DEV: matlab proof of concept

matlab/distXY.m

@@ -0,0 +1,21 @@
+function D = distXY(X, Y)
+%distXY Calculate an m x n Euclidean distance matrix D of X and Y
+%
+% Calculate an m x n Euclidean distance matrix D between two set
+% points X and Y of m and n points respectively
+%
+% X : [m x d]   Corpus data points (d dimensions)
+% Y : [n x d]   Query data points (d dimensions)
+% D : [m x n]   Distance matrix where D(i,j) the distance of X(i,:) and Y(j,:)
+
+    [m, d1] = size(X);
+    [n, d2] = size(Y);
+    if d1 == d2
+        d = d1;
+    else
+        error('Corpus(X) and Query(Y) data points must have the same dimensions (d)');
+    end
+    D = (X.*X) * ones(d,1)*ones(1,n) -2 * X*Y.' + ones(m,1)*ones(1,d) * (Y.*Y).';
+    %D = sum(X.^2, 2) - 2 * X*Y.' + sum(Y.^2, 2).'
+    D = sqrt(D);
+end

matlab/distXY.m~

@@ -0,0 +1,18 @@
+function D = distXY(X, Y)
+%distXY Calculate an m x n Euclidean distance matrix 𝐷 of X and Y
+%
+% Calculate an m x n Euclidean distance matrix 𝐷     between two sets points 𝑋 and 𝑌 of 𝑚 and 𝑛 points respectively
+% X : [m x d]   Corpus data points (d dimensions)
+% Y : [n x d]   Query data poinsts (d dimensions)
+% D : [m x n]   Distance matrix where D(i,j) the distance of X(i) and Y(j)
+
+    [m d1] = size(X);
+    [n d2] = size(Y);
+    if d1 == d2
+        d = d1;
+    else
+        error('Corpus(X) and Query(Y) data points have to have the same dimensions');
+    end
+    %D = (X.*X) * ones(d,1)*ones(1,n) -2 * X*Y.' + ones(m,1)*ones(1,d) * (Y.*Y).';
+    D = sum(X.^2, 2) - 2 * X*Y.' + sum(Y.^2, 2).'
+end

matlab/kNN.m

@@ -0,0 +1,30 @@
+function [I, D] = kNN(X, Y, k)
+%kNN return the k-nearest neighbors Of Y into dataset X
+%
+% Outputs:
+% I : [n x k]   The indexes of X where the nearest neighbors of Y lies
+% D : [n x k]   The distances of each neighbor
+%
+% Inputs:
+% X : [m x d]   Corpus data points (d dimensions)
+% Y : [n x d]   Query data points (d dimensions)
+% k : [scalar]  The number of neighbors
+
+    disMat = distXY(X, Y);
+    [m, n] = size(disMat);
+
+    II = repmat([1:k].', 1, n);         % init the min algorithm
+    DD = disMat(1:k,:);
+    for j = 1:n
+        for i = k+1:m
+            % calculate candidate and canditate index
+            [tail, taili] = maxIdx(DD(:, j));
+            if disMat(i,j) < tail
+                DD(taili, j) = disMat(i,j);
+                II(taili, j) = i;
+            end
+        end
+    end
+    I = II.';
+    D = DD.';
+end

matlab/kNN.m~

@@ -0,0 +1,29 @@
+function [I, D] = kNN(X, Y, k)
+%kNN return the k-nearest neighbors Of Y into dataset X
+%
+% Outputs:
+% I : [n x k]   The indexes of X where the nearest neighbors of Y lies
+% D : [n x k]   The distances of each neighbor
+%
+% Inputs:
+% X : [m x d]   Corpus data points (d dimensions)
+% Y : [n x d]   Query data points (d dimensions)
+% k : [scalar]  The number of neighbors
+
+    disMat = distXY(X, Y);
+    [m, n] = size(disMat);
+
+    II = repmat([1:k].', 1, n);     % init the min algorithm
+    DD = disMat(1:k,:);
+    for i = k+1:m
+        for j = 1:n
+            [c, ci] = tail(DD);     % calculate candidate and canditate index
+            if disMat(i,j) < c(j)
+                DD()
+            end
+        end
+    end
+    I = II.';
+    D = DD.';
+end
+

matlab/maxIdx.m

@@ -0,0 +1,14 @@
+function [M, I] = maxIdx(Vec)
+%maxIdx   Calculate the max,index pair of each element of a vector
+%
+    n = length(Vec);
+    I = 0;
+    M = -Inf;
+    for j = 1:n
+        if M < Vec(j)
+            M = Vec(j);
+            I = j;
+        end
+    end
+end
+

matlab/tail.m~

@@ -0,0 +1,14 @@
+function [M, I] = maxIdx(Vec)
+%tail   Calculate the max,index pair of each Vec(:)
+%
+    n = length(Vec);
+    I = 0;
+    M = -1;
+    for j = 1:n
+        if M < Vec(j)
+            M(j) = Mat(i,j);
+            I(j) = i;
+        end
+    end
+end
+