_n,j,1, . . . , and p_n,j,P.sbsb.n,j for each node j in layer n.

30. A method according to claim 25, wherein said plurality of layers further includes an output layer different from said input layer and said n'"'"'th layer.

31. A method according to claim 30, wherein f_n is a linear function and the node functions for all of said layers except said input layer and said n'"'"'th layer are sigmoid functions.

32. A method according to claim 31, wherein layer n-1 is said input layer.

33. A method according to claim 25, wherein for each node j in layer n, w_n,j (i, p_n,j,1, . . . , p_n,j,P.sbsb.n,j)≠

0 for all values of i between i1_j and i2_j, inclusive, where 1≦

i1_j ≦

N_n-1, 1≦

i2_j ≦

N_n-1, and i1_j <

i2_j, i1_j and i2_j being such that at least one value of i exists within 1≦

i≦

N_n-1, but not within i1_j ≦

i≦

i2_j ;

and wherein w_n,j i, p_n,j,1, . . . , p_n,j,P.sbsb.n,j for all values of i within 1≦

i≦

N_n-1 but not within i1_j ≦

i≦

i2_j.

34. A method according to claim 25, wherein for all nodes j in layer n, w_n,j (i, p_n,j,1, . . . , p_n,j,P.sbsb.n,j) is convex in i.

35. A method according to claim 34, wherein for all nodes j in layer n, w_n,j (i, p_n,j,1, . . . , p_n,j,P.sbsb.n,j) is bell-shaped in i.

36. A method according to claim 25, wherein for all nodes j in layer n, p_n,j =3 and ##EQU20##

37. A method according to claim 25, wherein for all nodes j in layer n, p_n,j =3 and ##EQU21##

43. A product produced by the method of claim 25.

38. A method for analyzing a plurality of input signals, comprising the steps of:

providing adaptive learning apparatus having a plurality of nodes each having an output carrying a respective output value y, said nodes being grouped into a plurality of layers including an input layer and an n'"'"'th layer different from said input layer, each node in said input layer receiving a respective one of said input signals, each k'"'"'th layer having N_k nodes, the (n-1)'"'"'th layer having more than one node, and each j'"'"'th node in each k'"'"'th layer except said input layer producing its output value y_k,j according to the node function ##EQU22## where i indexes the nodes of layer k-1 and all the w_k,i,j are connection weights, wherein for all nodes j in said n'"'"'th layer,

space="preserve" listing-type="equation">w.sub.n,j (i, p.sub.n,j,1, . . . , p.sub.n,j,P.sbsb.n,j)

P_n,j being an integer greater than zero and w_n,j (i,p_n,j,1, . . . , p_n,j,P.sbsb.n,j) being bell-shaped in i; and

training said apparatus by setting values for p_n,j,1, . . . , and p_n,j,P.sbsb.n,j.

39. A method for analyzing a plurality of N input signals each having a respective value x_i, comprising the steps of:

providing a computational network having a plurality of nodes each having an output carrying a respective output value y, each j'"'"'th one of said nodes producing its output value Y_j according to the node function ##EQU23## and training said computational network by setting values for a_j, b_j and c_j, for each j'"'"'th one of said nodes.

40. A method according to claim 39, wherein f is linear.

44. A method according to claim 39, further comprising the steps of:

producing a plasma adjacent to a subject surface, said plasma producing an optical frequency spectrum dependent upon a plurality of process parameters;

forming an amplitude value corresponding to each of a plurality of wavelengths in said optical frequency spectrum;

providing each of said amplitude values as respective ones of said input signals x_i ; and

after said step of training, producing a control signal for one of said process parameters in response to the output value of at least one of said nodes.

41. A method for analyzing a plurality of input signals each having a respective value x_i, comprising the steps of:

providing a computational network having a plurality of nodes each having an output carrying a respective output value y, for use with N input signal each having a respective value x_i, each j'"'"'th one of said nodes producing its output value y_j according to the node function ##EQU24## and training said computational network by setting values for at least one of a_j, b_j and c_j, for each j'"'"'th one of said nodes.

42. A method for use with a plurality of N₀ input signals x_i produced by a system to be analyzed, comprising the steps of:

selecting a parameterized membership function of said input signals;

providing adaptive learning apparatus having a plurality of nodes each having an output carrying a respective output value y, each j'"'"'th one of said nodes producing its output value y_j according to the node function ##EQU25## where i indexes the input signals, wherein for all nodes j,

space="preserve" listing-type="equation">w.sub.i,j =w.sub.j (i, p.sub.j,1, . . . , p.sub.j,p)

the parameters p_j,1, . . . , and p_j,p being trainable parameters, P being an integer greater than zero;

training said apparatus by setting values for said parameters p_j,1, . . . , p_j,p for each of said nodes j; and

observing said trained values for said parameters p_j,1, . . . , and p_j,p.