I have a few points in multiple dimensions. I am able to compute similarity between those items (using, say Cosine distance). For example,
dim1 dim2 dim3
point1 100 1 0
point2 50 1 0
point3 100 0 1
point4 20 0 1
point5 50 0 1
point6 100 0 1
point7 20 0 1
point1 point2 point3 point4 point5 point6
point2 0.9999500
point3 0.9999000 0.9997501
point4 0.9987024 0.9985526 0.9992018
point5 0.9997501 0.9996002 0.9999500 0.9995512
point6 0.9999000 0.9997501 1.0000000 0.9992018 0.9999500
point7 0.9987024 0.9985526 0.9992018 1.0000000 0.9995512 0.9992018
Now I want to find items dissimilar to multiple points. For example, I know from above that point1 and point7 are very dissimilar. If I want to find the point most dissimilar to both of them, my intuition is point4 is the most dissimilar to both.
I tried adding up the similarity scores but it doesn't give me exactly what I want.
What is the mathematically sound way to compute distance from multiple points?
point1
(first component is 100) andpoint7
(first component is 20) necessarily will have first components as close as possible to (100+20)/2 = 60. The best candidates arepoint2
andpoint5
but definitely notpoint4
(which coincides withpoint7
!). This naturally raises the prior question (which ought to be settled before we go on), what is your similarity measure trying to represent? $\endgroup$ – whuber♦ Jun 3 '14 at 22:39point2
is more similar topoint1
because dim2 and dim3 are equivalent, even though by dim1 it is closest topoint5
. But I am not married to the measure, would Euclidean distance be more appropriate for this? $\endgroup$ – ignorant Jun 4 '14 at 15:46library(proxy); prods2.mat <- as.matrix(dist(prods2, method = "Euclidean")); colnames(prods2.mat)[order(prods2.mat["point1",] + prods2.mat["point4", ], decreasing=TRUE)]; prods2.mat <- as.matrix(dist(scale(prods2), method = "Cosine")); colnames(prods2.mat)[order(prods2.mat["point1",] + prods2.mat["point4", ], decreasing=TRUE)];
I am not sure if this is a happy coincidence or correct. $\endgroup$ – ignorant Jun 4 '14 at 18:18