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Since cg arid c1 are linearly independent, any point in the plane can be uniquely represented by N O C O Q I C I , where 00 and are real numbers. If we restrict the coefficients to integers, that is, we require tha,t a and a1 0 are integers, then we obtain a lattice consisting of discrete points in thc plane. Figure 6.1 illustrates the lattice spanned by co and c1. In general, a lattice C is thc set of all linear combinations of a set of column vectors ci with integer coefficients. Given an m x n matrix A and an r n x 1 matrix B , suppose we want to find a solut,ion U t o t,he matrix equation AU = B , with the restriction that U consist,s cntirely of 0s and 1s. I f U is a solution to AU = B >then the block



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var doSomething:Function = function (arg:Object):void { // function code goes here. }

Anonymous functions behave slightly differently from function declarations. Most importantly, they are an expression rather than a declaration. They de ne and evaluate to an object of type Function.





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holds true, since M V = W is equivalent to U = U and AU - B = 0. Consequently, finding a solution V to the block matrix equation M V = W is equivalent to finding a solution U to the original matrix equation AU = B . Note that the columns of M are linearly independent, since the n x n identity matrix appears in the upper left and the final column begins with n zeros. Let CO, c1, c2,. . . , c , be the n 1 columns of the matrix M in (6.2) and let v g , v1, v 2 , . . . , vn be the elements of V. Then

TABLE 3-1

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Table 16.1 Feature extraction and classification algorithms used in our experiments. Parameter used LAR(Deterding) LAR(Deterding) LAR(Deterding) LAR(Deterding) MFCC(TIMIT) MFCC(TIMIT) MFCC(TIMIT) MFCC(TIMIT) LAR(Deterding) LAR(Deterding) MFCC(TIMIT) Dimension 10 10 10 10 21 21 21 21 10 10 21 Feature extractor PCA LDA MCE GMCE PCA LDA MCE GMCE NONE NONE NONE Classifier Minimum distance Minimum distance Minimum distance Minimum distance Minimum distance Minimum distance Minimum distance Minimum distance SVM one vs. one SVM one vs. all SVM one vs. one (Mahalanobis) (Mahalanobis) (Mahalanobis) (Mahalanobis) (Mahalanobis) (Mahalanobis) (Mahalanobis) (Mahalanobis)

Can be called at any point in the code regardless of where in the code the function is de ned. Can be called as a method by using dot syntax; acts as part of the object s interface. Belongs to the object it s de ned on. Cannot be rewritten or deleted.

(6.3)

Like a variable declaration, is available only in the scope the function is de ned. Cannot be used as a method. Exists in scope it s de ned in. Anonymous functions stored in variables can be reassigned a new value or deleted.

For most situations, I recommend that you use function declarations rather than anonymous functions in your code. Their consistency and ease of use make them the superior choice. However, sometimes using a function expression can provide exibility and usefulness that a function statement cannot. These may include the following: Functions that need to be used only once Functions useful only within another function Changing the functionality of a method at runtime Passing a function Using functional programming paradigms like Array.map()

and we want to determine U . Instead of solving linear equations to obtain V ,we will find U by determining W . Note that because of (6.3), W is in the lattice C.spanned by thc columns of M . The Euclidean length of a vector Y = [yo, y ~. , . ,ylL+nL- is .

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