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Doubt in KNN classifier using Chi Square distance

Asked by Shan Sha on 29 Jan 2019
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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