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xi = q + in .NET Creator bar code 39 in .NET xi = q +




How to generate, print barcode using .NET, Java sdk library control with example project source code free download:
xi = q + using barcode integrating for visual studio .net control to generate, create uss code 39 image in visual studio .net applications. About Micro QR Code x2 = q . (14.71). Any other vector in the same direction, actually. De ne Ii to be the set of tr aining examples from class i. For any point in I1 , T x q > , and for any point in I2 , T x q < . We need to nd two things.

(1) A pair of points, one2 in each class, which are as close together as possible. We will call these points support vectors. (2) A vector onto which to project the support vectors so that their projections are maximally far apart.

We solve this problem as follows. Recall that was a unit vector. It is thus equal to some other vector in the same direction divided by its magnitude, = w/ w .

We will look for one such vector, with certain properties which will be introduced in a moment: For now, let x1 denote any point in I1 , not necessarily a support vector, and similarly for x2 . Then w w. x1 q x2 q (14.72). It is possible to have more than one support vector in each class, since two points might both be precisely the same distance from the hyperplane.. Topic 14A Statistical pattern recognition which leads to wT x1 q w w wT x2 q w w . (14.73).

De ne b = q w , and we then 3 of 9 for .NET add a constraint to w to require that its magnitude have a particular property: w = 1/ . (14.

74). Now we have two equations wh ich describe behavior for any points in class 1 or class 2: wT x1 + b 1. From this point on in this d VS .NET 39 barcode erivation, the subscript on the x no longer denotes the class to which x belongs, but rather just its index, as an element of the training set..

wT x2 + b 1. (14.75). Since we wish to nd the lin e which maximizes the margin, , from Eq. (14.74), we see that this is the same as nding the projection vector w whose magnitude is minimal, thus we seek a minimizer w = arg min( 1 wT w).

Unfortunately, the null vector would minimize this, so we 2 need to add some constraints to avoid this trivial solution. Let yi be the label for point xi , and de ne the labels as yi = 1 1 if if x i I1 x i I2 (14.76).

and consider the expression VS .NET Code-39 yi = (wT xi + b). This will always be greater than or equal to 1, regardless of the class of xi .

We thus have a constraint, and our minimization problem becomes: Find the w which minimizes wT w such that yi (wT xi + b) 1. This can be accomplished by setting up the following constrained optimization problem: L(w, b, ) = 1 T w w 2. l i (yi (w i=1 T xi + b) 1). (14.77). where l is the number of the .net framework Code-39 samples in the training set. The Lagrange multipliers will all be positive.

Take the partial derivative with respect to w, L =w w and setting this to zero we nd w= Similarly, take the derivative with respect to b, L = b. i yi i xi yi . i xi yi (14.78). (14.79). = 0.. (14.80). With these two observations, the equation for L is simpli ed to L= 1 2 i yi i j T j y j xi x j i yi T j y j xi x j i yi (14.81). where the rst and second term are the same except for the 1/2. The third term is zero. Statistical pattern recognition De ning the matrix A by A = yi y j xiT x j allows us to write L in a matrix form L= 1 2 (14.82). + 1T ,. (14.83). where 1 denotes a vector of Code 3 of 9 for .NET all ones. Finding the vector of Lagrange multipliers ( ) which minimizes L is a quadratic optimization problem.

There are several numerical packages available which perform such operations. Once we have the set of Lagrange multipliers, the optimal projection vector is found by Eq. (14.

79), which we observe requires a summation over all the elements of the training set. To solve for b, we need to make use of the Kuhn-Tucker [14.5] conditions:.

T i (yi (w xi + b) 1) = 0 i. (14.84). In principle, Eq. (14.84) ma barcode 3/9 for .

NET y be solved for b using any i, but it is numerically better to use an average. Similarly, we note the dimension of A is the same as the number of samples in the training set. Thus, unless some ltering is done on the training set prior to building the SVM, the computational complexity can be substantial.

. 14A.2.2.

Nonlinear support vector mac USS Code 39 for .NET hines Instead of dealing with the actual samples, we apply a nonlinear transformation which produces a vector of higher dimension, yi = (xi ). For example, if x = [x1 , x2 ]T is of dimension 2, y might be.

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