Doubt in KNN classifier using Chi Square distance

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Shan Sha 2019-1-29

The rows of X and Y correspond to observations, and the columns are, in general, dimensions (for example, predictors).

The chi-square distance between j-dimensional points x and z is

where is the weight associated with dimension j.

Choose weights for each dimension, and specify the chi-square distance function. The distance function must:

Take as input arguments one row of X, e.g., x, and the matrix Z.
Compare x to each row of Z.
Return a vector D of length , where is the number of rows of Z. Each element of D is the distance between the observation corresponding to x and the observations corresponding to each row of Z.

w = [0.4; 0.6];

chiSqrDist = @(x,Z)sqrt((bsxfun(@minus,x,Z).^2)*w);

This example uses arbitrary weights for illustration.

Find the indices of the three nearest observations in X to each observation in Y.

k = 3;

[Idx,D] = knnsearch(X,Y,'Distance',chiSqrDist,'k',k);

I have referred this in mathworks. I m not clear with what Z represent. so please explain in detail?

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