# Evolving
Clustering Method (ECM)

## ECM Algorithm

This is based on the concept of dynamically adding and modifying the
clusters as new data is presented, where the modification to the clusters
affects both the position of the clusters and the size of the cluster, in terms
of a radius parameter associated with each cluster that determines the
boundaries of that cluster. ECM has only one parameter, which drives the
addition of clusters, known as the distance threshold
${D}_{\mathrm{thr}}$. When new clusters are added, their centres are set to equal the
example that triggered their creation, and the radius
$R$of a new cluster is initially set to zero.
$R$grows as more vectors are allocated to the cluster. Due to the mechanism
by which $R$is updated, it cannot exceed
${D}_{\mathrm{thr}}$. The ECM algorithm is shown below:

Create the first cluster centre from the first example
${I}_{0}$

**for** each subsequent vector
${I}_{n}$**do**

Find the minimum distance
${D}_{min}$ between ${I}_{n}$ and each cluster centre
${C}_{n}$

**if**
${D}_{min}$ is less than any cluster radius **then**

Add ${I}_{n}$ to the nearest cluster

**else**

FInd the cluster
$a$ with minimum value of ${S}_{i,j}$, where ${S}_{i,j}={D}_{i,j}+{R}_{i,j}$, ${D}_{i,j}$ is the distance between the cluster centre and vector
$j$, and ${R}_{i}$ is the radius of cluster
$i$

**if**
${S}_{i,a}>2{D}_{\mathrm{thr}}$ **then**

Create a new cluster

**else**

Update
$a$

**end if**

**end if**

**end for**

When cluster $a$ is updated, its centre is shifted closer to
${I}_{n}$ and its radius ${R}_{a}\left(t+1\right)$ is set according to the equation below:

${R}_{a}\left(t+1\right)=\frac{{S}_{i,a}}{2}$

The new centre of $a,{C}_{a}\left(t+1\right)$ is set so that its distance is on the line between
${C}_{a}\left(t\right)$ and ${I}_{n}$ at a distance of ${R}_{a}\left(t+1\right).$

Maintained by Dr Michael J. Watts