Nonlinear Multilayer Networks + in Visual Studio .NET

Paint Denso QR Bar Code in Visual Studio .NET Nonlinear Multilayer Networks +
Nonlinear Multilayer Networks +
QR Code 2d Barcode Scanner In .NET Framework
Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in Visual Studio .NET applications.
10 scale = 05
Create QR Code ISO/IEC18004 In .NET
Using Barcode creation for .NET Control to generate, create Quick Response Code image in VS .NET applications.
05
QR-Code Scanner In VS .NET
Using Barcode decoder for VS .NET Control to read, scan read, scan image in .NET framework applications.
00 05 Xin,target[1] ,y[1] ,ERR 100
Bar Code Generator In VS .NET
Using Barcode encoder for .NET framework Control to generate, create bar code image in Visual Studio .NET applications.
FIGURE 6-4b Training display produced by the sinusoid-learning program of Figure 6-4a The network output y(t) and the target sinusoid target(t) match very accurately, well within the display-curve width The time history at the bottom represents one hundred times the absolute value of the matching error error
Barcode Scanner In Visual Studio .NET
Using Barcode scanner for .NET framework Control to read, scan read, scan image in VS .NET applications.
1 scale = 2
QR Code Maker In C#
Using Barcode generator for Visual Studio .NET Control to generate, create QR Code ISO/IEC18004 image in VS .NET applications.
1e+05 MSQERR vs t
Creating QR Code In Visual Studio .NET
Using Barcode creator for ASP.NET Control to generate, create QR Code JIS X 0510 image in ASP.NET applications.
2e+05
Quick Response Code Maker In Visual Basic .NET
Using Barcode drawer for Visual Studio .NET Control to generate, create QR Code 2d barcode image in .NET applications.
FIGURE 6-4c Squared-error training histories of 32 pattern-matching errors produced by a larger backpropagation network with one hidden layer and nine hidden neurons Such optimizations often converge even after temporary instabilities due to excessively large learning rates
Code 128C Drawer In VS .NET
Using Barcode generator for Visual Studio .NET Control to generate, create Code 128 Code Set B image in .NET applications.
Vector Models of Neural Networks
Drawing GS1-128 In VS .NET
Using Barcode creation for .NET framework Control to generate, create GS1 128 image in .NET applications.
must then find n parameters W1, W2, , Wn that minimize the sample average of g = [y(x) Y]2 This procedure is readily extended to mean-square regression of ny-dimensional pattern vectors y(x) on nx-dimensional pattern inputs x (Section 6-6) We shall approximate the desired output pattern y = Y(x) with a single neuron layer that implements
Bar Code Creator In VS .NET
Using Barcode maker for .NET framework Control to generate, create barcode image in Visual Studio .NET applications.
y[i]=
Printing C 2 Of 5 In VS .NET
Using Barcode drawer for VS .NET Control to generate, create Code 2 of 5 image in .NET applications.
W[i, k]fk{x[1], x[2]), , x[nx]}
Recognizing Code 3/9 In .NET Framework
Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET applications.
(i=1, 2, , ny)
Creating UCC - 12 In Visual Basic .NET
Using Barcode maker for VS .NET Control to generate, create EAN 128 image in Visual Studio .NET applications.
(6-31)
Generate Barcode In VB.NET
Using Barcode creator for Visual Studio .NET Control to generate, create bar code image in VS .NET applications.
with
Decoding EAN-13 Supplement 5 In .NET Framework
Using Barcode reader for Visual Studio .NET Control to read, scan read, scan image in .NET applications.
Vector y = W * f
Code128 Creation In VB.NET
Using Barcode maker for .NET framework Control to generate, create USS Code 128 image in .NET applications.
(6-32)
Reading Barcode In Visual Studio .NET
Using Barcode recognizer for .NET Control to read, scan read, scan image in .NET applications.
where f is an n-dimensional vector of basis functions f[1], f[2], , f[n] Once these basis functions are computed, we only need to optimize a simple linear network layer If a minimum exists, successive approximations of the optimal connection weights W[i,k] are easily computed with the LMS algorithm of Section 6-9, namely,
Generating EAN-13 In Visual Basic .NET
Using Barcode printer for VS .NET Control to generate, create EAN13 image in .NET framework applications.
Vector error = Y y | DELTA W = lrate * error * f
Making Barcode In C#.NET
Using Barcode generator for .NET framework Control to generate, create barcode image in .NET applications.
The matching error error is again defined as in Section 6-10
(b) Radial Basis Functions
Radial-basis-function (RBF) networks employ n hyperspherically symmetrical basis functions f[k] of the form
f[k] = f(||x Xk||; a[k], b[k], ) (k = 1, 2, , n)
where the n radii ||x Xk|| are the pattern-space distances between the input vector x and n specified radial-basis centers Xk in the nx-dimensional pattern space a[k], b[k], are parameters that identify the kth basis function f[k] The Xk and a[k], b[k], must be judiciously preselected Truly optimal choices may or may not exist The most commonly used radial basis functions are
f[k] = exp( a[k]||x Xk||2) exp( a[k]rr[k]) (k = 1, 2, , n) (6-33)
which can be recognized as Gaussian bumps for nx = 1 and nx = 2 The radial-basis-function layer is then represented by the simple vector assignment
Vector y = W * exp( a * rr)
(6-34)
where y is an ny-dimensional vector, a and rr are n-dimensional vectors, and W is an ny n connection-weight matrix
Nonlinear Multilayer Networks
It remains to compute the vector rr of squared radii rr[k] = ||x Xk||2 Following DP Casasent [16] we write the n specified radial-basis-center vectors Xk as the n rows of an n-by-nx pattern-row matrix (template matrix) P, that is,
(P[k,1], P[k,2], , P[k,nx]) (Xk[1], Xk[2], , Xk[nx]) (k = 1, 2, , n)
(Section 6-5b) Then
nx nx nx nx
rr [k]=
(x[ j ] P[k, j ])2=
x2[ j ] 2
P[k, j]x[ j ]+
P2[kj ] (k = 1, 2, , n)
The last term, namely,
P2[kj] = pp[k]
(k = 1, 2, , n)
defines an n-dimensional vector pp that depends only on the given radial basis centers The DESIRE experiment-protocol script declares and precomputes this constant vector with
ARRAY pp[n] for k = 1 to n pp[k] = 0 for j = 1 to nx | pp[k] = pp[k] + P[k,j]^2 | next next
The DYNAMIC program segment can then generate the desired vector rr with
DOT xx = x * x | Vector rr = xx 2 * P * x + pp
(6-35)
But normally, there is no need to compute rr explicitly From Eq (6-34), the complete radial-basis-function algorithm is efficiently represented by
DOT xx = x * x | Vector f = exp(a * ( 2 * P * x xx pp)) Vector y = W * f Vector error = Y y DELTA W = lrate * error * f (6-36)
If desired, one can adjoin a constant bias term to the f layer as in Footnote 3 This combination of Casasent s algorithm and DESIRE vector assignments makes it easy to program RBF networks when we know the number and location of the radial basis centers Xk and the Gaussian-spread parameters a[k] But their selection is a real problem, especially when the pattern dimension nx