30 (1). --- k-means clustering Prototype

Prototype cluster prototype-based clustering structure assumed by a set of cluster prototypes characterization.

Common prototype clusters are:

1. k-means algorithm k-means
2. Learning vector quantization algorithm Learning Vector Quantization: LVQ
3. Gaussian mixture clustering Mixture-of-Gaussian

A, k-means algorithm

1.k-means

A given sample set $ D = {X_1, X_2, ..., X_N} $, divided assuming a $ C = {C_1, C_2, ..., C_K} $, the partition is defined as the square error:

$ Err = \ sum_ {k = 1} ^ K \ sum_ {x = 1, X_i \ in C_k} || X_i - u_k || _2 ^ 2 $, where $ u_k = \ frac {1} {| C_k |} \ sum_ {X_i \ in C_k} X_i $ $ C_k $ cluster is the mean vector.

2.k-means++

3.k-modes

4.x-medoids

5.mini-batch k-means