A dynamic niching clustering algorithm based on individual-connectedness and its application to color image segmentation

Abstract
Automatically evolve the optimal number of clusters as well as the cluster centers of data set based on the proposed adaptive compact k-distance neighborhood algorithm.

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Notations

X $X$: The dataset. Where X={x1,x2,…,xn}$X=\{x_1,x_2,\dots,x_n\}$, xi∈Rd $x_i\in \mathbb{R}^d$.

NK(x) $N_K(x)$: The K $K$-NN set of object x$x$.

Adaptive compact k-distance neighborhood algorithm

1. Evaluate each object x $x$’s neighbor-based density factor by
   NDF(x)=|{y|x∈NK(y)}||NK(x)| $$\begin{equation} NDF(x)=\frac{\left|\{y| x\in N_K(y)\}\right|}{|N_K(x)|} \end{equation}$$
   And for each x∈X $x \in X$, compute the optimal K $K$ using MANOVA(multivariate analysis of variance).

2. When NDF(x)≥1$NDF(x)\geq 1$, call x $x$ a dense point, and denote O={x|NDF(x)≥1}$O=\{x| NDF(x)\geq 1\}$ .

3. Build the graph G=(O,E) $G=(O, E)$, where E={⟨x,y⟩|x∈O∩NK(y),y∈O∩NK(x)} $E=\{\langle x, y\rangle| x \in O \cap N_K(y), y \in O \cap N_K(x)\}$.

4. Clustering O $O$ by the connectedness in G$G$, and the elements of X−O $X-O$ are assigned by the principle of proximity.

Pit

There is a pit that I can’t understand the procedure that find the optimal cluster number and cluster centers by GA(Genetic Algorithm).