CLUSTERING

Clustering manage the problem of arrange data in a series of $k$ cluster such as the intra-cluster similarity is maximized.

So given a set of $N$ object with $D$ features the result of clustering is a clustering scheme, a function that maps each object in a $[\mathrm{1....}k]$ clusters or to noise

$$\forall x_1,x_2\in Xclust(x_1)=clust(x_2)if{x}_{1}issimilarto{x}_2$$ $$\forall x_1,x_2\in Xclust(x_1)\ne clust(x_2)if{x}_{1}isnotsimilarto{x}_2$$

CENTROID

A point which is the center of gravity of the cluster, for each cluster $k$ and dimension $d$, the $d$ coordinate of the centroid is

$$centroi{d}_d^k=\frac{1}{x_i:clust(x_i)=k}\sum _{x_i:clust(x_i)=k}{x}_{id}$$

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