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ttnphns
ttnphns
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Do $k$-means, dbscan, and hierarchical clustering all rely on pseudometrics(pseudo)metrics?

I seems to me that the clustering methods $k$-means, dbscan, and hierarchical clustering all work on distance measures $d$ that are pseudometrics(pseudo)metrics, i.e., fulfill the following requirements: $$ d(x,x)=0 $$ $$ d(x,y) = d(y,x) $$ $$ d(x,z) \leqslant d(x,y) + d(y,z) $$

I am wondering whether this algorithms also work on distance measures between two datapoints that do not fulfill those requirements, for example by not fulfilling the triangle inequality?

Do $k$-means, dbscan, and hierarchical clustering all rely on pseudometrics?

I seems to me that the clustering methods $k$-means, dbscan, and hierarchical clustering all work on distance measures $d$ that are pseudometrics, i.e., fulfill the following requirements: $$ d(x,x)=0 $$ $$ d(x,y) = d(y,x) $$ $$ d(x,z) \leqslant d(x,y) + d(y,z) $$

I am wondering whether this algorithms also work on distance measures between two datapoints that do not fulfill those requirements, for example by not fulfilling the triangle inequality?

Do $k$-means, dbscan, and hierarchical clustering all rely on (pseudo)metrics?

I seems to me that the clustering methods $k$-means, dbscan, and hierarchical clustering all work on distance measures $d$ that are (pseudo)metrics, i.e., fulfill the following requirements: $$ d(x,x)=0 $$ $$ d(x,y) = d(y,x) $$ $$ d(x,z) \leqslant d(x,y) + d(y,z) $$

I am wondering whether this algorithms also work on distance measures between two datapoints that do not fulfill those requirements, for example by not fulfilling the triangle inequality?

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Thomas
Thomas
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Do $k$-means, dbscan, and hierarchical clustering all rely on pseudometrics?

I seems to me that the clustering methods $k$-means, dbscan, and hierarchical clustering all work on distance measures $d$ that are pseudometrics, i.e., fulfill the following requirements: $$ d(x,x)=0 $$ $$ d(x,y) = d(y,x) $$ $$ d(x,z) \leqslant d(x,y) + d(y,z) $$

I am wondering whether this algorithms also work on distance measures between two datapoints that do not fulfill those requirements, for example by not fulfilling the triangle inequality?